%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRA169-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 06:34:22 PM UTC 2026
% Result : Unsatisfiable 1.24s 1.48s
% Output : Proof 2.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRA169-1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.12/0.30 % Computer : n005.cluster.edu
% 0.12/0.30 % Model : x86_64 x86_64
% 0.12/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.30 % Memory : 8042.1875MB
% 0.12/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.30 % CPULimit : 300
% 0.12/0.30 % WCLimit : 300
% 0.12/0.30 % DateTime : Tue May 5 00:54:17 EDT 2026
% 0.12/0.30 % CPUTime :
% 1.24/1.48 % SZS status Unsatisfiable
% 1.24/1.48 % SZS output start Proof
% 1.24/1.48 tff(b_type, type, (
% 1.24/1.48 b: ( $i * $i ) > $o)).
% 1.24/1.48 tff(s_type, type, (
% 1.24/1.48 s: $i > $i)).
% 1.24/1.48 tff(elem_1_type, type, (
% 1.24/1.48 elem_1: $i)).
% 1.24/1.48 tff(z_type, type, (
% 1.24/1.48 z: $i)).
% 1.24/1.48 tff(r_type, type, (
% 1.24/1.48 r: ( $i * $i ) > $o)).
% 1.24/1.48 tff(inj_0_type, type, (
% 1.24/1.48 inj_0: $i > $i)).
% 1.24/1.48 tff(1,assumption,(~b(s(s(s(z))), elem!1)), introduced(assumption)).
% 1.24/1.48 tff(2,assumption,(~b(elem!1, z)), introduced(assumption)).
% 1.24/1.48 tff(3,assumption,(~b(elem!1, s(s(s(z))))), introduced(assumption)).
% 1.24/1.48 tff(4,assumption,(r(s(z), elem!1)), introduced(assumption)).
% 1.24/1.48 tff(5,assumption,(~b(elem!1, s(z))), introduced(assumption)).
% 1.24/1.48 tff(6,assumption,(~r(s(s(elem!1)), elem!1)), introduced(assumption)).
% 1.24/1.48 tff(7,assumption,(~r(z, elem!1)), introduced(assumption)).
% 1.24/1.48 tff(8,assumption,(b(s(z), s(s(s(z))))), introduced(assumption)).
% 1.24/1.48 tff(9,assumption,(~b(s(s(s(z))), s(z))), introduced(assumption)).
% 1.24/1.48 tff(10,assumption,(elem!1 = s(z)), introduced(assumption)).
% 1.24/1.48 tff(11,plain,
% 1.24/1.48 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(z))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[10])).
% 1.24/1.48 tff(12,plain,
% 1.24/1.48 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), elem!1)),
% 1.24/1.48 inference(symmetry,[status(thm)],[11])).
% 1.24/1.48 tff(13,plain,
% 1.24/1.48 ((~b(s(s(elem!1)), s(z))) <=> (~b(s(s(elem!1)), elem!1))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[12])).
% 1.24/1.48 tff(14,plain,
% 1.24/1.48 (s(elem!1) = s(s(z))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[10])).
% 1.24/1.48 tff(15,plain,
% 1.24/1.48 (s(s(elem!1)) = s(s(s(z)))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[14])).
% 1.24/1.48 tff(16,assumption,(~(s(s(elem!1)) = s(s(s(z))))), introduced(assumption)).
% 1.24/1.48 tff(17,plain,
% 1.24/1.48 ($false),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[16, 15])).
% 1.24/1.48 tff(18,plain,((~(elem!1 = s(z))) | (s(s(elem!1)) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.48 tff(19,plain,
% 1.24/1.48 (s(s(elem!1)) = s(s(s(z)))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[18, 10])).
% 1.24/1.48 tff(20,assumption,(s(s(elem!1)) = s(s(s(z)))), introduced(assumption)).
% 1.24/1.48 tff(21,plain,
% 1.24/1.48 (s(s(s(z))) = s(s(elem!1))),
% 1.24/1.48 inference(symmetry,[status(thm)],[20])).
% 1.24/1.48 tff(22,plain,
% 1.24/1.48 (b(s(s(s(z))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[21])).
% 1.24/1.48 tff(23,plain,
% 1.24/1.48 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(z))), s(z))),
% 1.24/1.48 inference(symmetry,[status(thm)],[22])).
% 1.24/1.48 tff(24,assumption,(b(s(s(elem!1)), s(z))), introduced(assumption)).
% 1.24/1.48 tff(25,plain,
% 1.24/1.48 (b(s(s(s(z))), s(z))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[24, 23])).
% 1.24/1.48 tff(26,plain,
% 1.24/1.48 ($false),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[9, 25])).
% 1.24/1.48 tff(27,plain,((~(s(s(elem!1)) = s(s(s(z))))) | b(s(s(s(z))), s(z)) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.48 tff(28,plain,
% 1.24/1.48 (~b(s(s(elem!1)), s(z))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[27, 19, 9])).
% 1.24/1.48 tff(29,plain,
% 1.24/1.48 (~b(s(s(elem!1)), elem!1)),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[28, 13])).
% 1.24/1.48 tff(30,assumption,(b(s(s(elem!1)), elem!1)), introduced(assumption)).
% 1.24/1.48 tff(31,plain,
% 1.24/1.48 ($false),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[30, 29])).
% 1.24/1.48 tff(32,plain,((~(elem!1 = s(z))) | (~b(s(s(elem!1)), elem!1)) | b(s(s(s(z))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.48 tff(33,plain,
% 1.24/1.48 (~b(s(s(elem!1)), elem!1)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[32, 10, 9])).
% 1.24/1.48 tff(34,plain,
% 1.24/1.48 (^[Y: $i, X: $i] : refl(((X = Y) | b(X, Y) | r(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 1.24/1.48 inference(bind,[status(th)],[])).
% 1.24/1.48 tff(35,plain,
% 1.24/1.48 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.24/1.48 inference(quant_intro,[status(thm)],[34])).
% 1.24/1.48 tff(36,plain,
% 1.24/1.48 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(37,plain,
% 1.24/1.48 (^[Y: $i, X: $i] : rewrite((((X = Y) | r(X, Y)) | b(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 1.24/1.48 inference(bind,[status(th)],[])).
% 1.24/1.48 tff(38,plain,
% 1.24/1.48 (![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.24/1.48 inference(quant_intro,[status(thm)],[37])).
% 1.24/1.48 tff(39,axiom,(![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rb')).
% 1.24/1.48 tff(40,plain,
% 1.24/1.48 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[39, 38])).
% 1.24/1.48 tff(41,plain,
% 1.24/1.48 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[40, 36])).
% 1.24/1.48 tff(42,plain,(
% 1.24/1.48 ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.24/1.48 inference(skolemize,[status(sab)],[41])).
% 1.24/1.48 tff(43,plain,
% 1.24/1.48 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[42, 35])).
% 1.24/1.48 tff(44,plain,
% 1.24/1.48 (((~![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))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(45,plain,
% 1.24/1.48 ((~![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))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(46,plain,
% 1.24/1.48 ((~![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)),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[45, 44])).
% 1.24/1.48 tff(47,plain,
% 1.24/1.48 ((s(s(elem!1)) = elem!1) | b(s(s(elem!1)), elem!1) | r(s(s(elem!1)), elem!1)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[46, 43])).
% 1.24/1.48 tff(48,plain,
% 1.24/1.48 (s(s(elem!1)) = elem!1),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[47, 33, 6])).
% 1.24/1.48 tff(49,plain,
% 1.24/1.48 (s(s(elem!1)) = s(z)),
% 1.24/1.48 inference(transitivity,[status(thm)],[48, 10])).
% 1.24/1.48 tff(50,plain,
% 1.24/1.48 ((s(z) = s(s(elem!1))) <=> (s(s(elem!1)) = s(z))),
% 1.24/1.48 inference(commutativity,[status(thm)],[])).
% 1.24/1.48 tff(51,plain,
% 1.24/1.48 ((~(s(z) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = s(z)))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[50])).
% 1.24/1.48 tff(52,plain,
% 1.24/1.48 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(53,plain,
% 1.24/1.48 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(54,plain,
% 1.24/1.48 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(55,axiom,(![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','sinj')).
% 1.24/1.48 tff(56,plain,
% 1.24/1.48 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[55, 54])).
% 1.24/1.48 tff(57,plain,(
% 1.24/1.48 ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 1.24/1.48 inference(skolemize,[status(sab)],[56])).
% 1.24/1.48 tff(58,plain,
% 1.24/1.48 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[57, 53])).
% 1.24/1.48 tff(59,plain,
% 1.24/1.48 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[58, 52])).
% 1.24/1.48 tff(60,plain,
% 1.24/1.48 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(z)) = z)),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(61,plain,
% 1.24/1.48 (inj_0(s(z)) = z),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[60, 59])).
% 1.24/1.48 tff(62,assumption,(s(z) = s(s(elem!1))), introduced(assumption)).
% 1.24/1.48 tff(63,plain,
% 1.24/1.48 (inj_0(s(z)) = inj_0(s(s(elem!1)))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[62])).
% 1.24/1.48 tff(64,plain,
% 1.24/1.48 (inj_0(s(s(elem!1))) = inj_0(s(z))),
% 1.24/1.48 inference(symmetry,[status(thm)],[63])).
% 1.24/1.48 tff(65,plain,
% 1.24/1.48 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(elem!1))) = s(elem!1))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(66,plain,
% 1.24/1.48 (inj_0(s(s(elem!1))) = s(elem!1)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[65, 59])).
% 1.24/1.48 tff(67,plain,
% 1.24/1.48 (s(elem!1) = inj_0(s(s(elem!1)))),
% 1.24/1.48 inference(symmetry,[status(thm)],[66])).
% 1.24/1.48 tff(68,plain,
% 1.24/1.48 (s(elem!1) = z),
% 1.24/1.48 inference(transitivity,[status(thm)],[67, 64, 61])).
% 1.24/1.48 tff(69,plain,
% 1.24/1.48 (^[X: $i] : refl((~(s(X) = z)) <=> (~(s(X) = z)))),
% 1.24/1.48 inference(bind,[status(th)],[])).
% 1.24/1.48 tff(70,plain,
% 1.24/1.48 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 1.24/1.48 inference(quant_intro,[status(thm)],[69])).
% 1.24/1.48 tff(71,plain,
% 1.24/1.48 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(72,axiom,(![X: $i] : (~(s(X) = z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','snz')).
% 1.24/1.48 tff(73,plain,
% 1.24/1.48 (![X: $i] : (~(s(X) = z))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[72, 71])).
% 1.24/1.48 tff(74,plain,(
% 1.24/1.48 ![X: $i] : (~(s(X) = z))),
% 1.24/1.48 inference(skolemize,[status(sab)],[73])).
% 1.24/1.48 tff(75,plain,
% 1.24/1.48 (![X: $i] : (~(s(X) = z))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[74, 70])).
% 1.24/1.48 tff(76,plain,
% 1.24/1.48 ((~![X: $i] : (~(s(X) = z))) | (~(s(elem!1) = z))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(77,plain,
% 1.24/1.48 (~(s(elem!1) = z)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[76, 75])).
% 1.24/1.48 tff(78,plain,
% 1.24/1.48 ($false),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[77, 68])).
% 1.24/1.48 tff(79,plain,(~(s(z) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.48 tff(80,plain,
% 1.24/1.48 (~(s(s(elem!1)) = s(z))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[79, 51])).
% 1.24/1.48 tff(81,plain,
% 1.24/1.48 ($false),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[80, 49])).
% 1.24/1.48 tff(82,plain,((~(elem!1 = s(z))) | r(s(s(elem!1)), elem!1) | b(s(s(s(z))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.48 tff(83,plain,
% 1.24/1.48 (~(elem!1 = s(z))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[82, 9, 6])).
% 1.24/1.48 tff(84,plain,
% 1.24/1.48 ((s(z) = elem!1) <=> (elem!1 = s(z))),
% 1.24/1.48 inference(commutativity,[status(thm)],[])).
% 1.24/1.48 tff(85,assumption,(s(z) = elem!1), introduced(assumption)).
% 1.24/1.48 tff(86,plain,
% 1.24/1.48 (elem!1 = s(z)),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[85, 84])).
% 1.24/1.48 tff(87,assumption,(~(elem!1 = s(z))), introduced(assumption)).
% 1.24/1.48 tff(88,plain,
% 1.24/1.48 ($false),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[87, 86])).
% 1.24/1.48 tff(89,plain,((~(s(z) = elem!1)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.48 tff(90,plain,
% 1.24/1.48 (~(s(z) = elem!1)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[89, 83])).
% 1.24/1.48 tff(91,assumption,(~(s(s(elem!1)) = elem!1)), introduced(assumption)).
% 1.24/1.48 tff(92,plain,
% 1.24/1.48 (b(s(s(elem!1)), elem!1)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[47, 91, 6])).
% 1.24/1.48 tff(93,plain,
% 1.24/1.48 (~(elem!1 = s(z))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[32, 92, 9])).
% 1.24/1.48 tff(94,plain,
% 1.24/1.48 (((~![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)))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(95,plain,
% 1.24/1.48 ((~![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)))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(96,plain,
% 1.24/1.48 ((~![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))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[95, 94])).
% 1.24/1.48 tff(97,plain,
% 1.24/1.48 ((elem!1 = s(z)) | r(elem!1, s(z))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[96, 43, 5])).
% 1.24/1.48 tff(98,plain,
% 1.24/1.48 (r(elem!1, s(z))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[97, 93])).
% 1.24/1.48 tff(99,assumption,(s(s(s(z))) = s(z)), introduced(assumption)).
% 1.24/1.48 tff(100,plain,
% 1.24/1.48 (inj_0(s(s(s(z)))) = inj_0(s(z))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[99])).
% 1.24/1.48 tff(101,plain,
% 1.24/1.48 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(z)))) = s(s(z)))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(102,plain,
% 1.24/1.48 (inj_0(s(s(s(z)))) = s(s(z))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[101, 59])).
% 1.24/1.48 tff(103,plain,
% 1.24/1.48 (s(s(z)) = inj_0(s(s(s(z))))),
% 1.24/1.48 inference(symmetry,[status(thm)],[102])).
% 1.24/1.48 tff(104,plain,
% 1.24/1.48 (s(s(z)) = z),
% 1.24/1.48 inference(transitivity,[status(thm)],[103, 100, 61])).
% 1.24/1.48 tff(105,plain,
% 1.24/1.48 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(z)) = z))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(106,plain,
% 1.24/1.48 (~(s(s(z)) = z)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[105, 75])).
% 1.24/1.48 tff(107,plain,
% 1.24/1.48 ($false),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[106, 104])).
% 1.24/1.48 tff(108,plain,(~(s(s(s(z))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.48 tff(109,plain,
% 1.24/1.48 (((~![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)))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(110,plain,
% 1.24/1.48 ((~![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)))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(111,plain,
% 1.24/1.48 ((~![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))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[110, 109])).
% 1.24/1.48 tff(112,plain,
% 1.24/1.48 ((s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[111, 43])).
% 1.24/1.48 tff(113,plain,
% 1.24/1.48 (b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[112, 108])).
% 1.24/1.48 tff(114,plain,
% 1.24/1.48 (r(s(s(s(z))), s(z))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[113, 9])).
% 1.24/1.48 tff(115,plain,
% 1.24/1.48 (^[X0: $i, X2: $i, X1: $i] : refl(((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))) <=> ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))))),
% 1.24/1.48 inference(bind,[status(th)],[])).
% 1.24/1.48 tff(116,plain,
% 1.24/1.48 (![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))) <=> ![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.24/1.48 inference(quant_intro,[status(thm)],[115])).
% 1.24/1.48 tff(117,plain,
% 1.24/1.48 (![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))) <=> ![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(118,plain,
% 1.24/1.48 (^[X0: $i, X2: $i, X1: $i] : rewrite((((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2))) <=> ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))))),
% 1.24/1.48 inference(bind,[status(th)],[])).
% 1.24/1.48 tff(119,plain,
% 1.24/1.48 (![X0: $i, X2: $i, X1: $i] : (((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2))) <=> ![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.24/1.48 inference(quant_intro,[status(thm)],[118])).
% 1.24/1.48 tff(120,axiom,(![X0: $i, X2: $i, X1: $i] : (((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axr')).
% 1.24/1.48 tff(121,plain,
% 1.24/1.48 (![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[120, 119])).
% 1.24/1.48 tff(122,plain,
% 1.24/1.48 (![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[121, 117])).
% 1.24/1.48 tff(123,plain,(
% 1.24/1.48 ![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.24/1.48 inference(skolemize,[status(sab)],[122])).
% 1.24/1.48 tff(124,plain,
% 1.24/1.48 (![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[123, 116])).
% 1.24/1.48 tff(125,plain,
% 1.24/1.48 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(126,plain,
% 1.24/1.48 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(127,plain,
% 1.24/1.48 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z)))))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[126, 125])).
% 1.24/1.48 tff(128,plain,
% 1.24/1.48 (~r(elem!1, s(s(s(z))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[127, 124, 114, 98])).
% 1.24/1.48 tff(129,plain,
% 1.24/1.48 (((~![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)))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(130,plain,
% 1.24/1.48 ((~![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)))))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(131,plain,
% 1.24/1.48 ((~![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))))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[130, 129])).
% 1.24/1.48 tff(132,plain,
% 1.24/1.48 ((elem!1 = s(s(s(z)))) | r(elem!1, s(s(s(z))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[131, 43, 3])).
% 1.24/1.48 tff(133,plain,
% 1.24/1.48 (elem!1 = s(s(s(z)))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[132, 128])).
% 1.24/1.48 tff(134,plain,
% 1.24/1.48 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(elem!1)) = elem!1)),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(135,plain,
% 1.24/1.48 (inj_0(s(elem!1)) = elem!1),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[134, 59])).
% 1.24/1.48 tff(136,assumption,(s(s(s(elem!1))) = s(elem!1)), introduced(assumption)).
% 1.24/1.48 tff(137,plain,
% 1.24/1.48 (inj_0(s(s(s(elem!1)))) = inj_0(s(elem!1))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[136])).
% 1.24/1.48 tff(138,plain,
% 1.24/1.48 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(139,plain,
% 1.24/1.48 (inj_0(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[138, 59])).
% 1.24/1.48 tff(140,plain,
% 1.24/1.48 (s(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 1.24/1.48 inference(symmetry,[status(thm)],[139])).
% 1.24/1.48 tff(141,plain,
% 1.24/1.48 (s(s(elem!1)) = elem!1),
% 1.24/1.48 inference(transitivity,[status(thm)],[140, 137, 135])).
% 1.24/1.48 tff(142,plain,
% 1.24/1.48 ($false),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[91, 141])).
% 1.24/1.48 tff(143,plain,((~(s(s(s(elem!1))) = s(elem!1))) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.24/1.48 tff(144,plain,
% 1.24/1.48 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[143, 91])).
% 1.24/1.48 tff(145,assumption,(s(s(elem!1)) = s(s(s(elem!1)))), introduced(assumption)).
% 1.24/1.48 tff(146,plain,
% 1.24/1.48 (inj_0(s(s(elem!1))) = inj_0(s(s(s(elem!1))))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[145])).
% 1.24/1.48 tff(147,plain,
% 1.24/1.48 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(elem!1)))),
% 1.24/1.48 inference(symmetry,[status(thm)],[146])).
% 1.24/1.48 tff(148,plain,
% 1.24/1.48 (s(s(s(elem!1))) = s(s(elem!1))),
% 1.24/1.48 inference(symmetry,[status(thm)],[145])).
% 1.24/1.48 tff(149,plain,
% 1.24/1.48 (s(s(s(elem!1))) = s(elem!1)),
% 1.24/1.48 inference(transitivity,[status(thm)],[148, 140, 147, 66])).
% 1.24/1.48 tff(150,assumption,(~(s(s(s(elem!1))) = s(elem!1))), introduced(assumption)).
% 1.24/1.48 tff(151,plain,
% 1.24/1.48 ($false),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[150, 149])).
% 1.24/1.48 tff(152,plain,((~(s(s(elem!1)) = s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.48 tff(153,plain,
% 1.24/1.48 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[152, 144])).
% 1.24/1.48 tff(154,plain,
% 1.24/1.48 ((s(s(s(elem!1))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 1.24/1.48 inference(commutativity,[status(thm)],[])).
% 1.24/1.48 tff(155,assumption,(s(s(s(elem!1))) = s(s(elem!1))), introduced(assumption)).
% 1.24/1.48 tff(156,plain,
% 1.24/1.48 (s(s(elem!1)) = s(s(s(elem!1)))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[155, 154])).
% 1.24/1.48 tff(157,assumption,(~(s(s(elem!1)) = s(s(s(elem!1))))), introduced(assumption)).
% 1.24/1.48 tff(158,plain,
% 1.24/1.48 ($false),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[157, 156])).
% 1.24/1.48 tff(159,plain,((~(s(s(s(elem!1))) = s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.48 tff(160,plain,
% 1.24/1.48 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[159, 153])).
% 1.24/1.48 tff(161,plain,
% 1.24/1.48 ((elem!1 = z) <=> (z = elem!1)),
% 1.24/1.48 inference(commutativity,[status(thm)],[])).
% 1.24/1.48 tff(162,plain,
% 1.24/1.48 ((z = elem!1) <=> (elem!1 = z)),
% 1.24/1.48 inference(symmetry,[status(thm)],[161])).
% 1.24/1.48 tff(163,plain,
% 1.24/1.48 (s(s(s(z))) = elem!1),
% 1.24/1.48 inference(symmetry,[status(thm)],[133])).
% 1.24/1.48 tff(164,plain,
% 1.24/1.48 ((s(s(s(z))) = z) <=> (elem!1 = z)),
% 1.24/1.48 inference(monotonicity,[status(thm)],[163])).
% 1.24/1.48 tff(165,plain,
% 1.24/1.48 ((s(s(s(z))) = z) <=> (z = elem!1)),
% 1.24/1.48 inference(transitivity,[status(thm)],[164, 161])).
% 1.24/1.48 tff(166,plain,
% 1.24/1.48 ((s(s(s(z))) = z) <=> (elem!1 = z)),
% 1.24/1.48 inference(transitivity,[status(thm)],[165, 162])).
% 1.24/1.48 tff(167,plain,
% 1.24/1.48 ((~(s(s(s(z))) = z)) <=> (~(elem!1 = z))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[166])).
% 1.24/1.48 tff(168,plain,
% 1.24/1.48 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(z))) = z))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(169,plain,
% 1.24/1.49 (~(s(s(s(z))) = z)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[168, 75])).
% 1.24/1.49 tff(170,plain,
% 1.24/1.49 (~(elem!1 = z)),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[169, 167])).
% 1.24/1.49 tff(171,plain,
% 1.24/1.49 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = z) | b(elem!1, z) | r(elem!1, z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = z) | b(elem!1, z) | r(elem!1, z))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(172,plain,
% 1.24/1.49 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = z) | b(elem!1, z) | r(elem!1, z))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(173,plain,
% 1.24/1.49 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = z) | b(elem!1, z) | r(elem!1, z)),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[172, 171])).
% 1.24/1.49 tff(174,plain,
% 1.24/1.49 ((elem!1 = z) | b(elem!1, z) | r(elem!1, z)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[173, 43])).
% 1.24/1.49 tff(175,plain,
% 1.24/1.49 (r(elem!1, z)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[174, 170, 2])).
% 1.24/1.49 tff(176,assumption,(s(elem!1) = elem!1), introduced(assumption)).
% 1.24/1.49 tff(177,plain,
% 1.24/1.49 (s(s(elem!1)) = s(elem!1)),
% 1.24/1.49 inference(monotonicity,[status(thm)],[176])).
% 1.24/1.49 tff(178,plain,
% 1.24/1.49 (s(s(elem!1)) = elem!1),
% 1.24/1.49 inference(transitivity,[status(thm)],[177, 176])).
% 1.24/1.49 tff(179,plain,
% 1.24/1.49 ($false),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[91, 178])).
% 1.24/1.49 tff(180,plain,((~(s(elem!1) = elem!1)) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.24/1.49 tff(181,plain,
% 1.24/1.49 (~(s(elem!1) = elem!1)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[180, 91])).
% 1.24/1.49 tff(182,plain,
% 1.24/1.49 ((elem!1 = s(s(elem!1))) <=> (s(s(elem!1)) = elem!1)),
% 1.24/1.49 inference(commutativity,[status(thm)],[])).
% 1.24/1.49 tff(183,assumption,(elem!1 = s(s(elem!1))), introduced(assumption)).
% 1.24/1.49 tff(184,plain,
% 1.24/1.49 (s(s(elem!1)) = elem!1),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[183, 182])).
% 1.24/1.49 tff(185,plain,
% 1.24/1.49 ($false),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[91, 184])).
% 1.24/1.49 tff(186,plain,((~(elem!1 = s(s(elem!1)))) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.24/1.49 tff(187,plain,
% 1.24/1.49 (~(elem!1 = s(s(elem!1)))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[186, 91])).
% 1.24/1.49 tff(188,assumption,(s(s(elem!1)) = s(elem!1)), introduced(assumption)).
% 1.24/1.49 tff(189,plain,
% 1.24/1.49 (s(elem!1) = s(s(elem!1))),
% 1.24/1.49 inference(symmetry,[status(thm)],[188])).
% 1.24/1.49 tff(190,plain,
% 1.24/1.49 (inj_0(s(elem!1)) = inj_0(s(s(elem!1)))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[189])).
% 1.24/1.49 tff(191,plain,
% 1.24/1.49 (inj_0(s(s(elem!1))) = inj_0(s(elem!1))),
% 1.24/1.49 inference(symmetry,[status(thm)],[190])).
% 1.24/1.49 tff(192,plain,
% 1.24/1.49 (s(elem!1) = elem!1),
% 1.24/1.49 inference(transitivity,[status(thm)],[67, 191, 135])).
% 1.24/1.49 tff(193,assumption,(~(s(elem!1) = elem!1)), introduced(assumption)).
% 1.24/1.49 tff(194,plain,
% 1.24/1.49 ($false),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[193, 192])).
% 1.24/1.49 tff(195,plain,((~(s(s(elem!1)) = s(elem!1))) | (s(elem!1) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.24/1.49 tff(196,plain,
% 1.24/1.49 (~(s(s(elem!1)) = s(elem!1))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[195, 181])).
% 1.24/1.49 tff(197,plain,
% 1.24/1.49 (b(elem!1, z) <=> b(s(s(s(z))), z)),
% 1.24/1.49 inference(monotonicity,[status(thm)],[133])).
% 1.24/1.49 tff(198,plain,
% 1.24/1.49 ((~b(elem!1, z)) <=> (~b(s(s(s(z))), z))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[197])).
% 1.24/1.49 tff(199,plain,
% 1.24/1.49 (~b(s(s(s(z))), z)),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[2, 198])).
% 1.24/1.49 tff(200,plain,
% 1.24/1.49 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(201,plain,
% 1.24/1.49 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(202,plain,
% 1.24/1.49 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z)),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[201, 200])).
% 1.24/1.49 tff(203,plain,
% 1.24/1.49 (r(s(s(s(z))), z)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[202, 43, 169, 199])).
% 1.24/1.49 tff(204,assumption,(r(s(z), z)), introduced(assumption)).
% 1.24/1.49 tff(205,assumption,(r(s(s(s(z))), z)), introduced(assumption)).
% 1.24/1.49 tff(206,assumption,(r(s(s(s(z))), s(z))), introduced(assumption)).
% 1.24/1.49 tff(207,plain,
% 1.24/1.49 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(208,plain,
% 1.24/1.49 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(209,plain,
% 1.24/1.49 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[208, 207])).
% 1.24/1.49 tff(210,plain,
% 1.24/1.49 ($false),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[209, 124, 206, 205, 204])).
% 1.24/1.49 tff(211,plain,((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.49 tff(212,plain,
% 1.24/1.49 (~r(s(z), z)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[211, 203, 114])).
% 1.24/1.49 tff(213,assumption,(~b(s(z), z)), introduced(assumption)).
% 1.24/1.49 tff(214,assumption,(~r(s(z), z)), introduced(assumption)).
% 1.24/1.49 tff(215,plain,
% 1.24/1.49 ((~![X: $i] : (~(s(X) = z))) | (~(s(z) = z))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(216,plain,
% 1.24/1.49 (~(s(z) = z)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[215, 75])).
% 1.24/1.49 tff(217,plain,
% 1.24/1.49 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = z) | b(s(z), z) | r(s(z), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = z) | b(s(z), z) | r(s(z), z))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(218,plain,
% 1.24/1.49 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = z) | b(s(z), z) | r(s(z), z))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(219,plain,
% 1.24/1.49 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = z) | b(s(z), z) | r(s(z), z)),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[218, 217])).
% 1.24/1.49 tff(220,plain,
% 1.24/1.49 ($false),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[219, 43, 216, 214, 213])).
% 1.24/1.49 tff(221,plain,(r(s(z), z) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 1.24/1.49 tff(222,plain,
% 1.24/1.49 (b(s(z), z)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[221, 212])).
% 1.24/1.49 tff(223,plain,
% 1.24/1.49 (s(elem!1) = s(s(s(s(z))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[133])).
% 1.24/1.49 tff(224,plain,
% 1.24/1.49 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[223])).
% 1.24/1.49 tff(225,plain,
% 1.24/1.49 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 1.24/1.49 inference(symmetry,[status(thm)],[224])).
% 1.24/1.49 tff(226,plain,
% 1.24/1.49 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[225])).
% 1.24/1.49 tff(227,plain,
% 1.24/1.49 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.24/1.49 inference(symmetry,[status(thm)],[226])).
% 1.24/1.49 tff(228,plain,
% 1.24/1.49 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(s(s(z))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[133])).
% 1.24/1.49 tff(229,plain,
% 1.24/1.49 (b(s(s(elem!1)), s(s(s(z))))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[92, 228])).
% 1.24/1.49 tff(230,plain,
% 1.24/1.49 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[229, 227])).
% 1.24/1.49 tff(231,assumption,(elem!1 = s(s(s(z)))), introduced(assumption)).
% 1.24/1.49 tff(232,plain,
% 1.24/1.49 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[152, 150])).
% 1.24/1.49 tff(233,plain,
% 1.24/1.49 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[159, 232])).
% 1.24/1.49 tff(234,plain,
% 1.24/1.49 (s(elem!1) = s(s(s(s(z))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[231])).
% 1.24/1.49 tff(235,plain,
% 1.24/1.49 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[234])).
% 1.24/1.49 tff(236,plain,
% 1.24/1.49 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 1.24/1.49 inference(symmetry,[status(thm)],[235])).
% 1.24/1.49 tff(237,plain,
% 1.24/1.49 (b(z, s(s(s(s(s(z)))))) <=> b(z, s(s(elem!1)))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[236])).
% 1.24/1.49 tff(238,plain,
% 1.24/1.49 ((~b(z, s(s(s(s(s(z))))))) <=> (~b(z, s(s(elem!1))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[237])).
% 1.24/1.49 tff(239,plain,
% 1.24/1.49 (s(s(s(s(z)))) = s(elem!1)),
% 1.24/1.49 inference(symmetry,[status(thm)],[234])).
% 1.24/1.49 tff(240,plain,
% 1.24/1.49 (s(s(s(elem!1))) = s(s(s(s(s(s(z))))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[235])).
% 1.24/1.49 tff(241,plain,
% 1.24/1.49 (s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))),
% 1.24/1.49 inference(symmetry,[status(thm)],[240])).
% 1.24/1.49 tff(242,plain,
% 1.24/1.49 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[241, 239])).
% 1.24/1.49 tff(243,plain,
% 1.24/1.49 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.24/1.49 inference(symmetry,[status(thm)],[242])).
% 1.24/1.49 tff(244,assumption,(r(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 1.24/1.49 tff(245,assumption,(b(s(s(s(s(s(z))))), s(s(s(z))))), introduced(assumption)).
% 1.24/1.49 tff(246,assumption,(r(elem!1, z)), introduced(assumption)).
% 1.24/1.49 tff(247,assumption,(b(s(z), z)), introduced(assumption)).
% 1.24/1.49 tff(248,plain,
% 1.24/1.49 (s(s(s(z))) = elem!1),
% 1.24/1.49 inference(symmetry,[status(thm)],[231])).
% 1.24/1.49 tff(249,plain,
% 1.24/1.49 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(elem!1) = elem!1)),
% 1.24/1.49 inference(monotonicity,[status(thm)],[239, 248])).
% 1.24/1.49 tff(250,plain,
% 1.24/1.49 ((s(elem!1) = elem!1) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 1.24/1.49 inference(symmetry,[status(thm)],[249])).
% 1.24/1.49 tff(251,plain,
% 1.24/1.49 ((~(s(elem!1) = elem!1)) <=> (~(s(s(s(s(z)))) = s(s(s(z)))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[250])).
% 1.24/1.49 tff(252,plain,
% 1.24/1.49 (~(s(s(s(s(z)))) = s(s(s(z))))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[193, 251])).
% 1.24/1.49 tff(253,plain,
% 1.24/1.49 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(elem!1, s(elem!1))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[248, 239])).
% 1.24/1.49 tff(254,plain,
% 1.24/1.49 (r(elem!1, s(elem!1)) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 1.24/1.49 inference(symmetry,[status(thm)],[253])).
% 1.24/1.49 tff(255,assumption,(r(elem!1, s(elem!1))), introduced(assumption)).
% 1.24/1.49 tff(256,plain,
% 1.24/1.49 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[255, 254])).
% 1.24/1.49 tff(257,plain,
% 1.24/1.49 (b(z, s(s(s(s(z))))) <=> b(z, s(elem!1))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[239])).
% 1.24/1.49 tff(258,plain,
% 1.24/1.49 (b(z, s(elem!1)) <=> b(z, s(s(s(s(z)))))),
% 1.24/1.49 inference(symmetry,[status(thm)],[257])).
% 1.24/1.49 tff(259,plain,
% 1.24/1.49 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(260,plain,
% 1.24/1.49 (((~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z))) <=> ((~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(261,plain,
% 1.24/1.49 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1)))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[260])).
% 1.24/1.49 tff(262,plain,
% 1.24/1.49 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))),
% 1.24/1.49 inference(transitivity,[status(thm)],[261, 259])).
% 1.24/1.49 tff(263,plain,
% 1.24/1.49 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(264,plain,
% 1.24/1.49 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1)))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[263, 262])).
% 1.24/1.49 tff(265,plain,
% 1.24/1.49 ((~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1)))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[264, 124])).
% 1.24/1.49 tff(266,plain,
% 1.24/1.49 (~r(z, s(elem!1))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[265, 255, 246])).
% 1.24/1.49 tff(267,plain,
% 1.24/1.49 ((z = s(elem!1)) <=> (s(elem!1) = z)),
% 1.24/1.49 inference(commutativity,[status(thm)],[])).
% 1.24/1.49 tff(268,plain,
% 1.24/1.49 ((s(elem!1) = z) <=> (z = s(elem!1))),
% 1.24/1.49 inference(symmetry,[status(thm)],[267])).
% 1.24/1.49 tff(269,plain,
% 1.24/1.49 ((~(s(elem!1) = z)) <=> (~(z = s(elem!1)))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[268])).
% 1.24/1.49 tff(270,plain,
% 1.24/1.49 (~(z = s(elem!1))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[77, 269])).
% 1.24/1.49 tff(271,plain,
% 1.24/1.49 (((~![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)))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(272,plain,
% 1.24/1.49 ((~![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)))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(273,plain,
% 1.24/1.49 ((~![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))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[272, 271])).
% 1.24/1.49 tff(274,plain,
% 1.24/1.49 ((z = s(elem!1)) | b(z, s(elem!1)) | r(z, s(elem!1))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[273, 43])).
% 1.24/1.49 tff(275,plain,
% 1.24/1.49 (b(z, s(elem!1)) | r(z, s(elem!1))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[274, 270])).
% 1.24/1.49 tff(276,plain,
% 1.24/1.49 (b(z, s(elem!1))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[275, 266])).
% 1.24/1.49 tff(277,plain,
% 1.24/1.49 (b(z, s(s(s(s(z)))))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[276, 258])).
% 1.24/1.49 tff(278,plain,
% 1.24/1.49 (r(s(s(s(s(z)))), z) <=> r(s(elem!1), z)),
% 1.24/1.49 inference(monotonicity,[status(thm)],[239])).
% 1.24/1.49 tff(279,plain,
% 1.24/1.49 (r(s(elem!1), z) <=> r(s(s(s(s(z)))), z)),
% 1.24/1.49 inference(symmetry,[status(thm)],[278])).
% 1.24/1.49 tff(280,plain,
% 1.24/1.49 ((~r(s(elem!1), z)) <=> (~r(s(s(s(s(z)))), z))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[279])).
% 1.24/1.49 tff(281,plain,
% 1.24/1.49 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(282,plain,
% 1.24/1.49 (((~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(283,plain,
% 1.24/1.49 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[282])).
% 1.24/1.49 tff(284,plain,
% 1.24/1.49 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)))),
% 1.24/1.49 inference(transitivity,[status(thm)],[283, 281])).
% 1.24/1.49 tff(285,plain,
% 1.24/1.49 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(286,plain,
% 1.24/1.49 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[285, 284])).
% 1.24/1.49 tff(287,plain,
% 1.24/1.49 ((~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[286, 124])).
% 1.24/1.49 tff(288,plain,
% 1.24/1.49 (~r(s(elem!1), z)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[287, 255, 246])).
% 1.24/1.49 tff(289,plain,
% 1.24/1.49 (~r(s(s(s(s(z)))), z)),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[288, 280])).
% 1.24/1.49 tff(290,plain,
% 1.24/1.49 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(z)))) = z))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(291,plain,
% 1.24/1.49 (~(s(s(s(s(z)))) = z)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[290, 75])).
% 1.24/1.49 tff(292,plain,
% 1.24/1.49 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = z) | b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = z) | b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(293,plain,
% 1.24/1.49 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = z) | b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(294,plain,
% 1.24/1.49 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = z) | b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z)),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[293, 292])).
% 1.24/1.49 tff(295,plain,
% 1.24/1.49 (b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[294, 43, 291])).
% 1.24/1.49 tff(296,plain,
% 1.24/1.49 (b(s(s(s(s(z)))), z)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[295, 289])).
% 1.24/1.49 tff(297,plain,
% 1.24/1.49 (^[X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : refl(((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) <=> ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))))),
% 1.24/1.49 inference(bind,[status(th)],[])).
% 1.24/1.49 tff(298,plain,
% 1.24/1.49 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) <=> ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.24/1.49 inference(quant_intro,[status(thm)],[297])).
% 1.24/1.49 tff(299,plain,
% 1.24/1.49 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) <=> ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(300,plain,
% 1.24/1.49 (^[X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) <=> ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))), (((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) <=> (((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X2, X3))))), rewrite((((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X2, X3))) <=> ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))), (((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) <=> ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))))), ((((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) | (~b(X3, X4))) <=> (((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X3, X4))))), rewrite((((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X3, X4))) <=> ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))), ((((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) | (~b(X3, X4))) <=> ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))))),
% 1.24/1.49 inference(bind,[status(th)],[])).
% 1.24/1.49 tff(301,plain,
% 1.24/1.49 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : (((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) | (~b(X3, X4))) <=> ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.24/1.49 inference(quant_intro,[status(thm)],[300])).
% 1.24/1.49 tff(302,axiom,(![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : (((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) | (~b(X3, X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axb')).
% 1.24/1.49 tff(303,plain,
% 1.24/1.49 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[302, 301])).
% 1.24/1.49 tff(304,plain,
% 1.24/1.49 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[303, 299])).
% 1.24/1.49 tff(305,plain,(
% 1.24/1.49 ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.24/1.49 inference(skolemize,[status(sab)],[304])).
% 1.24/1.49 tff(306,plain,
% 1.24/1.49 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[305, 298])).
% 1.24/1.49 tff(307,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(308,plain,
% 1.24/1.49 (((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(309,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(z))))))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[308])).
% 1.24/1.49 tff(310,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))))),
% 1.24/1.49 inference(transitivity,[status(thm)],[309, 307])).
% 1.24/1.49 tff(311,plain,
% 1.24/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(312,plain,
% 1.24/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(z))))))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[311, 310])).
% 1.24/1.49 tff(313,plain,
% 1.24/1.49 ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z))))))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[312, 306, 296, 247])).
% 1.24/1.49 tff(314,plain,
% 1.24/1.49 (~b(s(s(s(s(z)))), s(z))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[313, 277])).
% 1.24/1.49 tff(315,assumption,(s(s(s(s(z)))) = s(z)), introduced(assumption)).
% 1.24/1.49 tff(316,plain,
% 1.24/1.49 (s(z) = s(s(s(s(z))))),
% 1.24/1.49 inference(symmetry,[status(thm)],[315])).
% 1.24/1.49 tff(317,plain,
% 1.24/1.49 (inj_0(s(z)) = inj_0(s(s(s(s(z)))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[316])).
% 1.24/1.49 tff(318,plain,
% 1.24/1.49 (inj_0(s(s(s(s(z))))) = inj_0(s(z))),
% 1.24/1.49 inference(symmetry,[status(thm)],[317])).
% 1.24/1.49 tff(319,plain,
% 1.24/1.49 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(z))))) = s(s(s(z))))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(320,plain,
% 1.24/1.49 (inj_0(s(s(s(s(z))))) = s(s(s(z)))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[319, 59])).
% 1.24/1.49 tff(321,plain,
% 1.24/1.49 (s(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 1.24/1.49 inference(symmetry,[status(thm)],[320])).
% 1.24/1.49 tff(322,plain,
% 1.24/1.49 (s(s(s(z))) = z),
% 1.24/1.49 inference(transitivity,[status(thm)],[321, 318, 61])).
% 1.24/1.49 tff(323,plain,
% 1.24/1.49 ($false),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[169, 322])).
% 1.24/1.49 tff(324,plain,(~(s(s(s(s(z)))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.49 tff(325,plain,
% 1.24/1.49 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z)))),
% 1.24/1.50 inference(rewrite,[status(thm)],[])).
% 1.24/1.50 tff(326,plain,
% 1.24/1.50 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z)))),
% 1.24/1.50 inference(quant_inst,[status(thm)],[])).
% 1.24/1.50 tff(327,plain,
% 1.24/1.50 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z))),
% 1.24/1.50 inference(modus_ponens,[status(thm)],[326, 325])).
% 1.24/1.50 tff(328,plain,
% 1.24/1.50 (r(s(s(s(s(z)))), s(z))),
% 1.24/1.50 inference(unit_resolution,[status(thm)],[327, 43, 324, 314])).
% 1.24/1.50 tff(329,plain,
% 1.24/1.50 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.24/1.50 inference(rewrite,[status(thm)],[])).
% 1.24/1.50 tff(330,plain,
% 1.24/1.50 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.24/1.50 inference(rewrite,[status(thm)],[])).
% 1.24/1.50 tff(331,plain,
% 1.24/1.50 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))))),
% 1.24/1.50 inference(monotonicity,[status(thm)],[330])).
% 1.24/1.50 tff(332,plain,
% 1.24/1.50 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.24/1.50 inference(transitivity,[status(thm)],[331, 329])).
% 1.24/1.50 tff(333,plain,
% 1.24/1.50 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.24/1.50 inference(quant_inst,[status(thm)],[])).
% 1.24/1.50 tff(334,plain,
% 1.24/1.50 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))),
% 1.24/1.50 inference(modus_ponens,[status(thm)],[333, 332])).
% 1.24/1.50 tff(335,plain,
% 1.24/1.50 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.24/1.50 inference(unit_resolution,[status(thm)],[334, 124, 206, 328])).
% 1.24/1.50 tff(336,plain,
% 1.24/1.50 ($false),
% 1.24/1.50 inference(unit_resolution,[status(thm)],[335, 256])).
% 1.24/1.50 tff(337,plain,((~r(elem!1, s(elem!1))) | (~(elem!1 = s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.50 tff(338,plain,
% 1.24/1.50 (~r(elem!1, s(elem!1))),
% 1.24/1.50 inference(unit_resolution,[status(thm)],[337, 231, 206, 247, 246])).
% 1.24/1.50 tff(339,plain,
% 1.24/1.50 ((s(s(s(z))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 1.24/1.50 inference(commutativity,[status(thm)],[])).
% 1.24/1.50 tff(340,plain,
% 1.24/1.50 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(z)))))),
% 1.24/1.50 inference(symmetry,[status(thm)],[339])).
% 1.24/1.50 tff(341,plain,
% 1.24/1.50 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(s(s(z))))))),
% 1.24/1.50 inference(monotonicity,[status(thm)],[340])).
% 1.24/1.50 tff(342,assumption,(~(s(s(s(s(z)))) = s(s(s(z))))), introduced(assumption)).
% 1.24/1.50 tff(343,plain,
% 1.24/1.50 (~(s(s(s(z))) = s(s(s(s(z)))))),
% 1.24/1.50 inference(modus_ponens,[status(thm)],[342, 341])).
% 1.24/1.50 tff(344,plain,
% 1.24/1.50 ((~r(elem!1, s(elem!1))) <=> (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.24/1.50 inference(monotonicity,[status(thm)],[254])).
% 1.24/1.50 tff(345,assumption,(~r(elem!1, s(elem!1))), introduced(assumption)).
% 1.24/1.50 tff(346,plain,
% 1.24/1.50 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.24/1.50 inference(modus_ponens,[status(thm)],[345, 344])).
% 1.24/1.50 tff(347,assumption,(~b(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 1.34/1.50 tff(348,plain,
% 1.34/1.50 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(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))))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(349,plain,
% 1.34/1.50 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z))))))),
% 1.34/1.50 inference(quant_inst,[status(thm)],[])).
% 1.34/1.50 tff(350,plain,
% 1.34/1.50 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z)))))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[349, 348])).
% 1.34/1.50 tff(351,plain,
% 1.34/1.50 ((s(s(s(z))) = s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z)))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[350, 43, 347])).
% 1.34/1.50 tff(352,plain,
% 1.34/1.50 ($false),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[351, 346, 343])).
% 1.34/1.50 tff(353,plain,(r(elem!1, s(elem!1)) | b(s(s(s(z))), s(s(s(s(z))))) | (~(elem!1 = s(s(s(z))))) | (s(s(s(s(z)))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.50 tff(354,plain,
% 1.34/1.50 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[353, 338, 231, 252])).
% 1.34/1.50 tff(355,plain,
% 1.34/1.50 ((s(s(s(z))) = z) <=> (elem!1 = z)),
% 1.34/1.50 inference(monotonicity,[status(thm)],[248])).
% 1.34/1.50 tff(356,plain,
% 1.34/1.50 ((s(s(s(z))) = z) <=> (z = elem!1)),
% 1.34/1.50 inference(transitivity,[status(thm)],[355, 161])).
% 1.34/1.50 tff(357,plain,
% 1.34/1.50 ((~(s(s(s(z))) = z)) <=> (~(z = elem!1))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[356])).
% 1.34/1.50 tff(358,plain,
% 1.34/1.50 (~(z = elem!1)),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[169, 357])).
% 1.34/1.50 tff(359,assumption,(r(elem!1, s(z))), introduced(assumption)).
% 1.34/1.50 tff(360,assumption,(~(elem!1 = s(s(elem!1)))), introduced(assumption)).
% 1.34/1.50 tff(361,assumption,(elem!1 = s(elem!1)), introduced(assumption)).
% 1.34/1.50 tff(362,plain,
% 1.34/1.50 (s(elem!1) = elem!1),
% 1.34/1.50 inference(symmetry,[status(thm)],[361])).
% 1.34/1.50 tff(363,plain,
% 1.34/1.50 ($false),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[193, 362])).
% 1.34/1.50 tff(364,plain,((~(elem!1 = s(elem!1))) | (s(elem!1) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.34/1.50 tff(365,plain,
% 1.34/1.50 (~(elem!1 = s(elem!1))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[364, 193])).
% 1.34/1.50 tff(366,assumption,(~(elem!1 = s(elem!1))), introduced(assumption)).
% 1.34/1.50 tff(367,assumption,(~b(elem!1, s(elem!1))), introduced(assumption)).
% 1.34/1.50 tff(368,plain,
% 1.34/1.50 (((~![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)))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(369,plain,
% 1.34/1.50 ((~![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)))),
% 1.34/1.50 inference(quant_inst,[status(thm)],[])).
% 1.34/1.50 tff(370,plain,
% 1.34/1.50 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(elem!1)) | b(elem!1, s(elem!1)) | r(elem!1, s(elem!1))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[369, 368])).
% 1.34/1.50 tff(371,plain,
% 1.34/1.50 ($false),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[370, 43, 345, 367, 366])).
% 1.34/1.50 tff(372,plain,(r(elem!1, s(elem!1)) | b(elem!1, s(elem!1)) | (elem!1 = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.50 tff(373,plain,
% 1.34/1.50 (b(elem!1, s(elem!1))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[372, 338, 365])).
% 1.34/1.50 tff(374,assumption,(r(z, elem!1)), introduced(assumption)).
% 1.34/1.50 tff(375,plain,
% 1.34/1.50 ((z = s(z)) <=> (s(z) = z)),
% 1.34/1.50 inference(commutativity,[status(thm)],[])).
% 1.34/1.50 tff(376,plain,
% 1.34/1.50 ((s(z) = z) <=> (z = s(z))),
% 1.34/1.50 inference(symmetry,[status(thm)],[375])).
% 1.34/1.50 tff(377,plain,
% 1.34/1.50 ((~(s(z) = z)) <=> (~(z = s(z)))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[376])).
% 1.34/1.50 tff(378,plain,
% 1.34/1.50 (~(z = s(z))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[216, 377])).
% 1.34/1.50 tff(379,plain,
% 1.34/1.50 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(z))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(380,plain,
% 1.34/1.50 (((~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(z))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(381,plain,
% 1.34/1.50 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(z)))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[380])).
% 1.34/1.50 tff(382,plain,
% 1.34/1.50 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(z))))),
% 1.34/1.50 inference(transitivity,[status(thm)],[381, 379])).
% 1.34/1.50 tff(383,plain,
% 1.34/1.50 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1)))),
% 1.34/1.50 inference(quant_inst,[status(thm)],[])).
% 1.34/1.50 tff(384,plain,
% 1.34/1.50 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(z)))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[383, 382])).
% 1.34/1.50 tff(385,plain,
% 1.34/1.50 ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(z)))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[384, 124])).
% 1.34/1.50 tff(386,plain,
% 1.34/1.50 (~r(z, s(z))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[385, 374, 359])).
% 1.34/1.50 tff(387,plain,
% 1.34/1.50 (((~![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)))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(388,plain,
% 1.34/1.50 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(z)) | b(z, s(z)) | r(z, s(z)))),
% 1.34/1.50 inference(quant_inst,[status(thm)],[])).
% 1.34/1.50 tff(389,plain,
% 1.34/1.50 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(z)) | b(z, s(z)) | r(z, s(z))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[388, 387])).
% 1.34/1.50 tff(390,plain,
% 1.34/1.50 ((z = s(z)) | b(z, s(z))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[389, 43, 386])).
% 1.34/1.50 tff(391,plain,
% 1.34/1.50 (b(z, s(z))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[390, 378])).
% 1.34/1.50 tff(392,plain,
% 1.34/1.50 (~(s(s(elem!1)) = s(elem!1))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[195, 193])).
% 1.34/1.50 tff(393,assumption,(b(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 1.34/1.50 tff(394,plain,
% 1.34/1.50 (r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[241, 236])).
% 1.34/1.50 tff(395,plain,
% 1.34/1.50 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 1.34/1.50 inference(symmetry,[status(thm)],[394])).
% 1.34/1.50 tff(396,plain,
% 1.34/1.50 (b(z, s(s(elem!1))) <=> b(z, s(s(s(s(s(z))))))),
% 1.34/1.50 inference(symmetry,[status(thm)],[237])).
% 1.34/1.50 tff(397,assumption,(r(s(s(s(s(z)))), z)), introduced(assumption)).
% 1.34/1.50 tff(398,plain,
% 1.34/1.50 ((s(elem!1) = s(s(elem!1))) <=> (s(s(elem!1)) = s(elem!1))),
% 1.34/1.50 inference(commutativity,[status(thm)],[])).
% 1.34/1.50 tff(399,plain,
% 1.34/1.50 ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) <=> (s(elem!1) = s(s(elem!1)))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[239, 236])).
% 1.34/1.50 tff(400,plain,
% 1.34/1.50 ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) <=> (s(s(elem!1)) = s(elem!1))),
% 1.34/1.50 inference(transitivity,[status(thm)],[399, 398])).
% 1.34/1.50 tff(401,plain,
% 1.34/1.50 ((s(s(elem!1)) = s(elem!1)) <=> (s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 1.34/1.50 inference(symmetry,[status(thm)],[400])).
% 1.34/1.50 tff(402,plain,
% 1.34/1.50 ((~(s(s(elem!1)) = s(elem!1))) <=> (~(s(s(s(s(z)))) = s(s(s(s(s(z)))))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[401])).
% 1.34/1.50 tff(403,assumption,(~(s(s(elem!1)) = s(elem!1))), introduced(assumption)).
% 1.34/1.50 tff(404,plain,
% 1.34/1.50 (~(s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[403, 402])).
% 1.34/1.50 tff(405,plain,
% 1.34/1.50 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(elem!1), elem!1)),
% 1.34/1.50 inference(monotonicity,[status(thm)],[239, 248])).
% 1.34/1.50 tff(406,plain,
% 1.34/1.50 (r(s(elem!1), elem!1) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 1.34/1.50 inference(symmetry,[status(thm)],[405])).
% 1.34/1.50 tff(407,plain,
% 1.34/1.50 ((~r(s(elem!1), elem!1)) <=> (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[406])).
% 1.34/1.50 tff(408,assumption,(~r(s(elem!1), z)), introduced(assumption)).
% 1.34/1.50 tff(409,plain,
% 1.34/1.50 (~r(s(s(s(s(z)))), z)),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[408, 280])).
% 1.34/1.50 tff(410,plain,
% 1.34/1.50 ($false),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[397, 409])).
% 1.34/1.50 tff(411,plain,(r(s(elem!1), z) | (~r(s(s(s(s(z)))), z)) | (~(elem!1 = s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.50 tff(412,plain,
% 1.34/1.50 (r(s(elem!1), z)),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[411, 397, 231])).
% 1.34/1.50 tff(413,plain,
% 1.34/1.50 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(414,plain,
% 1.34/1.50 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))),
% 1.34/1.50 inference(quant_inst,[status(thm)],[])).
% 1.34/1.50 tff(415,plain,
% 1.34/1.50 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[414, 413])).
% 1.34/1.50 tff(416,plain,
% 1.34/1.50 ((~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[415, 124])).
% 1.34/1.50 tff(417,plain,
% 1.34/1.50 (~r(s(elem!1), elem!1)),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[416, 412, 374])).
% 1.34/1.50 tff(418,plain,
% 1.34/1.50 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[417, 407])).
% 1.34/1.50 tff(419,plain,
% 1.34/1.50 (((~![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)))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(420,plain,
% 1.34/1.50 ((~![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)))))),
% 1.34/1.50 inference(quant_inst,[status(thm)],[])).
% 1.34/1.50 tff(421,plain,
% 1.34/1.50 ((~![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))))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[420, 419])).
% 1.34/1.50 tff(422,plain,
% 1.34/1.50 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[421, 43, 342, 418])).
% 1.34/1.50 tff(423,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), 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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(424,plain,
% 1.34/1.50 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(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(z))), 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))))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(425,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[424])).
% 1.34/1.50 tff(426,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.34/1.50 inference(transitivity,[status(thm)],[425, 423])).
% 1.34/1.50 tff(427,plain,
% 1.34/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~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))))))))),
% 1.34/1.50 inference(quant_inst,[status(thm)],[])).
% 1.34/1.50 tff(428,plain,
% 1.34/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), 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)))))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[427, 426])).
% 1.34/1.50 tff(429,plain,
% 1.34/1.50 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[428, 306, 393, 422, 245])).
% 1.34/1.50 tff(430,plain,
% 1.34/1.50 (((~![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)))))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(431,plain,
% 1.34/1.50 ((~![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)))))))),
% 1.34/1.50 inference(quant_inst,[status(thm)],[])).
% 1.34/1.50 tff(432,plain,
% 1.34/1.50 ((~![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))))))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[431, 430])).
% 1.34/1.50 tff(433,plain,
% 1.34/1.50 ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) | r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[432, 43, 429])).
% 1.34/1.50 tff(434,plain,
% 1.34/1.50 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[433, 404])).
% 1.34/1.50 tff(435,plain,
% 1.34/1.50 (r(z, s(s(s(s(s(z)))))) <=> r(z, s(s(elem!1)))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[236])).
% 1.34/1.50 tff(436,plain,
% 1.34/1.50 (r(z, s(s(elem!1))) <=> r(z, s(s(s(s(s(z))))))),
% 1.34/1.50 inference(symmetry,[status(thm)],[435])).
% 1.34/1.50 tff(437,assumption,(r(z, s(s(elem!1)))), introduced(assumption)).
% 1.34/1.50 tff(438,plain,
% 1.34/1.50 (r(z, s(s(s(s(s(z))))))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[437, 436])).
% 1.34/1.50 tff(439,assumption,(r(s(s(s(s(z)))), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.34/1.50 tff(440,plain,
% 1.34/1.50 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(s(z))))))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(441,plain,
% 1.34/1.50 (((~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(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))))))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(442,plain,
% 1.34/1.50 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(s(z)))))))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[441])).
% 1.34/1.50 tff(443,plain,
% 1.34/1.50 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(s(z))))))))),
% 1.34/1.50 inference(transitivity,[status(thm)],[442, 440])).
% 1.34/1.50 tff(444,plain,
% 1.34/1.50 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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)))),
% 1.34/1.50 inference(quant_inst,[status(thm)],[])).
% 1.34/1.50 tff(445,plain,
% 1.34/1.50 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(s(z)))))))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[444, 443])).
% 1.34/1.50 tff(446,plain,
% 1.34/1.50 (~r(z, s(s(s(s(s(z))))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[445, 124, 397, 439])).
% 1.34/1.50 tff(447,plain,
% 1.34/1.50 ($false),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[446, 438])).
% 1.34/1.50 tff(448,plain,((~r(z, s(s(elem!1)))) | (~(elem!1 = s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.50 tff(449,plain,
% 1.34/1.50 (~r(z, s(s(elem!1)))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[448, 434, 397, 231])).
% 1.34/1.50 tff(450,plain,
% 1.34/1.50 ((z = s(s(elem!1))) <=> (s(s(elem!1)) = z)),
% 1.34/1.50 inference(commutativity,[status(thm)],[])).
% 1.34/1.50 tff(451,plain,
% 1.34/1.50 ((s(s(elem!1)) = z) <=> (z = s(s(elem!1)))),
% 1.34/1.50 inference(symmetry,[status(thm)],[450])).
% 1.34/1.50 tff(452,plain,
% 1.34/1.50 ((~(s(s(elem!1)) = z)) <=> (~(z = s(s(elem!1))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[451])).
% 1.34/1.50 tff(453,plain,
% 1.34/1.50 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(elem!1)) = z))),
% 1.34/1.50 inference(quant_inst,[status(thm)],[])).
% 1.34/1.50 tff(454,plain,
% 1.34/1.50 (~(s(s(elem!1)) = z)),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[453, 75])).
% 1.34/1.50 tff(455,plain,
% 1.34/1.50 (~(z = s(s(elem!1)))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[454, 452])).
% 1.34/1.50 tff(456,plain,
% 1.34/1.50 (((~![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))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(457,plain,
% 1.34/1.50 ((~![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))))),
% 1.34/1.50 inference(quant_inst,[status(thm)],[])).
% 1.34/1.50 tff(458,plain,
% 1.34/1.50 ((~![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)))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[457, 456])).
% 1.34/1.50 tff(459,plain,
% 1.34/1.50 ((z = s(s(elem!1))) | b(z, s(s(elem!1))) | r(z, s(s(elem!1)))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[458, 43])).
% 1.34/1.50 tff(460,plain,
% 1.34/1.50 (b(z, s(s(elem!1))) | r(z, s(s(elem!1)))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[459, 455])).
% 1.34/1.50 tff(461,plain,
% 1.34/1.50 (b(z, s(s(elem!1)))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[460, 449])).
% 1.34/1.50 tff(462,plain,
% 1.34/1.50 (b(z, s(s(s(s(s(z))))))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[461, 396])).
% 1.34/1.50 tff(463,plain,
% 1.34/1.50 (b(s(s(s(s(s(z))))), z) <=> b(s(s(elem!1)), z)),
% 1.34/1.50 inference(monotonicity,[status(thm)],[236])).
% 1.34/1.50 tff(464,plain,
% 1.34/1.50 (b(s(s(elem!1)), z) <=> b(s(s(s(s(s(z))))), z)),
% 1.34/1.50 inference(symmetry,[status(thm)],[463])).
% 1.34/1.50 tff(465,assumption,(r(s(s(elem!1)), z)), introduced(assumption)).
% 1.34/1.50 tff(466,assumption,(r(s(elem!1), z)), introduced(assumption)).
% 1.34/1.50 tff(467,plain,
% 1.34/1.50 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(468,plain,
% 1.34/1.51 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(469,plain,
% 1.34/1.51 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1)))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[468, 467])).
% 1.34/1.51 tff(470,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[469, 124, 466, 244, 465])).
% 1.34/1.51 tff(471,plain,((~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(472,plain,
% 1.34/1.51 (~r(s(s(elem!1)), z)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[471, 412, 244])).
% 1.34/1.51 tff(473,plain,
% 1.34/1.51 (((~![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))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(474,plain,
% 1.34/1.51 ((~![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))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(475,plain,
% 1.34/1.51 ((~![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)),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[474, 473])).
% 1.34/1.51 tff(476,plain,
% 1.34/1.51 (b(s(s(elem!1)), z) | r(s(s(elem!1)), z)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[475, 43, 454])).
% 1.34/1.51 tff(477,plain,
% 1.34/1.51 (b(s(s(elem!1)), z)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[476, 472])).
% 1.34/1.51 tff(478,plain,
% 1.34/1.51 (b(s(s(s(s(s(z))))), z)),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[477, 464])).
% 1.34/1.51 tff(479,plain,
% 1.34/1.51 (b(s(s(s(z))), s(s(s(s(s(z)))))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[236])).
% 1.34/1.51 tff(480,plain,
% 1.34/1.51 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.34/1.51 inference(symmetry,[status(thm)],[479])).
% 1.34/1.51 tff(481,plain,
% 1.34/1.51 (b(elem!1, s(s(elem!1))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[231])).
% 1.34/1.51 tff(482,plain,
% 1.34/1.51 (b(elem!1, s(s(elem!1))) <=> b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.34/1.51 inference(transitivity,[status(thm)],[481, 480])).
% 1.34/1.51 tff(483,plain,
% 1.34/1.51 (r(s(s(s(z))), s(s(s(s(s(z)))))) <=> r(elem!1, s(s(elem!1)))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[248, 236])).
% 1.34/1.51 tff(484,plain,
% 1.34/1.51 ((~r(s(s(s(z))), s(s(s(s(s(z))))))) <=> (~r(elem!1, s(s(elem!1))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[483])).
% 1.34/1.51 tff(485,assumption,(b(z, s(z))), introduced(assumption)).
% 1.34/1.51 tff(486,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(487,plain,
% 1.34/1.51 (((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(488,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[487])).
% 1.34/1.51 tff(489,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.34/1.51 inference(transitivity,[status(thm)],[488, 486])).
% 1.34/1.51 tff(490,plain,
% 1.34/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(491,plain,
% 1.34/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[490, 489])).
% 1.34/1.51 tff(492,plain,
% 1.34/1.51 (~b(s(s(s(s(s(z))))), s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[491, 306, 247, 478, 485])).
% 1.34/1.51 tff(493,assumption,(s(s(s(s(s(z))))) = s(z)), introduced(assumption)).
% 1.34/1.51 tff(494,plain,
% 1.34/1.51 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(z))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[493])).
% 1.34/1.51 tff(495,plain,
% 1.34/1.51 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(z)))))) = s(s(s(s(z)))))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(496,plain,
% 1.34/1.51 (inj_0(s(s(s(s(s(z)))))) = s(s(s(s(z))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[495, 59])).
% 1.34/1.51 tff(497,plain,
% 1.34/1.51 (s(s(s(s(z)))) = inj_0(s(s(s(s(s(z))))))),
% 1.34/1.51 inference(symmetry,[status(thm)],[496])).
% 1.34/1.51 tff(498,plain,
% 1.34/1.51 (s(s(s(s(z)))) = z),
% 1.34/1.51 inference(transitivity,[status(thm)],[497, 494, 61])).
% 1.34/1.51 tff(499,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[291, 498])).
% 1.34/1.51 tff(500,plain,(~(s(s(s(s(s(z))))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(501,plain,
% 1.34/1.51 (((~![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)))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(502,plain,
% 1.34/1.51 ((~![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)))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(503,plain,
% 1.34/1.51 ((~![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))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[502, 501])).
% 1.34/1.51 tff(504,plain,
% 1.34/1.51 (r(s(s(s(s(s(z))))), s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[503, 43, 500, 492])).
% 1.34/1.51 tff(505,plain,
% 1.34/1.51 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(506,plain,
% 1.34/1.51 (((~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(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(507,plain,
% 1.34/1.51 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[506])).
% 1.34/1.51 tff(508,plain,
% 1.34/1.51 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.34/1.51 inference(transitivity,[status(thm)],[507, 505])).
% 1.34/1.51 tff(509,plain,
% 1.34/1.51 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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))))))))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(510,plain,
% 1.34/1.51 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[509, 508])).
% 1.34/1.51 tff(511,plain,
% 1.34/1.51 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[510, 124, 206, 504])).
% 1.34/1.51 tff(512,plain,
% 1.34/1.51 (~r(elem!1, s(s(elem!1)))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[511, 484])).
% 1.34/1.51 tff(513,plain,
% 1.34/1.51 (((~![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))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(514,plain,
% 1.34/1.51 ((~![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))))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(515,plain,
% 1.34/1.51 ((~![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)))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[514, 513])).
% 1.34/1.51 tff(516,plain,
% 1.34/1.51 ((elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1)))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[515, 43])).
% 1.34/1.51 tff(517,plain,
% 1.34/1.51 (b(elem!1, s(s(elem!1)))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[516, 512, 360])).
% 1.34/1.51 tff(518,plain,
% 1.34/1.51 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[517, 482])).
% 1.34/1.51 tff(519,plain,
% 1.34/1.51 (b(z, s(s(s(s(s(s(z))))))) <=> b(z, s(s(s(elem!1))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[241])).
% 1.34/1.51 tff(520,plain,
% 1.34/1.51 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(s(s(s(s(z)))))))),
% 1.34/1.51 inference(symmetry,[status(thm)],[519])).
% 1.34/1.51 tff(521,assumption,(b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.34/1.51 tff(522,assumption,(b(s(s(s(s(s(z))))), z)), introduced(assumption)).
% 1.34/1.51 tff(523,assumption,(b(z, s(s(s(s(s(z))))))), introduced(assumption)).
% 1.34/1.51 tff(524,assumption,(b(s(s(s(z))), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.34/1.51 tff(525,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(526,plain,
% 1.34/1.51 (((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(527,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[526])).
% 1.34/1.51 tff(528,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.34/1.51 inference(transitivity,[status(thm)],[527, 525])).
% 1.34/1.51 tff(529,plain,
% 1.34/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(530,plain,
% 1.34/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[529, 528])).
% 1.34/1.51 tff(531,plain,
% 1.34/1.51 ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[530, 306, 524, 523, 522])).
% 1.34/1.51 tff(532,plain,
% 1.34/1.51 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[531, 521])).
% 1.34/1.51 tff(533,plain,
% 1.34/1.51 (r(s(s(s(z))), s(s(s(s(s(s(z))))))) <=> r(elem!1, s(s(s(elem!1))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[248, 241])).
% 1.34/1.51 tff(534,plain,
% 1.34/1.51 (r(elem!1, s(s(s(elem!1)))) <=> r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.34/1.51 inference(symmetry,[status(thm)],[533])).
% 1.34/1.51 tff(535,plain,
% 1.34/1.51 ((~r(elem!1, s(s(s(elem!1))))) <=> (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[534])).
% 1.34/1.51 tff(536,assumption,(~r(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 1.34/1.51 tff(537,plain,
% 1.34/1.51 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[536, 535])).
% 1.34/1.51 tff(538,assumption,(~b(s(s(s(z))), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.34/1.51 tff(539,plain,
% 1.34/1.51 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z))))))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(540,plain,
% 1.34/1.51 (inj_0(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[539, 59])).
% 1.34/1.51 tff(541,assumption,(s(s(s(z))) = s(s(s(s(s(s(z))))))), introduced(assumption)).
% 1.34/1.51 tff(542,plain,
% 1.34/1.51 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[541])).
% 1.34/1.51 tff(543,plain,
% 1.34/1.51 (s(s(z)) = s(s(s(s(s(z)))))),
% 1.34/1.51 inference(transitivity,[status(thm)],[103, 542, 540])).
% 1.34/1.51 tff(544,plain,
% 1.34/1.51 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(z))))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[543])).
% 1.34/1.51 tff(545,plain,
% 1.34/1.51 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(z))) = s(z))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(546,plain,
% 1.34/1.51 (inj_0(s(s(z))) = s(z)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[545, 59])).
% 1.34/1.51 tff(547,plain,
% 1.34/1.51 (s(z) = inj_0(s(s(z)))),
% 1.34/1.51 inference(symmetry,[status(thm)],[546])).
% 1.34/1.51 tff(548,plain,
% 1.34/1.51 (s(z) = s(s(s(s(z))))),
% 1.34/1.51 inference(transitivity,[status(thm)],[547, 544, 496])).
% 1.34/1.51 tff(549,plain,
% 1.34/1.51 (inj_0(s(z)) = inj_0(s(s(s(s(z)))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[548])).
% 1.34/1.51 tff(550,plain,
% 1.34/1.51 (inj_0(s(s(s(s(z))))) = inj_0(s(z))),
% 1.34/1.51 inference(symmetry,[status(thm)],[549])).
% 1.34/1.51 tff(551,plain,
% 1.34/1.51 (s(s(s(s(s(s(z)))))) = s(s(s(z)))),
% 1.34/1.51 inference(symmetry,[status(thm)],[541])).
% 1.34/1.51 tff(552,plain,
% 1.34/1.51 (s(s(s(s(s(s(z)))))) = z),
% 1.34/1.51 inference(transitivity,[status(thm)],[551, 321, 550, 61])).
% 1.34/1.51 tff(553,plain,
% 1.34/1.51 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(s(z)))))) = z))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(554,plain,
% 1.34/1.51 (~(s(s(s(s(s(s(z)))))) = z)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[553, 75])).
% 1.34/1.51 tff(555,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[554, 552])).
% 1.34/1.51 tff(556,plain,(~(s(s(s(z))) = s(s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(557,plain,
% 1.34/1.51 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(s(s(z))))))) | b(s(s(s(z))), s(s(s(s(s(s(z))))))) | r(s(s(s(z))), s(s(s(s(s(s(z))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(s(s(z))))))) | b(s(s(s(z))), s(s(s(s(s(s(z))))))) | r(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(558,plain,
% 1.34/1.51 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(s(s(z))))))) | b(s(s(s(z))), s(s(s(s(s(s(z))))))) | r(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(559,plain,
% 1.34/1.51 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(s(s(z))))))) | b(s(s(s(z))), s(s(s(s(s(s(z))))))) | r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[558, 557])).
% 1.34/1.51 tff(560,plain,
% 1.34/1.51 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[559, 43, 556, 538])).
% 1.34/1.51 tff(561,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[560, 537])).
% 1.34/1.51 tff(562,plain,(r(elem!1, s(s(s(elem!1)))) | (~(elem!1 = s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(563,plain,
% 1.34/1.51 (r(elem!1, s(s(s(elem!1))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[562, 532, 231])).
% 1.34/1.51 tff(564,assumption,(r(z, s(s(s(elem!1))))), introduced(assumption)).
% 1.34/1.51 tff(565,assumption,(r(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 1.34/1.51 tff(566,plain,
% 1.34/1.51 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(567,plain,
% 1.34/1.51 (((~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(568,plain,
% 1.34/1.51 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1)))))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[567])).
% 1.34/1.51 tff(569,plain,
% 1.34/1.51 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))))),
% 1.34/1.51 inference(transitivity,[status(thm)],[568, 566])).
% 1.34/1.51 tff(570,plain,
% 1.34/1.51 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(571,plain,
% 1.34/1.51 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1)))))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[570, 569])).
% 1.34/1.52 tff(572,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[571, 124, 374, 565, 564])).
% 1.34/1.52 tff(573,plain,((~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(574,plain,
% 1.34/1.52 (~r(z, s(s(s(elem!1))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[573, 563, 374])).
% 1.34/1.52 tff(575,plain,
% 1.34/1.52 ((z = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = z)),
% 1.34/1.52 inference(commutativity,[status(thm)],[])).
% 1.34/1.52 tff(576,plain,
% 1.34/1.52 ((s(s(s(elem!1))) = z) <=> (z = s(s(s(elem!1))))),
% 1.34/1.52 inference(symmetry,[status(thm)],[575])).
% 1.34/1.52 tff(577,plain,
% 1.34/1.52 ((~(s(s(s(elem!1))) = z)) <=> (~(z = s(s(s(elem!1)))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[576])).
% 1.34/1.52 tff(578,plain,
% 1.34/1.52 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(elem!1))) = z))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(579,plain,
% 1.34/1.52 (~(s(s(s(elem!1))) = z)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[578, 75])).
% 1.34/1.52 tff(580,plain,
% 1.34/1.52 (~(z = s(s(s(elem!1))))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[579, 577])).
% 1.34/1.52 tff(581,plain,
% 1.34/1.52 (((~![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)))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(582,plain,
% 1.34/1.52 ((~![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)))))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(583,plain,
% 1.34/1.52 ((~![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))))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[582, 581])).
% 1.34/1.52 tff(584,plain,
% 1.34/1.52 ((z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[583, 43])).
% 1.34/1.52 tff(585,plain,
% 1.34/1.52 (b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[584, 580])).
% 1.34/1.52 tff(586,plain,
% 1.34/1.52 (b(z, s(s(s(elem!1))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[585, 574])).
% 1.34/1.52 tff(587,plain,
% 1.34/1.52 (b(z, s(s(s(s(s(s(z)))))))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[586, 520])).
% 1.34/1.52 tff(588,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(589,plain,
% 1.34/1.52 (((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(590,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[589])).
% 1.34/1.52 tff(591,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.34/1.52 inference(transitivity,[status(thm)],[590, 588])).
% 1.34/1.52 tff(592,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(593,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[592, 591])).
% 1.34/1.52 tff(594,plain,
% 1.34/1.52 ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(z))))))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[593, 306, 523, 522])).
% 1.34/1.52 tff(595,plain,
% 1.34/1.52 (~b(z, s(s(s(s(s(s(z)))))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[594, 521])).
% 1.34/1.52 tff(596,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[595, 587])).
% 1.34/1.52 tff(597,plain,((~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~(elem!1 = s(s(s(z))))) | (~r(z, elem!1)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(598,plain,
% 1.34/1.52 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[597, 518, 374, 478, 462, 231])).
% 1.34/1.52 tff(599,plain,
% 1.34/1.52 (b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[241, 236])).
% 1.34/1.52 tff(600,plain,
% 1.34/1.52 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 1.34/1.52 inference(symmetry,[status(thm)],[599])).
% 1.34/1.52 tff(601,assumption,(b(s(s(s(elem!1))), s(s(elem!1)))), introduced(assumption)).
% 1.34/1.52 tff(602,plain,
% 1.34/1.52 (b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[601, 600])).
% 1.34/1.52 tff(603,assumption,(~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.34/1.52 tff(604,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[603, 602])).
% 1.34/1.52 tff(605,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))) | (~(elem!1 = s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(606,plain,
% 1.34/1.52 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[605, 598, 231])).
% 1.34/1.52 tff(607,plain,
% 1.34/1.52 (((~![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))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(608,plain,
% 1.34/1.52 ((~![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))))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(609,plain,
% 1.34/1.52 ((~![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)))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[608, 607])).
% 1.34/1.52 tff(610,plain,
% 1.34/1.52 ((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)))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[609, 43])).
% 1.34/1.52 tff(611,plain,
% 1.34/1.52 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[610, 606, 233])).
% 1.34/1.52 tff(612,plain,
% 1.34/1.52 (r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[611, 395])).
% 1.34/1.52 tff(613,plain,
% 1.34/1.52 ((s(z) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(z))),
% 1.34/1.52 inference(commutativity,[status(thm)],[])).
% 1.34/1.52 tff(614,plain,
% 1.34/1.52 ((s(s(s(s(s(z))))) = s(z)) <=> (s(z) = s(s(s(s(s(z))))))),
% 1.34/1.52 inference(symmetry,[status(thm)],[613])).
% 1.34/1.52 tff(615,plain,
% 1.34/1.52 ((~(s(s(s(s(s(z))))) = s(z))) <=> (~(s(z) = s(s(s(s(s(z)))))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[614])).
% 1.34/1.52 tff(616,plain,
% 1.34/1.52 (~(s(z) = s(s(s(s(s(z))))))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[500, 615])).
% 1.34/1.52 tff(617,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(618,plain,
% 1.34/1.52 (((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(619,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[618])).
% 1.34/1.52 tff(620,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.34/1.52 inference(transitivity,[status(thm)],[619, 617])).
% 1.34/1.52 tff(621,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(622,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[621, 620])).
% 1.34/1.52 tff(623,plain,
% 1.34/1.52 (~b(s(z), s(s(s(s(s(z))))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[622, 306, 247, 478, 485])).
% 1.34/1.52 tff(624,plain,
% 1.34/1.52 (((~![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)))))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(625,plain,
% 1.34/1.52 ((~![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)))))))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(626,plain,
% 1.34/1.52 ((~![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))))))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[625, 624])).
% 1.34/1.52 tff(627,plain,
% 1.34/1.52 ((s(z) = s(s(s(s(s(z)))))) | r(s(z), s(s(s(s(s(z))))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[626, 43, 623])).
% 1.34/1.52 tff(628,plain,
% 1.34/1.52 (r(s(z), s(s(s(s(s(z))))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[627, 616])).
% 1.34/1.52 tff(629,plain,
% 1.34/1.52 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(630,plain,
% 1.34/1.52 (((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(z)))) <=> ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(631,plain,
% 1.34/1.52 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[630])).
% 1.34/1.52 tff(632,plain,
% 1.34/1.52 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))),
% 1.34/1.52 inference(transitivity,[status(thm)],[631, 629])).
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% 1.34/1.52 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
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% 1.34/1.52 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[633, 632])).
% 1.34/1.52 tff(635,plain,
% 1.34/1.52 ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[634, 124, 628])).
% 1.34/1.52 tff(636,plain,
% 1.34/1.52 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[635, 612])).
% 1.34/1.52 tff(637,assumption,(s(s(s(s(s(s(z)))))) = s(z)), introduced(assumption)).
% 1.34/1.52 tff(638,plain,
% 1.34/1.52 (s(z) = s(s(s(s(s(s(z))))))),
% 1.34/1.52 inference(symmetry,[status(thm)],[637])).
% 1.34/1.52 tff(639,plain,
% 1.34/1.52 (s(z) = s(s(s(elem!1)))),
% 1.34/1.52 inference(transitivity,[status(thm)],[638, 241])).
% 1.34/1.52 tff(640,assumption,(s(z) = s(s(s(elem!1)))), introduced(assumption)).
% 1.34/1.52 tff(641,plain,
% 1.34/1.52 (inj_0(s(z)) = inj_0(s(s(s(elem!1))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[640])).
% 1.34/1.52 tff(642,plain,
% 1.34/1.52 (inj_0(s(s(s(elem!1)))) = inj_0(s(z))),
% 1.34/1.52 inference(symmetry,[status(thm)],[641])).
% 1.34/1.52 tff(643,plain,
% 1.34/1.52 (s(s(elem!1)) = z),
% 1.34/1.52 inference(transitivity,[status(thm)],[140, 642, 61])).
% 1.34/1.52 tff(644,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[454, 643])).
% 1.34/1.52 tff(645,plain,(~(s(z) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(646,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[645, 639])).
% 1.34/1.52 tff(647,plain,((~(s(s(s(s(s(s(z)))))) = s(z))) | (~(elem!1 = s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(648,plain,
% 1.34/1.52 (~(s(s(s(s(s(s(z)))))) = s(z))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[647, 231])).
% 1.34/1.52 tff(649,plain,
% 1.34/1.52 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(z)) | b(s(s(s(s(s(s(z)))))), s(z)) | r(s(s(s(s(s(s(z)))))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(z)) | b(s(s(s(s(s(s(z)))))), s(z)) | r(s(s(s(s(s(s(z)))))), s(z)))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(650,plain,
% 1.34/1.52 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(z)) | b(s(s(s(s(s(s(z)))))), s(z)) | r(s(s(s(s(s(s(z)))))), s(z)))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(651,plain,
% 1.34/1.52 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(z)) | b(s(s(s(s(s(s(z)))))), s(z)) | r(s(s(s(s(s(s(z)))))), s(z))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[650, 649])).
% 1.34/1.52 tff(652,plain,
% 1.34/1.52 (b(s(s(s(s(s(s(z)))))), s(z))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[651, 43, 648, 636])).
% 1.34/1.52 tff(653,assumption,(r(s(s(s(elem!1))), s(s(elem!1)))), introduced(assumption)).
% 1.34/1.52 tff(654,assumption,(r(s(s(s(elem!1))), s(elem!1))), introduced(assumption)).
% 1.34/1.52 tff(655,plain,
% 1.34/1.52 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(656,plain,
% 1.34/1.52 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(657,plain,
% 1.34/1.52 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[656, 655])).
% 1.34/1.52 tff(658,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[657, 124, 654, 244, 653])).
% 1.34/1.52 tff(659,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(660,plain,
% 1.34/1.52 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[659, 611, 244])).
% 1.34/1.52 tff(661,plain,
% 1.34/1.52 (((~![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)))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(662,plain,
% 1.34/1.52 ((~![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)))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(663,plain,
% 1.34/1.52 ((~![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))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[662, 661])).
% 1.34/1.52 tff(664,plain,
% 1.34/1.52 ((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))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[663, 43])).
% 1.34/1.52 tff(665,plain,
% 1.34/1.52 (b(s(s(s(elem!1))), s(elem!1))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[664, 660, 150])).
% 1.34/1.52 tff(666,plain,
% 1.34/1.52 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[665, 243])).
% 1.34/1.52 tff(667,plain,
% 1.34/1.52 ((s(z) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(z))),
% 1.34/1.52 inference(commutativity,[status(thm)],[])).
% 1.34/1.52 tff(668,plain,
% 1.34/1.52 ((s(s(s(s(z)))) = s(z)) <=> (s(z) = s(s(s(s(z)))))),
% 1.34/1.52 inference(symmetry,[status(thm)],[667])).
% 1.34/1.52 tff(669,plain,
% 1.34/1.52 ((~(s(s(s(s(z)))) = s(z))) <=> (~(s(z) = s(s(s(s(z))))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[668])).
% 1.34/1.52 tff(670,plain,
% 1.34/1.52 (~(s(z) = s(s(s(s(z)))))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[324, 669])).
% 1.34/1.52 tff(671,plain,
% 1.34/1.52 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(672,plain,
% 1.34/1.52 (((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(673,plain,
% 1.34/1.53 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z))))))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[672])).
% 1.34/1.53 tff(674,plain,
% 1.34/1.53 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.34/1.53 inference(transitivity,[status(thm)],[673, 671])).
% 1.34/1.53 tff(675,plain,
% 1.34/1.53 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(676,plain,
% 1.34/1.53 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z))))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[675, 674])).
% 1.34/1.53 tff(677,plain,
% 1.34/1.53 (~r(s(z), s(s(s(s(z)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[676, 124, 434, 628])).
% 1.34/1.53 tff(678,plain,
% 1.34/1.53 (((~![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))))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(679,plain,
% 1.34/1.53 ((~![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))))))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(680,plain,
% 1.34/1.53 ((~![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)))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[679, 678])).
% 1.34/1.53 tff(681,plain,
% 1.34/1.53 ((s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[680, 43, 677])).
% 1.34/1.53 tff(682,plain,
% 1.34/1.53 (b(s(z), s(s(s(s(z)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[681, 670])).
% 1.34/1.53 tff(683,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(684,plain,
% 1.34/1.53 (((~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(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(685,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[684])).
% 1.34/1.53 tff(686,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.34/1.53 inference(transitivity,[status(thm)],[685, 683])).
% 1.34/1.53 tff(687,plain,
% 1.34/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(688,plain,
% 1.34/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[687, 686])).
% 1.34/1.53 tff(689,plain,
% 1.34/1.53 ($false),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[688, 306, 393, 682, 422, 666, 652])).
% 1.34/1.53 tff(690,plain,((~r(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~(elem!1 = s(s(s(z))))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, elem!1)) | (elem!1 = s(s(elem!1))) | (s(s(elem!1)) = s(elem!1)) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(z))) | (s(s(s(s(z)))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.53 tff(691,plain,
% 1.34/1.53 (~r(s(s(s(s(z)))), z)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[690, 374, 231, 150, 244, 393, 360, 392, 206, 245, 247, 391, 252])).
% 1.34/1.53 tff(692,assumption,(~r(s(s(s(s(z)))), z)), introduced(assumption)).
% 1.34/1.53 tff(693,assumption,(~b(s(s(s(s(z)))), z)), introduced(assumption)).
% 1.34/1.53 tff(694,plain,
% 1.34/1.53 ($false),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[294, 43, 291, 693, 692])).
% 1.34/1.53 tff(695,plain,(r(s(s(s(s(z)))), z) | b(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 1.34/1.53 tff(696,plain,
% 1.34/1.53 (b(s(s(s(s(z)))), z)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[695, 691])).
% 1.34/1.53 tff(697,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(698,plain,
% 1.34/1.53 (((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(699,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[698])).
% 1.34/1.53 tff(700,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)))),
% 1.34/1.53 inference(transitivity,[status(thm)],[699, 697])).
% 1.34/1.53 tff(701,plain,
% 1.34/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(702,plain,
% 1.34/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[701, 700])).
% 1.34/1.53 tff(703,plain,
% 1.34/1.53 (~b(s(s(s(s(z)))), s(z))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[702, 306, 696, 247, 391])).
% 1.34/1.53 tff(704,plain,
% 1.34/1.53 (r(s(s(s(s(z)))), s(z))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[327, 43, 324, 703])).
% 1.34/1.53 tff(705,plain,
% 1.34/1.53 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(706,plain,
% 1.34/1.53 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(707,plain,
% 1.34/1.53 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[706, 705])).
% 1.34/1.53 tff(708,plain,
% 1.34/1.53 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[707, 124, 206, 704])).
% 1.34/1.53 tff(709,assumption,(~r(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 1.34/1.53 tff(710,assumption,(~b(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 1.34/1.53 tff(711,plain,
% 1.34/1.53 ($false),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[421, 43, 342, 710, 709])).
% 1.34/1.53 tff(712,plain,(r(s(s(s(s(z)))), s(s(s(z)))) | (s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.53 tff(713,plain,
% 1.34/1.53 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[712, 708, 252])).
% 1.34/1.53 tff(714,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(715,plain,
% 1.34/1.53 (((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(716,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[715])).
% 1.34/1.53 tff(717,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)))),
% 1.34/1.53 inference(transitivity,[status(thm)],[716, 714])).
% 1.34/1.53 tff(718,plain,
% 1.34/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(719,plain,
% 1.34/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[718, 717])).
% 1.34/1.53 tff(720,plain,
% 1.34/1.53 (~b(s(z), s(s(s(s(z)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[719, 306, 696, 247, 391])).
% 1.34/1.53 tff(721,plain,
% 1.34/1.53 ((s(z) = s(s(s(s(z))))) | r(s(z), s(s(s(s(z)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[680, 43, 720])).
% 1.34/1.53 tff(722,plain,
% 1.34/1.53 (r(s(z), s(s(s(s(z)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[721, 670])).
% 1.34/1.53 tff(723,plain,
% 1.34/1.53 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(elem!1))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[241, 239])).
% 1.34/1.53 tff(724,plain,
% 1.34/1.53 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.34/1.53 inference(symmetry,[status(thm)],[723])).
% 1.34/1.53 tff(725,plain,
% 1.34/1.53 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[654, 724])).
% 1.34/1.53 tff(726,assumption,(r(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 1.34/1.53 tff(727,plain,
% 1.34/1.53 (r(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> r(s(s(elem!1)), s(elem!1))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[236, 239])).
% 1.34/1.53 tff(728,plain,
% 1.34/1.53 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.34/1.53 inference(symmetry,[status(thm)],[727])).
% 1.34/1.53 tff(729,plain,
% 1.34/1.53 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[244, 728])).
% 1.34/1.53 tff(730,plain,
% 1.34/1.53 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(731,plain,
% 1.34/1.53 (((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z)))))))) <=> ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(732,plain,
% 1.34/1.53 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[731])).
% 1.34/1.53 tff(733,plain,
% 1.34/1.53 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.34/1.53 inference(transitivity,[status(thm)],[732, 730])).
% 1.34/1.53 tff(734,plain,
% 1.34/1.53 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(735,plain,
% 1.34/1.53 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[734, 733])).
% 1.34/1.53 tff(736,plain,
% 1.34/1.53 (~r(s(z), s(s(s(s(s(z))))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[735, 124, 729, 726])).
% 1.34/1.53 tff(737,plain,
% 1.34/1.53 ((s(z) = s(s(s(s(s(z)))))) | b(s(z), s(s(s(s(s(z))))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[626, 43, 736])).
% 1.34/1.53 tff(738,plain,
% 1.34/1.53 (b(s(z), s(s(s(s(s(z))))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[737, 616])).
% 1.34/1.53 tff(739,assumption,(~(s(s(s(elem!1))) = s(s(elem!1)))), introduced(assumption)).
% 1.34/1.53 tff(740,plain,
% 1.34/1.53 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[659, 654, 244])).
% 1.34/1.53 tff(741,plain,
% 1.34/1.53 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[610, 740, 739])).
% 1.34/1.53 tff(742,plain,
% 1.34/1.53 (b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[605, 741, 231])).
% 1.34/1.53 tff(743,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(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(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(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(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(744,plain,
% 1.34/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(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(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(745,plain,
% 1.34/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(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(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[744, 743])).
% 1.34/1.53 tff(746,plain,
% 1.34/1.53 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[745, 306, 393, 245, 742, 738])).
% 1.34/1.53 tff(747,plain,
% 1.34/1.53 (r(s(s(s(s(s(s(z)))))), s(z))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[651, 43, 648, 746])).
% 1.34/1.53 tff(748,plain,
% 1.34/1.53 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(749,plain,
% 1.34/1.53 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z)))) <=> ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(750,plain,
% 1.34/1.53 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z)))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[749])).
% 1.34/1.53 tff(751,plain,
% 1.34/1.53 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 1.34/1.54 inference(transitivity,[status(thm)],[750, 748])).
% 1.34/1.54 tff(752,plain,
% 1.34/1.54 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(753,plain,
% 1.34/1.54 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z)))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[752, 751])).
% 1.34/1.54 tff(754,plain,
% 1.34/1.54 ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z)))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[753, 124, 726])).
% 1.34/1.54 tff(755,plain,
% 1.34/1.54 ($false),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[754, 747, 725])).
% 1.34/1.54 tff(756,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(s(z)))))) | (~(elem!1 = s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.54 tff(757,plain,
% 1.34/1.54 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[756, 722, 231, 393, 245, 233, 244])).
% 1.34/1.54 tff(758,plain,
% 1.34/1.54 (b(s(s(s(elem!1))), s(elem!1))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[664, 757, 150])).
% 1.34/1.54 tff(759,assumption,(b(s(s(s(elem!1))), s(elem!1))), introduced(assumption)).
% 1.34/1.54 tff(760,plain,
% 1.34/1.54 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[759, 243])).
% 1.34/1.54 tff(761,assumption,(b(s(s(s(z))), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.34/1.54 tff(762,assumption,(b(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 1.34/1.54 tff(763,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(764,plain,
% 1.34/1.54 (((~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(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(765,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[764])).
% 1.34/1.54 tff(766,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.34/1.54 inference(transitivity,[status(thm)],[765, 763])).
% 1.34/1.54 tff(767,plain,
% 1.34/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(768,plain,
% 1.34/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[767, 766])).
% 1.34/1.54 tff(769,plain,
% 1.34/1.54 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[768, 306, 393, 762, 761])).
% 1.34/1.54 tff(770,plain,
% 1.34/1.54 ($false),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[769, 760])).
% 1.34/1.54 tff(771,plain,((~b(s(s(s(elem!1))), s(elem!1))) | (~(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(z))), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.54 tff(772,plain,
% 1.34/1.54 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[771, 758, 393, 231, 713])).
% 1.34/1.54 tff(773,plain,
% 1.34/1.54 (r(elem!1, s(s(s(elem!1))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[562, 772, 231])).
% 1.34/1.54 tff(774,plain,
% 1.34/1.54 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(775,plain,
% 1.34/1.54 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z)))) <=> ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(776,plain,
% 1.34/1.54 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[775])).
% 1.34/1.54 tff(777,plain,
% 1.34/1.54 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.34/1.54 inference(transitivity,[status(thm)],[776, 774])).
% 1.34/1.54 tff(778,plain,
% 1.34/1.54 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(779,plain,
% 1.34/1.54 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[778, 777])).
% 1.34/1.54 tff(780,plain,
% 1.34/1.54 (~r(s(s(s(s(s(z))))), s(z))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[779, 124, 729, 722])).
% 1.34/1.54 tff(781,plain,
% 1.34/1.54 (b(s(s(s(s(s(z))))), s(z))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[503, 43, 500, 780])).
% 1.34/1.54 tff(782,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(783,plain,
% 1.34/1.54 (((~b(z, s(z))) | (~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(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(784,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z)))))))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[783])).
% 1.34/1.54 tff(785,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.34/1.54 inference(transitivity,[status(thm)],[784, 782])).
% 1.34/1.54 tff(786,plain,
% 1.34/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~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))))))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(787,plain,
% 1.34/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z)))))))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[786, 785])).
% 1.34/1.54 tff(788,plain,
% 1.34/1.54 (~b(z, s(s(s(s(s(z))))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[787, 306, 247, 391, 781])).
% 1.34/1.54 tff(789,plain,
% 1.34/1.54 (~b(z, s(s(elem!1)))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[788, 238])).
% 1.34/1.54 tff(790,plain,
% 1.34/1.54 (r(z, s(s(elem!1)))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[460, 789])).
% 1.34/1.54 tff(791,assumption,(r(z, s(elem!1))), introduced(assumption)).
% 1.34/1.54 tff(792,plain,
% 1.34/1.54 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(793,plain,
% 1.34/1.54 (((~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(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(794,plain,
% 1.34/1.54 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1))))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[793])).
% 1.34/1.54 tff(795,plain,
% 1.34/1.54 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))))),
% 1.34/1.54 inference(transitivity,[status(thm)],[794, 792])).
% 1.34/1.54 tff(796,plain,
% 1.34/1.54 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1)))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(797,plain,
% 1.34/1.54 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1))))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[796, 795])).
% 1.34/1.54 tff(798,plain,
% 1.34/1.54 ($false),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[797, 124, 791, 244, 437])).
% 1.34/1.54 tff(799,plain,((~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.54 tff(800,plain,
% 1.34/1.54 (~r(z, s(elem!1))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[799, 790, 244])).
% 1.34/1.54 tff(801,plain,
% 1.34/1.54 (b(z, s(elem!1))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[275, 800])).
% 1.34/1.54 tff(802,assumption,(r(s(elem!1), elem!1)), introduced(assumption)).
% 1.34/1.54 tff(803,plain,
% 1.34/1.54 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[802, 406])).
% 1.34/1.54 tff(804,plain,
% 1.34/1.54 ($false),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[709, 803])).
% 1.34/1.54 tff(805,plain,(r(s(s(s(s(z)))), s(s(s(z)))) | (~r(s(elem!1), elem!1)) | (~(elem!1 = s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.54 tff(806,plain,
% 1.34/1.54 (~r(s(elem!1), elem!1)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[805, 708, 231])).
% 1.34/1.54 tff(807,assumption,(~b(s(elem!1), elem!1)), introduced(assumption)).
% 1.34/1.54 tff(808,assumption,(~r(s(elem!1), elem!1)), introduced(assumption)).
% 1.34/1.54 tff(809,plain,
% 1.34/1.54 (((~![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))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(810,plain,
% 1.34/1.54 ((~![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))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(811,plain,
% 1.34/1.54 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = elem!1) | b(s(elem!1), elem!1) | r(s(elem!1), elem!1)),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[810, 809])).
% 1.34/1.54 tff(812,plain,
% 1.34/1.54 ($false),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[811, 43, 808, 807, 193])).
% 1.34/1.54 tff(813,plain,(b(s(elem!1), elem!1) | r(s(elem!1), elem!1) | (s(elem!1) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.34/1.54 tff(814,plain,
% 1.34/1.54 (b(s(elem!1), elem!1)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[813, 806, 193])).
% 1.34/1.54 tff(815,assumption,(b(elem!1, s(elem!1))), introduced(assumption)).
% 1.34/1.54 tff(816,assumption,(b(s(elem!1), elem!1)), introduced(assumption)).
% 1.34/1.54 tff(817,assumption,(b(z, s(elem!1))), introduced(assumption)).
% 1.34/1.54 tff(818,assumption,(b(z, s(s(s(elem!1))))), introduced(assumption)).
% 1.34/1.54 tff(819,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(820,plain,
% 1.34/1.54 (((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(821,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1)))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[820])).
% 1.34/1.54 tff(822,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))),
% 1.34/1.54 inference(transitivity,[status(thm)],[821, 819])).
% 1.34/1.54 tff(823,plain,
% 1.34/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1))))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(824,plain,
% 1.34/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1)))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[823, 822])).
% 1.34/1.54 tff(825,plain,
% 1.34/1.54 ($false),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[824, 306, 759, 818, 817, 816, 815])).
% 1.34/1.54 tff(826,plain,((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.54 tff(827,plain,
% 1.34/1.54 (~b(z, s(s(s(elem!1))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[826, 758, 815, 814, 801])).
% 1.34/1.54 tff(828,plain,
% 1.34/1.54 (r(z, s(s(s(elem!1))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[585, 827])).
% 1.34/1.54 tff(829,plain,
% 1.34/1.54 ($false),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[573, 828, 773, 374])).
% 1.34/1.54 tff(830,plain,((~r(z, elem!1)) | (~(elem!1 = s(s(s(z))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(elem!1))) | (~b(s(z), z)) | (s(elem!1) = elem!1) | (~r(s(s(s(z))), s(z))) | (elem!1 = s(s(elem!1))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.54 tff(831,plain,
% 1.34/1.54 (~r(z, elem!1)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[830, 244, 373, 354, 150, 245, 231, 247, 193, 206, 360, 359])).
% 1.34/1.54 tff(832,plain,
% 1.34/1.54 (((~![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))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(833,plain,
% 1.34/1.54 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = elem!1) | b(z, elem!1) | r(z, elem!1))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(834,plain,
% 1.34/1.54 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = elem!1) | b(z, elem!1) | r(z, elem!1)),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[833, 832])).
% 1.34/1.54 tff(835,plain,
% 1.34/1.54 ((z = elem!1) | b(z, elem!1) | r(z, elem!1)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[834, 43])).
% 1.34/1.54 tff(836,plain,
% 1.34/1.54 (b(z, elem!1)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[835, 831, 358])).
% 1.34/1.54 tff(837,plain,
% 1.34/1.54 (b(z, elem!1) <=> b(z, s(s(s(z))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[231])).
% 1.34/1.54 tff(838,assumption,(b(z, elem!1)), introduced(assumption)).
% 1.34/1.54 tff(839,plain,
% 1.34/1.54 (b(z, s(s(s(z))))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[838, 837])).
% 1.34/1.54 tff(840,assumption,(~b(z, s(s(s(z))))), introduced(assumption)).
% 1.34/1.54 tff(841,plain,
% 1.34/1.54 ($false),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[840, 839])).
% 1.34/1.54 tff(842,plain,((~b(z, elem!1)) | b(z, s(s(s(z)))) | (~(elem!1 = s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.54 tff(843,plain,
% 1.34/1.54 (b(z, s(s(s(z))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[842, 836, 231])).
% 1.34/1.54 tff(844,plain,
% 1.34/1.54 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[565, 534])).
% 1.34/1.54 tff(845,plain,
% 1.34/1.54 (r(s(s(s(s(s(s(z)))))), z) <=> r(s(s(s(elem!1))), z)),
% 1.34/1.54 inference(monotonicity,[status(thm)],[241])).
% 1.34/1.54 tff(846,plain,
% 1.34/1.54 (r(s(s(s(elem!1))), z) <=> r(s(s(s(s(s(s(z)))))), z)),
% 1.34/1.54 inference(symmetry,[status(thm)],[845])).
% 1.34/1.54 tff(847,plain,
% 1.34/1.54 ((~r(s(s(s(elem!1))), z)) <=> (~r(s(s(s(s(s(s(z)))))), z))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[846])).
% 1.34/1.54 tff(848,plain,
% 1.34/1.54 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(849,plain,
% 1.34/1.54 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(850,plain,
% 1.34/1.54 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1)))))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[849, 848])).
% 1.34/1.54 tff(851,plain,
% 1.34/1.54 ((~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1)))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[850, 124])).
% 1.34/1.54 tff(852,plain,
% 1.34/1.54 (~r(s(s(s(elem!1))), z)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[851, 565, 246])).
% 1.34/1.54 tff(853,plain,
% 1.34/1.54 (~r(s(s(s(s(s(s(z)))))), z)),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[852, 847])).
% 1.34/1.54 tff(854,plain,
% 1.34/1.54 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = z) | b(s(s(s(s(s(s(z)))))), z) | r(s(s(s(s(s(s(z)))))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = z) | b(s(s(s(s(s(s(z)))))), z) | r(s(s(s(s(s(s(z)))))), z))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(855,plain,
% 1.34/1.54 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = z) | b(s(s(s(s(s(s(z)))))), z) | r(s(s(s(s(s(s(z)))))), z))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(856,plain,
% 1.34/1.54 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = z) | b(s(s(s(s(s(s(z)))))), z) | r(s(s(s(s(s(s(z)))))), z)),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[855, 854])).
% 1.34/1.54 tff(857,plain,
% 1.34/1.54 (b(s(s(s(s(s(s(z)))))), z) | r(s(s(s(s(s(s(z)))))), z)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[856, 43, 554])).
% 1.34/1.54 tff(858,plain,
% 1.34/1.54 (b(s(s(s(s(s(s(z)))))), z)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[857, 853])).
% 1.34/1.54 tff(859,assumption,(b(z, s(s(s(z))))), introduced(assumption)).
% 1.34/1.54 tff(860,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(861,plain,
% 1.34/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(862,plain,
% 1.34/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[861, 860])).
% 1.34/1.54 tff(863,plain,
% 1.34/1.54 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[862, 306, 393, 859, 247, 858])).
% 1.34/1.54 tff(864,plain,
% 1.34/1.54 (r(s(s(s(s(s(s(z)))))), s(z))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[651, 43, 648, 863])).
% 1.34/1.54 tff(865,plain,
% 1.34/1.54 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(866,plain,
% 1.34/1.55 (((~r(s(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(s(z))))))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(867,plain,
% 1.34/1.55 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(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(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[866])).
% 1.34/1.55 tff(868,plain,
% 1.34/1.55 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(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(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.34/1.55 inference(transitivity,[status(thm)],[867, 865])).
% 1.34/1.55 tff(869,plain,
% 1.34/1.55 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(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(s(z)))))))))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(870,plain,
% 1.34/1.55 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[869, 868])).
% 1.34/1.55 tff(871,plain,
% 1.34/1.55 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[870, 124, 206, 864])).
% 1.34/1.55 tff(872,plain,
% 1.34/1.55 ($false),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[871, 844])).
% 1.34/1.55 tff(873,plain,((~r(elem!1, s(s(s(elem!1))))) | (~(elem!1 = s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.55 tff(874,plain,
% 1.34/1.55 (~r(elem!1, s(s(s(elem!1))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[873, 843, 206, 354, 231, 247, 246])).
% 1.34/1.55 tff(875,plain,
% 1.34/1.55 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[562, 874, 231])).
% 1.34/1.55 tff(876,plain,
% 1.34/1.55 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[236, 241])).
% 1.34/1.55 tff(877,plain,
% 1.34/1.55 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 1.34/1.55 inference(symmetry,[status(thm)],[876])).
% 1.34/1.55 tff(878,assumption,(r(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 1.34/1.55 tff(879,plain,
% 1.34/1.55 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(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))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(880,plain,
% 1.34/1.55 (((~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))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(881,plain,
% 1.34/1.55 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1)))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[880])).
% 1.34/1.55 tff(882,plain,
% 1.34/1.55 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.34/1.55 inference(transitivity,[status(thm)],[881, 879])).
% 1.34/1.55 tff(883,plain,
% 1.34/1.55 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(884,plain,
% 1.34/1.55 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1)))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[883, 882])).
% 1.34/1.55 tff(885,plain,
% 1.34/1.55 ($false),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[884, 124, 654, 244, 878])).
% 1.34/1.55 tff(886,plain,((~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)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.55 tff(887,plain,
% 1.34/1.55 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[886, 654, 244])).
% 1.34/1.55 tff(888,plain,
% 1.34/1.55 (((~![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)))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(889,plain,
% 1.34/1.55 ((~![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)))))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(890,plain,
% 1.34/1.55 ((~![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))))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[889, 888])).
% 1.34/1.55 tff(891,plain,
% 1.34/1.55 ((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))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[890, 43])).
% 1.34/1.55 tff(892,plain,
% 1.34/1.55 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[891, 887, 157])).
% 1.34/1.55 tff(893,plain,
% 1.34/1.55 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[892, 877])).
% 1.34/1.55 tff(894,plain,
% 1.34/1.55 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[159, 157])).
% 1.34/1.55 tff(895,plain,
% 1.34/1.55 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[610, 740, 894])).
% 1.34/1.55 tff(896,plain,
% 1.34/1.55 (b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[605, 895, 231])).
% 1.34/1.55 tff(897,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(898,plain,
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% 1.34/1.55 inference(rewrite,[status(thm)],[])).
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% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[898])).
% 1.34/1.55 tff(900,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.34/1.55 inference(transitivity,[status(thm)],[899, 897])).
% 1.34/1.55 tff(901,plain,
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% 1.34/1.55 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[902, 306, 761, 245, 896])).
% 1.34/1.55 tff(904,plain,
% 1.34/1.55 ($false),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[903, 893])).
% 1.34/1.55 tff(905,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~(elem!1 = s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.55 tff(906,plain,
% 1.34/1.55 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[905, 875, 231, 245, 232, 244])).
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% 1.34/1.55 (b(s(s(s(elem!1))), s(elem!1))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[664, 906, 150])).
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% 1.34/1.55 inference(modus_ponens,[status(thm)],[907, 243])).
% 1.34/1.55 tff(909,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(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(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(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(s(z)))))))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
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% 1.34/1.55 (((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(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(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(s(z)))))))))),
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% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(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(s(z))))))))))),
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% 1.34/1.55 tff(920,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
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% 1.34/1.55 (((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(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(s(s(z))))), z))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
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% 1.34/1.55 tff(922,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(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(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))))),
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% 1.34/1.55 inference(modus_ponens,[status(thm)],[653, 395])).
% 1.34/1.55 tff(934,plain,
% 1.34/1.55 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(935,plain,
% 1.34/1.55 (((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), z))) <=> ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(936,plain,
% 1.34/1.55 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[935])).
% 1.34/1.55 tff(937,plain,
% 1.34/1.55 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[936, 934])).
% 1.34/1.56 tff(938,plain,
% 1.34/1.56 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), z)))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(939,plain,
% 1.34/1.56 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[938, 937])).
% 1.34/1.56 tff(940,plain,
% 1.34/1.56 ((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[939, 124, 438])).
% 1.34/1.56 tff(941,plain,
% 1.34/1.56 (~r(s(s(s(s(s(s(z)))))), z)),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[940, 933])).
% 1.34/1.56 tff(942,assumption,(b(s(s(s(s(z)))), z)), introduced(assumption)).
% 1.34/1.56 tff(943,plain,
% 1.34/1.56 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(944,plain,
% 1.34/1.56 (((~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(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(945,plain,
% 1.34/1.56 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1))))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[944])).
% 1.34/1.56 tff(946,plain,
% 1.34/1.56 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[945, 943])).
% 1.34/1.56 tff(947,plain,
% 1.34/1.56 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(948,plain,
% 1.34/1.56 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[947, 946])).
% 1.34/1.56 tff(949,plain,
% 1.34/1.56 ($false),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[948, 124, 437, 564, 653])).
% 1.34/1.56 tff(950,plain,((~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.56 tff(951,plain,
% 1.34/1.56 (~r(z, s(s(s(elem!1))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[950, 653, 437])).
% 1.34/1.56 tff(952,plain,
% 1.34/1.56 (b(z, s(s(s(elem!1))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[585, 951])).
% 1.34/1.56 tff(953,plain,
% 1.34/1.56 (b(z, s(s(s(s(s(s(z)))))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[818, 520])).
% 1.34/1.56 tff(954,assumption,(b(s(s(s(s(s(s(z)))))), z)), introduced(assumption)).
% 1.34/1.56 tff(955,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(956,plain,
% 1.34/1.56 (((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(957,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[956])).
% 1.34/1.56 tff(958,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[957, 955])).
% 1.34/1.56 tff(959,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(960,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[959, 958])).
% 1.34/1.56 tff(961,plain,
% 1.34/1.56 ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[960, 306, 942, 954])).
% 1.34/1.56 tff(962,plain,
% 1.34/1.56 ($false),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[961, 953, 760])).
% 1.34/1.56 tff(963,plain,((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(elem!1))))) | (~(elem!1 = s(s(s(z))))) | (~b(s(s(s(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.56 tff(964,plain,
% 1.34/1.56 (~b(s(s(s(s(s(s(z)))))), z)),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[963, 952, 942, 231, 759])).
% 1.34/1.56 tff(965,plain,
% 1.34/1.56 ($false),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[856, 43, 554, 964, 941])).
% 1.34/1.56 tff(966,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~(elem!1 = s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.56 tff(967,plain,
% 1.34/1.56 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[966, 932, 231, 907, 918])).
% 1.34/1.56 tff(968,plain,
% 1.34/1.56 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[610, 967, 233])).
% 1.34/1.56 tff(969,plain,
% 1.34/1.56 (b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[605, 968, 231])).
% 1.34/1.56 tff(970,assumption,(r(elem!1, s(s(elem!1)))), introduced(assumption)).
% 1.34/1.56 tff(971,plain,
% 1.34/1.56 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(972,plain,
% 1.34/1.56 (((~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z))) <=> ((~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(973,plain,
% 1.34/1.56 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1))))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[972])).
% 1.34/1.56 tff(974,plain,
% 1.34/1.56 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[973, 971])).
% 1.34/1.56 tff(975,plain,
% 1.34/1.56 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(976,plain,
% 1.34/1.56 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[975, 974])).
% 1.34/1.56 tff(977,plain,
% 1.34/1.56 ($false),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[976, 124, 246, 437, 970])).
% 1.34/1.56 tff(978,plain,((~r(z, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.56 tff(979,plain,
% 1.34/1.56 (~r(elem!1, s(s(elem!1)))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[978, 918, 246])).
% 1.34/1.56 tff(980,plain,
% 1.34/1.56 (b(elem!1, s(s(elem!1)))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[516, 979, 360])).
% 1.34/1.56 tff(981,plain,
% 1.34/1.56 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[980, 482])).
% 1.34/1.56 tff(982,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), 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(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), 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(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(983,plain,
% 1.34/1.56 (((~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(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(984,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), 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(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[983])).
% 1.34/1.56 tff(985,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), 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(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[984, 982])).
% 1.34/1.56 tff(986,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(987,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[986, 985])).
% 1.34/1.56 tff(988,plain,
% 1.34/1.56 ($false),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[987, 306, 354, 875, 981, 245, 969])).
% 1.34/1.56 tff(989,plain,((~r(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~(elem!1 = s(s(s(z))))) | (elem!1 = s(s(elem!1))) | (~r(elem!1, z)) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(s(s(z))), s(z))) | (~b(s(z), z)) | (s(elem!1) = elem!1) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.56 tff(990,plain,
% 1.34/1.56 (~r(s(s(elem!1)), s(elem!1))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[989, 230, 133, 187, 175, 144, 114, 222, 181, 98])).
% 1.34/1.56 tff(991,plain,
% 1.34/1.56 (((~![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)))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(992,plain,
% 1.34/1.56 ((~![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)))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(993,plain,
% 1.34/1.56 ((~![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))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[992, 991])).
% 1.34/1.56 tff(994,plain,
% 1.34/1.56 ((s(s(elem!1)) = s(elem!1)) | b(s(s(elem!1)), s(elem!1)) | r(s(s(elem!1)), s(elem!1))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[993, 43])).
% 1.34/1.56 tff(995,plain,
% 1.34/1.56 (b(s(s(elem!1)), s(elem!1))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[994, 990, 196])).
% 1.34/1.56 tff(996,plain,
% 1.34/1.56 (s(s(s(s(z)))) = s(elem!1)),
% 1.34/1.56 inference(symmetry,[status(thm)],[223])).
% 1.34/1.56 tff(997,plain,
% 1.34/1.56 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(elem!1) = elem!1)),
% 1.34/1.56 inference(monotonicity,[status(thm)],[996, 163])).
% 1.34/1.56 tff(998,plain,
% 1.34/1.56 ((s(elem!1) = elem!1) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 1.34/1.56 inference(symmetry,[status(thm)],[997])).
% 1.34/1.56 tff(999,plain,
% 1.34/1.56 ((~(s(elem!1) = elem!1)) <=> (~(s(s(s(s(z)))) = s(s(s(z)))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[998])).
% 1.34/1.56 tff(1000,plain,
% 1.34/1.56 (~(s(s(s(s(z)))) = s(s(s(z))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[181, 999])).
% 1.34/1.56 tff(1001,plain,
% 1.34/1.56 (~r(elem!1, s(elem!1))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[337, 133, 114, 222, 175])).
% 1.34/1.56 tff(1002,plain,
% 1.34/1.56 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[353, 1001, 133, 1000])).
% 1.34/1.56 tff(1003,assumption,(b(elem!1, s(s(elem!1)))), introduced(assumption)).
% 1.34/1.56 tff(1004,plain,
% 1.34/1.56 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[1003, 482])).
% 1.34/1.56 tff(1005,assumption,(b(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 1.34/1.56 tff(1006,plain,
% 1.34/1.56 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[235, 234])).
% 1.34/1.56 tff(1007,plain,
% 1.34/1.56 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[1005, 1006])).
% 1.34/1.56 tff(1008,assumption,(~b(s(s(s(s(s(z))))), s(s(s(s(z)))))), introduced(assumption)).
% 1.34/1.56 tff(1009,plain,
% 1.34/1.56 ($false),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1008, 1007])).
% 1.34/1.56 tff(1010,plain,((~b(s(s(elem!1)), s(elem!1))) | b(s(s(s(s(s(z))))), s(s(s(s(z))))) | (~(elem!1 = s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.56 tff(1011,plain,
% 1.34/1.56 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1010, 1005, 231])).
% 1.34/1.56 tff(1012,plain,
% 1.34/1.56 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[236])).
% 1.34/1.56 tff(1013,plain,
% 1.34/1.56 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.34/1.56 inference(symmetry,[status(thm)],[1012])).
% 1.34/1.56 tff(1014,plain,
% 1.34/1.56 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(s(s(z))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[231])).
% 1.34/1.56 tff(1015,plain,
% 1.34/1.56 (b(s(s(elem!1)), s(s(s(z))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[30, 1014])).
% 1.34/1.56 tff(1016,plain,
% 1.34/1.56 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[1015, 1013])).
% 1.34/1.56 tff(1017,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(1018,plain,
% 1.34/1.56 (((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(1019,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[1018])).
% 1.34/1.56 tff(1020,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[1019, 1017])).
% 1.34/1.56 tff(1021,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(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))))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(1022,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[1021, 1020])).
% 1.34/1.56 tff(1023,plain,
% 1.34/1.56 ($false),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1022, 306, 30, 1005, 1003, 816])).
% 1.34/1.56 tff(1024,plain,((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.56 tff(1025,plain,
% 1.34/1.56 (~b(s(elem!1), elem!1)),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1024, 1003, 30, 1005])).
% 1.34/1.56 tff(1026,plain,
% 1.34/1.56 (r(s(elem!1), elem!1)),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[813, 1025, 193])).
% 1.34/1.56 tff(1027,assumption,(b(s(s(s(s(s(z))))), s(s(s(s(z)))))), introduced(assumption)).
% 1.34/1.56 tff(1028,plain,
% 1.34/1.56 ((s(z) = s(s(s(z)))) <=> (s(s(s(z))) = s(z))),
% 1.34/1.56 inference(commutativity,[status(thm)],[])).
% 1.34/1.56 tff(1029,plain,
% 1.34/1.56 ((s(s(s(z))) = s(z)) <=> (s(z) = s(s(s(z))))),
% 1.34/1.56 inference(symmetry,[status(thm)],[1028])).
% 1.34/1.56 tff(1030,plain,
% 1.34/1.56 ((~(s(s(s(z))) = s(z))) <=> (~(s(z) = s(s(s(z)))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[1029])).
% 1.34/1.56 tff(1031,plain,
% 1.34/1.56 (~(s(z) = s(s(s(z))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[108, 1030])).
% 1.34/1.56 tff(1032,plain,
% 1.34/1.56 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[805, 802, 231])).
% 1.34/1.56 tff(1033,assumption,(r(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 1.34/1.56 tff(1034,assumption,(r(s(z), s(s(s(z))))), introduced(assumption)).
% 1.34/1.56 tff(1035,plain,
% 1.34/1.56 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(1036,plain,
% 1.34/1.56 (((~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(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(1037,plain,
% 1.34/1.56 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z)))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[1036])).
% 1.34/1.56 tff(1038,plain,
% 1.34/1.56 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[1037, 1035])).
% 1.34/1.56 tff(1039,plain,
% 1.34/1.56 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(1040,plain,
% 1.34/1.56 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z)))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[1039, 1038])).
% 1.34/1.56 tff(1041,plain,
% 1.34/1.56 (~r(s(s(s(s(z)))), s(z))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1040, 124, 1034, 1033])).
% 1.34/1.56 tff(1042,plain,
% 1.34/1.56 (b(s(s(s(s(z)))), s(z))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[327, 43, 324, 1041])).
% 1.34/1.56 tff(1043,plain,
% 1.34/1.56 (r(s(z), elem!1) <=> r(s(z), s(s(s(z))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[231])).
% 1.34/1.56 tff(1044,plain,
% 1.34/1.56 (r(s(z), s(s(s(z)))) <=> r(s(z), elem!1)),
% 1.34/1.56 inference(symmetry,[status(thm)],[1043])).
% 1.34/1.56 tff(1045,plain,
% 1.34/1.56 (r(s(z), elem!1)),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[1034, 1044])).
% 1.34/1.56 tff(1046,plain,
% 1.34/1.56 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1)))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(1047,plain,
% 1.34/1.56 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1)))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(1048,plain,
% 1.34/1.57 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[1047, 1046])).
% 1.34/1.57 tff(1049,plain,
% 1.34/1.57 ((~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1048, 124])).
% 1.34/1.57 tff(1050,plain,
% 1.34/1.57 (~r(s(z), z)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1049, 1045, 246])).
% 1.34/1.57 tff(1051,plain,
% 1.34/1.57 (b(s(z), z)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[219, 43, 216, 1050])).
% 1.34/1.57 tff(1052,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(1053,plain,
% 1.34/1.57 (((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), 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(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(1054,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[1053])).
% 1.34/1.57 tff(1055,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.34/1.57 inference(transitivity,[status(thm)],[1054, 1052])).
% 1.34/1.57 tff(1056,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(1057,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[1056, 1055])).
% 1.34/1.57 tff(1058,plain,
% 1.34/1.57 ($false),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1057, 306, 393, 1051, 1027, 245, 1042])).
% 1.34/1.57 tff(1059,plain,((~r(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~(elem!1 = s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.57 tff(1060,plain,
% 1.34/1.57 (~r(s(z), s(s(s(z))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1059, 393, 1027, 245, 246, 1032, 231])).
% 1.34/1.57 tff(1061,plain,
% 1.34/1.57 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z)))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(1062,plain,
% 1.34/1.57 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z)))))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(1063,plain,
% 1.34/1.57 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[1062, 1061])).
% 1.34/1.57 tff(1064,plain,
% 1.34/1.57 ((s(z) = s(s(s(z)))) | b(s(z), s(s(s(z))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1063, 43, 1060])).
% 1.34/1.57 tff(1065,plain,
% 1.34/1.57 (b(s(z), s(s(s(z))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1064, 1031])).
% 1.34/1.57 tff(1066,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(1067,plain,
% 1.34/1.57 (((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(1068,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[1067])).
% 1.34/1.57 tff(1069,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.34/1.57 inference(transitivity,[status(thm)],[1068, 1066])).
% 1.34/1.57 tff(1070,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(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))))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(1071,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[1070, 1069])).
% 1.34/1.57 tff(1072,plain,
% 1.34/1.57 (~b(s(s(s(s(s(z))))), s(z))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1071, 306, 1065, 1027, 524, 245])).
% 1.34/1.57 tff(1073,plain,
% 1.34/1.57 (r(s(s(s(s(s(z))))), s(z))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[503, 43, 500, 1072])).
% 1.34/1.57 tff(1074,plain,
% 1.34/1.57 (r(s(s(s(s(s(z))))), z) <=> r(s(s(elem!1)), z)),
% 1.34/1.57 inference(monotonicity,[status(thm)],[236])).
% 1.34/1.57 tff(1075,plain,
% 1.34/1.57 (r(s(s(elem!1)), z) <=> r(s(s(s(s(s(z))))), z)),
% 1.34/1.57 inference(symmetry,[status(thm)],[1074])).
% 1.34/1.57 tff(1076,plain,
% 1.34/1.57 (~r(s(elem!1), z)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[416, 374, 802])).
% 1.34/1.57 tff(1077,plain,
% 1.34/1.57 (~r(s(s(s(s(z)))), z)),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[1076, 280])).
% 1.34/1.57 tff(1078,plain,
% 1.34/1.57 (b(s(s(s(s(z)))), z)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[295, 1077])).
% 1.34/1.57 tff(1079,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, 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(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, 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(s(z))))), s(s(s(s(z)))))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(1080,plain,
% 1.34/1.57 (((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), 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(z, 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(s(z))))), s(s(s(s(z)))))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(1081,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, 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(s(z))))), s(s(s(s(z))))))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[1080])).
% 1.34/1.57 tff(1082,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, 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(s(z))))), s(s(s(s(z)))))))),
% 1.34/1.57 inference(transitivity,[status(thm)],[1081, 1079])).
% 1.34/1.57 tff(1083,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(1084,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[1083, 1082])).
% 1.34/1.57 tff(1085,plain,
% 1.34/1.57 ($false),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1084, 306, 393, 1078, 1027, 245, 391])).
% 1.34/1.57 tff(1086,plain,((~r(z, elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~(elem!1 = s(s(s(z))))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.57 tff(1087,plain,
% 1.34/1.57 (~r(z, elem!1)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1086, 393, 1027, 245, 231, 802, 359])).
% 1.34/1.57 tff(1088,plain,
% 1.34/1.57 (b(z, elem!1)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[835, 1087, 358])).
% 1.34/1.57 tff(1089,plain,
% 1.34/1.57 (b(z, s(s(s(z))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[1088, 837])).
% 1.34/1.57 tff(1090,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(1091,plain,
% 1.34/1.57 (((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(1092,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(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(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[1091])).
% 1.34/1.57 tff(1093,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(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(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.34/1.57 inference(transitivity,[status(thm)],[1092, 1090])).
% 1.34/1.57 tff(1094,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(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(s(s(z))))), z)))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(1095,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[1094, 1093])).
% 1.34/1.57 tff(1096,plain,
% 1.34/1.57 (~b(s(s(s(s(s(z))))), z)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1095, 306, 1089, 1027, 524, 245])).
% 1.34/1.57 tff(1097,plain,
% 1.34/1.57 (~b(s(s(elem!1)), z)),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[1096, 919])).
% 1.34/1.57 tff(1098,plain,
% 1.34/1.57 (r(s(s(elem!1)), z)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[476, 1097])).
% 1.34/1.57 tff(1099,plain,
% 1.34/1.57 (r(s(s(s(s(s(z))))), z)),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[1098, 1075])).
% 1.34/1.57 tff(1100,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(1101,plain,
% 1.34/1.58 (((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z))) <=> ((~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(1102,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[1101])).
% 1.34/1.58 tff(1103,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.34/1.58 inference(transitivity,[status(thm)],[1102, 1100])).
% 1.34/1.58 tff(1104,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(1105,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[1104, 1103])).
% 1.34/1.58 tff(1106,plain,
% 1.34/1.58 (~b(s(z), z)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1105, 306, 1065, 1089, 1027, 524])).
% 1.34/1.58 tff(1107,plain,
% 1.34/1.58 (r(s(z), z)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[219, 43, 216, 1106])).
% 1.34/1.58 tff(1108,plain,
% 1.34/1.58 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(1109,plain,
% 1.34/1.58 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(1110,plain,
% 1.34/1.58 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z)))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[1109, 1108])).
% 1.34/1.58 tff(1111,plain,
% 1.34/1.58 ($false),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1110, 124, 1107, 1099, 1073])).
% 1.34/1.58 tff(1112,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(elem!1, z)) | (~(elem!1 = s(s(s(z))))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.58 tff(1113,plain,
% 1.34/1.58 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1112, 1026, 393, 1016, 246, 231, 1011, 359])).
% 1.34/1.58 tff(1114,plain,
% 1.34/1.58 ($false),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1113, 1004])).
% 1.34/1.58 tff(1115,plain,((~b(elem!1, s(s(elem!1)))) | (~(elem!1 = s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, z)) | (~r(elem!1, s(z))) | (s(elem!1) = elem!1) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.58 tff(1116,plain,
% 1.34/1.58 (~b(elem!1, s(s(elem!1)))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1115, 133, 1002, 175, 98, 181, 92, 995])).
% 1.34/1.58 tff(1117,plain,
% 1.34/1.58 (r(elem!1, s(s(elem!1)))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[516, 1116, 187])).
% 1.34/1.58 tff(1118,plain,
% 1.34/1.58 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(elem!1))),
% 1.34/1.58 inference(symmetry,[status(thm)],[1006])).
% 1.34/1.58 tff(1119,plain,
% 1.34/1.58 ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) <=> (~b(s(s(elem!1)), s(elem!1)))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[1118])).
% 1.34/1.58 tff(1120,plain,
% 1.34/1.58 (b(s(s(s(s(s(s(z)))))), s(s(s(z)))) <=> b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.34/1.58 inference(monotonicity,[status(thm)],[248])).
% 1.34/1.58 tff(1121,plain,
% 1.34/1.58 (b(s(s(s(s(s(s(z)))))), elem!1) <=> b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.34/1.58 inference(symmetry,[status(thm)],[1120])).
% 1.34/1.58 tff(1122,plain,
% 1.34/1.58 ((s(s(s(s(s(s(z)))))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(s(s(z)))))))),
% 1.34/1.58 inference(commutativity,[status(thm)],[])).
% 1.34/1.58 tff(1123,plain,
% 1.34/1.58 ((s(s(s(s(s(s(z)))))) = elem!1) <=> (s(s(s(s(s(s(z)))))) = s(s(s(z))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[231])).
% 1.34/1.58 tff(1124,plain,
% 1.34/1.58 ((s(s(s(s(s(s(z)))))) = elem!1) <=> (s(s(s(z))) = s(s(s(s(s(s(z)))))))),
% 1.34/1.58 inference(transitivity,[status(thm)],[1123, 1122])).
% 1.34/1.58 tff(1125,plain,
% 1.34/1.58 ((s(s(s(z))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = elem!1)),
% 1.34/1.58 inference(symmetry,[status(thm)],[1124])).
% 1.34/1.58 tff(1126,plain,
% 1.34/1.58 ((~(s(s(s(z))) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(s(s(s(s(z)))))) = elem!1))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[1125])).
% 1.34/1.58 tff(1127,plain,
% 1.34/1.58 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[556, 1126])).
% 1.34/1.58 tff(1128,plain,
% 1.34/1.58 (r(s(s(s(s(s(s(z)))))), s(s(s(z)))) <=> r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.34/1.58 inference(monotonicity,[status(thm)],[248])).
% 1.34/1.58 tff(1129,plain,
% 1.34/1.58 ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) <=> (~r(s(s(s(s(s(s(z)))))), elem!1))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[1128])).
% 1.34/1.58 tff(1130,plain,
% 1.34/1.58 (r(elem!1, s(s(elem!1))) <=> r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.34/1.58 inference(symmetry,[status(thm)],[483])).
% 1.34/1.58 tff(1131,plain,
% 1.34/1.58 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[970, 1130])).
% 1.34/1.58 tff(1132,plain,
% 1.34/1.58 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(1133,plain,
% 1.34/1.58 (((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(1134,plain,
% 1.34/1.58 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[1133])).
% 1.34/1.58 tff(1135,plain,
% 1.34/1.58 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))),
% 1.34/1.58 inference(transitivity,[status(thm)],[1134, 1132])).
% 1.34/1.58 tff(1136,plain,
% 1.34/1.58 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(1137,plain,
% 1.34/1.58 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[1136, 1135])).
% 1.34/1.58 tff(1138,plain,
% 1.34/1.58 ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1137, 124, 933])).
% 1.34/1.58 tff(1139,plain,
% 1.34/1.58 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1138, 1131])).
% 1.34/1.58 tff(1140,plain,
% 1.34/1.58 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[1139, 1129])).
% 1.34/1.58 tff(1141,plain,
% 1.34/1.58 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = elem!1) | b(s(s(s(s(s(s(z)))))), elem!1) | r(s(s(s(s(s(s(z)))))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = elem!1) | b(s(s(s(s(s(s(z)))))), elem!1) | r(s(s(s(s(s(s(z)))))), elem!1))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(1142,plain,
% 1.34/1.58 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = elem!1) | b(s(s(s(s(s(s(z)))))), elem!1) | r(s(s(s(s(s(s(z)))))), elem!1))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(1143,plain,
% 1.34/1.58 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = elem!1) | b(s(s(s(s(s(s(z)))))), elem!1) | r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[1142, 1141])).
% 1.34/1.58 tff(1144,plain,
% 1.34/1.58 ((s(s(s(s(s(s(z)))))) = elem!1) | b(s(s(s(s(s(s(z)))))), elem!1) | r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1143, 43])).
% 1.34/1.58 tff(1145,plain,
% 1.34/1.58 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1144, 1140, 1127])).
% 1.34/1.58 tff(1146,plain,
% 1.34/1.58 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[1145, 1121])).
% 1.34/1.58 tff(1147,plain,
% 1.34/1.58 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(1148,plain,
% 1.34/1.58 (((~r(s(s(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(s(s(z))))))))) <=> ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(1149,plain,
% 1.34/1.58 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(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(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[1148])).
% 1.34/1.58 tff(1150,plain,
% 1.34/1.58 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(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(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))),
% 1.34/1.58 inference(transitivity,[status(thm)],[1149, 1147])).
% 1.34/1.58 tff(1151,plain,
% 1.34/1.58 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(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(s(s(z)))))))))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(1152,plain,
% 1.34/1.58 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[1151, 1150])).
% 1.34/1.58 tff(1153,plain,
% 1.34/1.58 ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1152, 124, 933])).
% 1.34/1.58 tff(1154,plain,
% 1.34/1.58 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1153, 1131])).
% 1.34/1.58 tff(1155,plain,
% 1.34/1.58 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[559, 43, 556, 1154])).
% 1.34/1.58 tff(1156,plain,
% 1.34/1.58 (b(s(elem!1), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[234])).
% 1.34/1.58 tff(1157,plain,
% 1.34/1.58 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(z))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[231])).
% 1.34/1.58 tff(1158,plain,
% 1.34/1.58 (b(s(elem!1), elem!1) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.34/1.58 inference(transitivity,[status(thm)],[1157, 1156])).
% 1.34/1.58 tff(1159,plain,
% 1.34/1.58 (~r(z, s(s(elem!1)))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[978, 970, 246])).
% 1.34/1.58 tff(1160,plain,
% 1.34/1.58 (b(z, s(s(elem!1)))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[460, 1159])).
% 1.34/1.58 tff(1161,plain,
% 1.34/1.58 (r(s(elem!1), elem!1)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[813, 807, 193])).
% 1.34/1.58 tff(1162,plain,
% 1.34/1.58 ((elem!1 = s(elem!1)) <=> (s(elem!1) = elem!1)),
% 1.34/1.58 inference(commutativity,[status(thm)],[])).
% 1.34/1.58 tff(1163,plain,
% 1.34/1.58 ((s(elem!1) = elem!1) <=> (elem!1 = s(elem!1))),
% 1.34/1.58 inference(symmetry,[status(thm)],[1162])).
% 1.34/1.58 tff(1164,plain,
% 1.34/1.58 ((~(s(elem!1) = elem!1)) <=> (~(elem!1 = s(elem!1)))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[1163])).
% 1.34/1.58 tff(1165,plain,
% 1.34/1.58 (s(elem!1) = s(s(s(elem!1)))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[183])).
% 1.34/1.58 tff(1166,plain,
% 1.34/1.58 (s(s(s(elem!1))) = s(elem!1)),
% 1.34/1.58 inference(symmetry,[status(thm)],[1165])).
% 1.34/1.58 tff(1167,plain,
% 1.34/1.58 ($false),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[150, 1166])).
% 1.34/1.58 tff(1168,plain,((~(elem!1 = s(s(elem!1)))) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.58 tff(1169,plain,
% 1.34/1.58 (~(elem!1 = s(s(elem!1)))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1168, 150])).
% 1.34/1.58 tff(1170,plain,
% 1.34/1.58 ((s(s(elem!1)) = elem!1) <=> (elem!1 = s(s(elem!1)))),
% 1.34/1.58 inference(symmetry,[status(thm)],[182])).
% 1.34/1.58 tff(1171,assumption,(s(s(elem!1)) = elem!1), introduced(assumption)).
% 1.34/1.58 tff(1172,plain,
% 1.34/1.58 (elem!1 = s(s(elem!1))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[1171, 1170])).
% 1.34/1.58 tff(1173,plain,
% 1.34/1.58 ($false),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[360, 1172])).
% 1.34/1.58 tff(1174,plain,((~(s(s(elem!1)) = elem!1)) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.58 tff(1175,plain,
% 1.34/1.58 (~(s(s(elem!1)) = elem!1)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1174, 1169])).
% 1.34/1.58 tff(1176,plain,
% 1.34/1.58 (~(s(elem!1) = elem!1)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[180, 1175])).
% 1.34/1.58 tff(1177,plain,
% 1.34/1.58 (~(elem!1 = s(elem!1))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[1176, 1164])).
% 1.34/1.58 tff(1178,plain,
% 1.34/1.58 (s(s(s(elem!1))) = s(s(elem!1))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[188])).
% 1.34/1.58 tff(1179,plain,
% 1.34/1.58 (s(s(s(elem!1))) = s(elem!1)),
% 1.34/1.58 inference(transitivity,[status(thm)],[1178, 188])).
% 1.34/1.58 tff(1180,plain,
% 1.34/1.58 ($false),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[150, 1179])).
% 1.34/1.58 tff(1181,plain,((~(s(s(elem!1)) = s(elem!1))) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.58 tff(1182,plain,
% 1.34/1.58 (~(s(s(elem!1)) = s(elem!1))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1181, 150])).
% 1.34/1.58 tff(1183,plain,
% 1.34/1.58 (((~![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))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(1184,plain,
% 1.34/1.58 ((~![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))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(1185,plain,
% 1.34/1.58 ((~![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)),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[1184, 1183])).
% 1.34/1.58 tff(1186,plain,
% 1.34/1.58 (b(s(elem!1), z)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1185, 43, 77, 1076])).
% 1.34/1.58 tff(1187,plain,
% 1.34/1.58 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(1188,plain,
% 1.34/1.58 (((~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(1189,plain,
% 1.34/1.58 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1))))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[1188])).
% 1.34/1.58 tff(1190,plain,
% 1.34/1.58 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))))),
% 1.34/1.58 inference(transitivity,[status(thm)],[1189, 1187])).
% 1.34/1.58 tff(1191,plain,
% 1.34/1.58 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, elem!1)))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(1192,plain,
% 1.34/1.58 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1))))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[1191, 1190])).
% 1.34/1.58 tff(1193,plain,
% 1.34/1.58 ($false),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1192, 124, 374, 437, 970])).
% 1.34/1.58 tff(1194,plain,((~r(z, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.58 tff(1195,plain,
% 1.34/1.58 (~r(z, s(s(elem!1)))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1194, 970, 374])).
% 1.34/1.58 tff(1196,plain,
% 1.34/1.58 (b(z, s(s(elem!1)))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[460, 1195])).
% 1.34/1.58 tff(1197,plain,
% 1.34/1.58 (~(elem!1 = s(elem!1))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[193, 1164])).
% 1.34/1.58 tff(1198,assumption,(b(z, s(s(elem!1)))), introduced(assumption)).
% 1.34/1.58 tff(1199,assumption,(b(s(elem!1), z)), introduced(assumption)).
% 1.34/1.58 tff(1200,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(1201,plain,
% 1.34/1.58 (((~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(elem!1), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(1202,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1)))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[1201])).
% 1.34/1.58 tff(1203,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 1.34/1.58 inference(transitivity,[status(thm)],[1202, 1200])).
% 1.34/1.58 tff(1204,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(1205,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1)))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[1204, 1203])).
% 1.34/1.58 tff(1206,plain,
% 1.34/1.58 ($false),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1205, 306, 30, 1199, 1005, 1198, 815])).
% 1.34/1.58 tff(1207,plain,((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.58 tff(1208,plain,
% 1.34/1.58 (~b(elem!1, s(elem!1))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1207, 1005, 1199, 30, 1198])).
% 1.34/1.58 tff(1209,plain,
% 1.34/1.58 ((elem!1 = s(elem!1)) | r(elem!1, s(elem!1))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[370, 43, 1208])).
% 1.34/1.58 tff(1210,plain,
% 1.34/1.58 (r(elem!1, s(elem!1))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1209, 1197])).
% 1.34/1.58 tff(1211,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(1212,plain,
% 1.34/1.58 (((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1))))) <=> ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(1213,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1)))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[1212])).
% 1.34/1.58 tff(1214,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.34/1.59 inference(transitivity,[status(thm)],[1213, 1211])).
% 1.34/1.59 tff(1215,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(1216,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1)))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[1215, 1214])).
% 1.34/1.59 tff(1217,plain,
% 1.34/1.59 ($false),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1216, 306, 1199, 817, 1005, 1198])).
% 1.34/1.59 tff(1218,plain,((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.59 tff(1219,plain,
% 1.34/1.59 (~b(z, s(elem!1))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1218, 1005, 1199, 1198])).
% 1.34/1.59 tff(1220,plain,
% 1.34/1.59 (r(z, s(elem!1))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[275, 1219])).
% 1.34/1.59 tff(1221,plain,
% 1.34/1.59 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(1222,plain,
% 1.34/1.59 (((~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(1223,plain,
% 1.34/1.59 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1)))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[1222])).
% 1.34/1.59 tff(1224,plain,
% 1.34/1.59 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))))),
% 1.34/1.59 inference(transitivity,[status(thm)],[1223, 1221])).
% 1.34/1.59 tff(1225,plain,
% 1.34/1.59 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, elem!1)))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(1226,plain,
% 1.34/1.59 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1)))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[1225, 1224])).
% 1.34/1.59 tff(1227,plain,
% 1.34/1.59 ($false),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1226, 124, 374, 1220, 1210])).
% 1.34/1.59 tff(1228,plain,((~b(s(s(elem!1)), s(elem!1))) | (~r(z, elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (s(elem!1) = elem!1) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.59 tff(1229,plain,
% 1.34/1.59 (~b(s(s(elem!1)), s(elem!1))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1228, 1196, 1186, 374, 1176, 30])).
% 1.34/1.59 tff(1230,plain,
% 1.34/1.59 (r(s(s(elem!1)), s(elem!1))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[994, 1229, 1182])).
% 1.34/1.59 tff(1231,plain,
% 1.34/1.59 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(1232,plain,
% 1.34/1.59 (((~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(s(elem!1)), s(elem!1))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(1233,plain,
% 1.34/1.59 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1)))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[1232])).
% 1.34/1.59 tff(1234,plain,
% 1.34/1.59 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.34/1.59 inference(transitivity,[status(thm)],[1233, 1231])).
% 1.34/1.59 tff(1235,plain,
% 1.34/1.59 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(1236,plain,
% 1.34/1.59 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1)))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[1235, 1234])).
% 1.34/1.59 tff(1237,plain,
% 1.34/1.59 ($false),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1236, 124, 255, 244, 970])).
% 1.34/1.59 tff(1238,plain,((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.59 tff(1239,plain,
% 1.34/1.59 (~r(elem!1, s(elem!1))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1238, 1230, 970])).
% 1.34/1.59 tff(1240,plain,
% 1.34/1.59 ((elem!1 = s(elem!1)) | b(elem!1, s(elem!1))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[370, 43, 1239])).
% 1.34/1.59 tff(1241,plain,
% 1.34/1.59 (b(elem!1, s(elem!1))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1240, 1177])).
% 1.34/1.59 tff(1242,plain,
% 1.34/1.59 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[659, 1230, 653])).
% 1.34/1.59 tff(1243,plain,
% 1.34/1.59 (b(s(s(s(elem!1))), s(elem!1))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[664, 1242, 150])).
% 1.34/1.59 tff(1244,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(elem!1))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(1245,plain,
% 1.34/1.59 (((~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(elem!1))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(1246,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(elem!1)))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[1245])).
% 1.34/1.59 tff(1247,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(elem!1))))),
% 1.34/1.59 inference(transitivity,[status(thm)],[1246, 1244])).
% 1.34/1.59 tff(1248,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(1249,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(elem!1)))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[1248, 1247])).
% 1.34/1.59 tff(1250,plain,
% 1.34/1.59 (~b(elem!1, s(s(s(elem!1))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1249, 306, 1243, 1186, 1196, 1241])).
% 1.34/1.59 tff(1251,plain,
% 1.34/1.59 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(1252,plain,
% 1.34/1.59 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1)))))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(1253,plain,
% 1.34/1.59 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1))))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[1252])).
% 1.34/1.59 tff(1254,plain,
% 1.34/1.59 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.34/1.59 inference(transitivity,[status(thm)],[1253, 1251])).
% 1.34/1.59 tff(1255,plain,
% 1.34/1.59 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(1256,plain,
% 1.34/1.59 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[1255, 1254])).
% 1.34/1.59 tff(1257,plain,
% 1.34/1.59 (~r(elem!1, s(s(s(elem!1))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1256, 124, 970, 653])).
% 1.34/1.59 tff(1258,plain,
% 1.34/1.59 (((~![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)))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(1259,plain,
% 1.34/1.59 ((~![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)))))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(1260,plain,
% 1.34/1.59 ((~![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))))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[1259, 1258])).
% 1.34/1.59 tff(1261,plain,
% 1.34/1.59 ((elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1260, 43, 1257])).
% 1.34/1.59 tff(1262,plain,
% 1.34/1.59 (elem!1 = s(s(s(elem!1)))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1261, 1250])).
% 1.34/1.59 tff(1263,plain,
% 1.34/1.59 (s(s(s(elem!1))) = elem!1),
% 1.34/1.59 inference(symmetry,[status(thm)],[1262])).
% 1.34/1.59 tff(1264,plain,
% 1.34/1.59 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.34/1.59 inference(monotonicity,[status(thm)],[1263])).
% 1.34/1.59 tff(1265,plain,
% 1.34/1.59 (b(s(s(s(s(s(elem!1))))), elem!1) <=> b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.34/1.59 inference(symmetry,[status(thm)],[1264])).
% 1.34/1.59 tff(1266,plain,
% 1.34/1.59 (s(elem!1) = s(s(s(s(elem!1))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[1262])).
% 1.34/1.59 tff(1267,plain,
% 1.34/1.59 (s(s(elem!1)) = s(s(s(s(s(elem!1)))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[1266])).
% 1.34/1.59 tff(1268,plain,
% 1.34/1.59 (s(s(s(s(s(elem!1))))) = s(s(elem!1))),
% 1.34/1.59 inference(symmetry,[status(thm)],[1267])).
% 1.34/1.59 tff(1269,plain,
% 1.34/1.59 (b(s(s(s(s(s(elem!1))))), elem!1) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[1268, 1262])).
% 1.34/1.59 tff(1270,plain,
% 1.34/1.59 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.34/1.59 inference(symmetry,[status(thm)],[1269])).
% 1.34/1.59 tff(1271,plain,
% 1.34/1.59 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[1262])).
% 1.34/1.59 tff(1272,plain,
% 1.34/1.59 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[30, 1271])).
% 1.34/1.59 tff(1273,plain,
% 1.34/1.59 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[1272, 1270])).
% 1.34/1.59 tff(1274,plain,
% 1.34/1.59 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[1273, 1265])).
% 1.34/1.59 tff(1275,plain,
% 1.34/1.59 (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)))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[1268])).
% 1.34/1.59 tff(1276,plain,
% 1.34/1.59 (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))))))),
% 1.34/1.59 inference(symmetry,[status(thm)],[1275])).
% 1.34/1.59 tff(1277,assumption,(s(s(s(s(elem!1)))) = s(s(elem!1))), introduced(assumption)).
% 1.34/1.59 tff(1278,plain,
% 1.34/1.59 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(elem!1)))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[1277])).
% 1.34/1.59 tff(1279,plain,
% 1.34/1.59 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(1280,plain,
% 1.34/1.59 (inj_0(s(s(s(s(elem!1))))) = s(s(s(elem!1)))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1279, 59])).
% 1.34/1.59 tff(1281,plain,
% 1.34/1.59 (s(s(s(elem!1))) = inj_0(s(s(s(s(elem!1)))))),
% 1.34/1.59 inference(symmetry,[status(thm)],[1280])).
% 1.34/1.59 tff(1282,plain,
% 1.34/1.59 (s(s(s(elem!1))) = s(elem!1)),
% 1.34/1.59 inference(transitivity,[status(thm)],[1281, 1278, 66])).
% 1.34/1.59 tff(1283,plain,
% 1.34/1.59 ($false),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[150, 1282])).
% 1.34/1.59 tff(1284,plain,((~(s(s(s(s(elem!1)))) = s(s(elem!1)))) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.59 tff(1285,plain,
% 1.34/1.59 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1284, 150])).
% 1.34/1.59 tff(1286,plain,
% 1.34/1.59 (r(s(elem!1), elem!1) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 1.34/1.59 inference(monotonicity,[status(thm)],[1266])).
% 1.34/1.59 tff(1287,plain,
% 1.34/1.59 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[802, 1286])).
% 1.34/1.59 tff(1288,assumption,(r(s(s(s(s(elem!1)))), s(s(elem!1)))), introduced(assumption)).
% 1.34/1.59 tff(1289,assumption,(r(s(s(s(s(elem!1)))), elem!1)), introduced(assumption)).
% 1.34/1.59 tff(1290,plain,
% 1.34/1.59 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(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)))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(1291,plain,
% 1.34/1.59 (((~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)))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(1292,plain,
% 1.34/1.59 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[1291])).
% 1.34/1.59 tff(1293,plain,
% 1.34/1.59 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.34/1.59 inference(transitivity,[status(thm)],[1292, 1290])).
% 1.34/1.59 tff(1294,plain,
% 1.34/1.59 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(1295,plain,
% 1.34/1.59 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[1294, 1293])).
% 1.34/1.59 tff(1296,plain,
% 1.34/1.59 ($false),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1295, 124, 970, 1289, 1288])).
% 1.34/1.59 tff(1297,plain,((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.59 tff(1298,plain,
% 1.34/1.59 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1297, 1287, 970])).
% 1.34/1.59 tff(1299,plain,
% 1.34/1.59 (((~![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))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(1300,plain,
% 1.34/1.59 ((~![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))))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(1301,plain,
% 1.34/1.59 ((~![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)))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[1300, 1299])).
% 1.34/1.59 tff(1302,plain,
% 1.34/1.59 ((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)))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1301, 43])).
% 1.34/1.59 tff(1303,plain,
% 1.34/1.59 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1302, 1298, 1285])).
% 1.34/1.59 tff(1304,plain,
% 1.34/1.59 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[1303, 1276])).
% 1.34/1.59 tff(1305,plain,
% 1.34/1.59 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[1263])).
% 1.34/1.59 tff(1306,plain,
% 1.34/1.59 (b(elem!1, s(s(s(s(elem!1))))) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.34/1.59 inference(symmetry,[status(thm)],[1305])).
% 1.34/1.59 tff(1307,plain,
% 1.34/1.59 (s(s(s(s(elem!1)))) = s(elem!1)),
% 1.34/1.59 inference(symmetry,[status(thm)],[1266])).
% 1.34/1.59 tff(1308,plain,
% 1.34/1.59 (b(elem!1, s(s(s(s(elem!1))))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[1262, 1307])).
% 1.34/1.59 tff(1309,plain,
% 1.34/1.59 (b(s(s(s(elem!1))), s(elem!1)) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 1.34/1.59 inference(symmetry,[status(thm)],[1308])).
% 1.34/1.59 tff(1310,plain,
% 1.34/1.59 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[1243, 1309])).
% 1.34/1.59 tff(1311,plain,
% 1.34/1.59 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[1310, 1306])).
% 1.34/1.59 tff(1312,plain,
% 1.34/1.59 (b(z, s(s(s(s(s(elem!1)))))) <=> b(z, s(s(elem!1)))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[1268])).
% 1.34/1.59 tff(1313,plain,
% 1.34/1.59 (b(z, s(s(elem!1))) <=> b(z, s(s(s(s(s(elem!1))))))),
% 1.34/1.59 inference(symmetry,[status(thm)],[1312])).
% 1.34/1.59 tff(1314,plain,
% 1.34/1.59 (b(z, s(s(s(s(s(elem!1))))))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[1196, 1313])).
% 1.34/1.59 tff(1315,plain,
% 1.34/1.59 (b(s(elem!1), z) <=> b(s(s(s(s(elem!1)))), z)),
% 1.34/1.59 inference(monotonicity,[status(thm)],[1266])).
% 1.34/1.59 tff(1316,plain,
% 1.34/1.59 (b(s(s(s(s(elem!1)))), z)),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[1186, 1315])).
% 1.34/1.59 tff(1317,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, 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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(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))))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(1318,plain,
% 1.34/1.59 (((~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(z, 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)))), z))) <=> ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(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))))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(1319,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, 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)))))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[1318])).
% 1.34/1.59 tff(1320,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, 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))))))),
% 1.34/1.59 inference(transitivity,[status(thm)],[1319, 1317])).
% 1.34/1.59 tff(1321,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(1322,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[1321, 1320])).
% 1.44/1.60 tff(1323,plain,
% 1.44/1.60 ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1322, 306, 1316])).
% 1.44/1.60 tff(1324,plain,
% 1.44/1.60 ($false),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1323, 1314, 1311, 1304, 1274])).
% 1.44/1.60 tff(1325,plain,((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.60 tff(1326,plain,
% 1.44/1.60 (~r(z, elem!1)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1325, 1161, 30, 150, 653, 970])).
% 1.44/1.60 tff(1327,plain,
% 1.44/1.60 (b(z, elem!1)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[835, 1326, 358])).
% 1.44/1.60 tff(1328,plain,
% 1.44/1.60 (b(z, s(s(s(z))))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[1327, 837])).
% 1.44/1.60 tff(1329,plain,
% 1.44/1.60 (b(z, s(s(s(s(s(z))))))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[1198, 396])).
% 1.44/1.60 tff(1330,assumption,(b(s(s(s(s(s(s(z)))))), s(s(s(z))))), introduced(assumption)).
% 1.44/1.60 tff(1331,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(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(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(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(s(z)))))))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(1332,plain,
% 1.44/1.60 (((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(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(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(s(z)))))))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(1333,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(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(s(z))))))))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[1332])).
% 1.44/1.60 tff(1334,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(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(s(z)))))))))),
% 1.44/1.60 inference(transitivity,[status(thm)],[1333, 1331])).
% 1.44/1.60 tff(1335,plain,
% 1.44/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(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))))))))),
% 1.44/1.60 inference(quant_inst,[status(thm)],[])).
% 1.44/1.60 tff(1336,plain,
% 1.44/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[1335, 1334])).
% 1.44/1.60 tff(1337,plain,
% 1.44/1.60 ($false),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1336, 306, 859, 761, 245, 1330, 523])).
% 1.44/1.60 tff(1338,plain,((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.60 tff(1339,plain,
% 1.44/1.60 (~b(z, s(s(s(z))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1338, 1329, 1016, 1146, 1155])).
% 1.44/1.60 tff(1340,plain,
% 1.44/1.60 ($false),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1339, 1328])).
% 1.44/1.60 tff(1341,plain,(b(s(elem!1), elem!1) | (~(elem!1 = s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (s(elem!1) = elem!1) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.60 tff(1342,plain,
% 1.44/1.60 (b(s(elem!1), elem!1)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1341, 970, 30, 150, 653, 231, 193, 1160])).
% 1.44/1.60 tff(1343,plain,
% 1.44/1.60 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[1342, 1158])).
% 1.44/1.60 tff(1344,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(1345,plain,
% 1.44/1.60 (((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(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(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(1346,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(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(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[1345])).
% 1.44/1.60 tff(1347,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(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(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.44/1.60 inference(transitivity,[status(thm)],[1346, 1344])).
% 1.44/1.60 tff(1348,plain,
% 1.44/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(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(s(s(z))))), s(s(s(s(z)))))))),
% 1.44/1.60 inference(quant_inst,[status(thm)],[])).
% 1.44/1.60 tff(1349,plain,
% 1.44/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[1348, 1347])).
% 1.44/1.60 tff(1350,plain,
% 1.44/1.60 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1349, 306, 1343, 1155, 1016, 1146])).
% 1.44/1.60 tff(1351,plain,
% 1.44/1.60 (~b(s(s(elem!1)), s(elem!1))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[1350, 1119])).
% 1.44/1.60 tff(1352,plain,
% 1.44/1.60 (r(s(s(elem!1)), s(elem!1))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[994, 1351, 392])).
% 1.44/1.60 tff(1353,plain,
% 1.44/1.60 ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) <=> (~b(s(s(s(elem!1))), s(elem!1)))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[242])).
% 1.44/1.60 tff(1354,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(1355,plain,
% 1.44/1.60 (((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(1356,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[1355])).
% 1.44/1.60 tff(1357,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.44/1.60 inference(transitivity,[status(thm)],[1356, 1354])).
% 1.44/1.60 tff(1358,plain,
% 1.44/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.44/1.60 inference(quant_inst,[status(thm)],[])).
% 1.44/1.60 tff(1359,plain,
% 1.44/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[1358, 1357])).
% 1.44/1.60 tff(1360,plain,
% 1.44/1.60 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1359, 306, 1343, 1155, 1146])).
% 1.44/1.60 tff(1361,plain,
% 1.44/1.60 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[1360, 1353])).
% 1.44/1.60 tff(1362,plain,
% 1.44/1.60 (r(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[664, 1361, 150])).
% 1.44/1.60 tff(1363,plain,
% 1.44/1.60 ($false),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[659, 1362, 1352, 653])).
% 1.44/1.60 tff(1364,plain,((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(s(elem!1))) = s(elem!1)) | (~(elem!1 = s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)) | (s(elem!1) = elem!1) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.60 tff(1365,plain,
% 1.44/1.60 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1364, 1117, 144, 133, 92, 181, 175])).
% 1.44/1.60 tff(1366,plain,
% 1.44/1.60 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[610, 1365, 160])).
% 1.44/1.60 tff(1367,plain,
% 1.44/1.60 (b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[605, 1366, 133])).
% 1.44/1.60 tff(1368,plain,
% 1.44/1.60 (b(s(s(s(s(s(s(z)))))), s(s(s(z)))) <=> b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.44/1.60 inference(monotonicity,[status(thm)],[163])).
% 1.44/1.60 tff(1369,plain,
% 1.44/1.60 (b(s(s(s(s(s(s(z)))))), elem!1) <=> b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.44/1.60 inference(symmetry,[status(thm)],[1368])).
% 1.44/1.60 tff(1370,plain,
% 1.44/1.60 ((s(s(s(s(s(s(z)))))) = elem!1) <=> (s(s(s(s(s(s(z)))))) = s(s(s(z))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[133])).
% 1.44/1.60 tff(1371,plain,
% 1.44/1.60 ((s(s(s(s(s(s(z)))))) = elem!1) <=> (s(s(s(z))) = s(s(s(s(s(s(z)))))))),
% 1.44/1.60 inference(transitivity,[status(thm)],[1370, 1122])).
% 1.44/1.60 tff(1372,plain,
% 1.44/1.60 ((s(s(s(z))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = elem!1)),
% 1.44/1.60 inference(symmetry,[status(thm)],[1371])).
% 1.44/1.60 tff(1373,plain,
% 1.44/1.60 ((~(s(s(s(z))) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(s(s(s(s(z)))))) = elem!1))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[1372])).
% 1.44/1.60 tff(1374,plain,
% 1.44/1.60 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[556, 1373])).
% 1.44/1.60 tff(1375,plain,
% 1.44/1.60 (r(s(s(s(s(s(s(z)))))), s(s(s(z)))) <=> r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.44/1.60 inference(monotonicity,[status(thm)],[163])).
% 1.44/1.60 tff(1376,plain,
% 1.44/1.60 ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) <=> (~r(s(s(s(s(s(s(z)))))), elem!1))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[1375])).
% 1.44/1.60 tff(1377,plain,
% 1.44/1.60 (b(z, s(s(s(s(s(z)))))) <=> b(z, s(s(elem!1)))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[225])).
% 1.44/1.60 tff(1378,plain,
% 1.44/1.60 (b(z, s(s(elem!1))) <=> b(z, s(s(s(s(s(z))))))),
% 1.44/1.60 inference(symmetry,[status(thm)],[1377])).
% 1.44/1.60 tff(1379,plain,
% 1.44/1.60 (~r(z, s(s(elem!1)))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[978, 1117, 175])).
% 1.44/1.60 tff(1380,plain,
% 1.44/1.60 (b(z, s(s(elem!1)))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[460, 1379])).
% 1.44/1.60 tff(1381,plain,
% 1.44/1.60 (b(z, s(s(s(s(s(z))))))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[1380, 1378])).
% 1.44/1.60 tff(1382,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(1383,plain,
% 1.44/1.60 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), z))) <=> ((~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(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(1384,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z)))))))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[1383])).
% 1.44/1.60 tff(1385,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.44/1.60 inference(transitivity,[status(thm)],[1384, 1382])).
% 1.44/1.60 tff(1386,plain,
% 1.44/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 1.44/1.60 inference(quant_inst,[status(thm)],[])).
% 1.44/1.60 tff(1387,plain,
% 1.44/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z)))))))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[1386, 1385])).
% 1.44/1.60 tff(1388,plain,
% 1.44/1.60 (~b(s(s(s(s(s(s(z)))))), z)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1387, 306, 1002, 230, 1381, 1367])).
% 1.44/1.60 tff(1389,plain,
% 1.44/1.60 (r(s(s(s(s(s(s(z)))))), z)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[856, 43, 554, 1388])).
% 1.44/1.60 tff(1390,plain,
% 1.44/1.60 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(1391,plain,
% 1.44/1.60 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.44/1.60 inference(quant_inst,[status(thm)],[])).
% 1.44/1.60 tff(1392,plain,
% 1.44/1.60 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[1391, 1390])).
% 1.44/1.60 tff(1393,plain,
% 1.44/1.60 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1392, 124, 203, 1389])).
% 1.44/1.60 tff(1394,plain,
% 1.44/1.60 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[1393, 1376])).
% 1.44/1.60 tff(1395,plain,
% 1.44/1.60 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1144, 1394, 1374])).
% 1.44/1.60 tff(1396,plain,
% 1.44/1.60 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[1395, 1369])).
% 1.44/1.60 tff(1397,plain,
% 1.44/1.60 (s(s(s(elem!1))) = s(s(s(s(s(s(z))))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[224])).
% 1.44/1.60 tff(1398,plain,
% 1.44/1.60 (s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))),
% 1.44/1.60 inference(symmetry,[status(thm)],[1397])).
% 1.44/1.60 tff(1399,plain,
% 1.44/1.60 (r(s(s(s(s(s(s(z)))))), z) <=> r(s(s(s(elem!1))), z)),
% 1.44/1.60 inference(monotonicity,[status(thm)],[1398])).
% 1.44/1.60 tff(1400,plain,
% 1.44/1.61 (r(s(s(s(elem!1))), z)),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[1389, 1399])).
% 1.44/1.61 tff(1401,plain,
% 1.44/1.61 (~r(elem!1, s(s(s(elem!1))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[851, 1400, 175])).
% 1.44/1.61 tff(1402,plain,
% 1.44/1.61 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[562, 1401, 133])).
% 1.44/1.61 tff(1403,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(1404,plain,
% 1.44/1.61 (((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(1405,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1404])).
% 1.44/1.61 tff(1406,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.44/1.61 inference(transitivity,[status(thm)],[1405, 1403])).
% 1.44/1.61 tff(1407,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(1408,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[1407, 1406])).
% 1.44/1.61 tff(1409,plain,
% 1.44/1.61 ($false),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1408, 306, 1402, 230, 1396, 1367])).
% 1.44/1.61 tff(1410,plain,((s(s(elem!1)) = elem!1) | b(elem!1, z) | b(elem!1, s(s(s(z)))) | b(elem!1, s(z)) | b(s(s(s(z))), s(z)) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.61 tff(1411,plain,
% 1.44/1.61 (s(s(elem!1)) = elem!1),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1410, 9, 3, 5, 2, 6])).
% 1.44/1.61 tff(1412,plain,
% 1.44/1.61 (elem!1 = s(s(elem!1))),
% 1.44/1.61 inference(symmetry,[status(thm)],[1411])).
% 1.44/1.61 tff(1413,plain,
% 1.44/1.61 ((s(s(elem!1)) = s(z)) <=> (elem!1 = s(z))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1411])).
% 1.44/1.61 tff(1414,plain,
% 1.44/1.61 ((elem!1 = s(s(s(z)))) <=> (s(s(s(z))) = elem!1)),
% 1.44/1.61 inference(commutativity,[status(thm)],[])).
% 1.44/1.61 tff(1415,plain,
% 1.44/1.61 ((s(s(elem!1)) = s(z)) <=> (elem!1 = s(z))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1171])).
% 1.44/1.61 tff(1416,plain,
% 1.44/1.61 ((~(s(s(elem!1)) = s(z))) <=> (~(elem!1 = s(z)))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1415])).
% 1.44/1.61 tff(1417,assumption,(~(s(s(elem!1)) = s(z))), introduced(assumption)).
% 1.44/1.61 tff(1418,plain,
% 1.44/1.61 (~(elem!1 = s(z))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[1417, 1416])).
% 1.44/1.61 tff(1419,plain,
% 1.44/1.61 (r(elem!1, s(z))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[97, 1418])).
% 1.44/1.61 tff(1420,plain,
% 1.44/1.61 (~r(elem!1, s(s(s(z))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[127, 124, 206, 1419])).
% 1.44/1.61 tff(1421,plain,
% 1.44/1.61 (elem!1 = s(s(s(z)))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[132, 1420])).
% 1.44/1.61 tff(1422,plain,
% 1.44/1.61 (s(s(s(z))) = elem!1),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[1421, 1414])).
% 1.44/1.61 tff(1423,plain,
% 1.44/1.61 (elem!1 = s(s(elem!1))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1174, 1171])).
% 1.44/1.61 tff(1424,plain,
% 1.44/1.61 (s(s(s(elem!1))) = s(elem!1)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1168, 1423])).
% 1.44/1.61 tff(1425,plain,
% 1.44/1.61 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1424])).
% 1.44/1.61 tff(1426,plain,
% 1.44/1.61 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 1.44/1.61 inference(symmetry,[status(thm)],[1425])).
% 1.44/1.61 tff(1427,plain,
% 1.44/1.61 (elem!1 = s(s(elem!1))),
% 1.44/1.61 inference(symmetry,[status(thm)],[1171])).
% 1.44/1.61 tff(1428,plain,
% 1.44/1.61 (elem!1 = s(s(s(s(elem!1))))),
% 1.44/1.61 inference(transitivity,[status(thm)],[1427, 1426])).
% 1.44/1.61 tff(1429,assumption,(elem!1 = s(s(s(s(elem!1))))), introduced(assumption)).
% 1.44/1.61 tff(1430,assumption,(s(s(s(z))) = elem!1), introduced(assumption)).
% 1.44/1.61 tff(1431,plain,
% 1.44/1.61 (s(s(s(z))) = s(s(s(s(elem!1))))),
% 1.44/1.61 inference(transitivity,[status(thm)],[1430, 1429])).
% 1.44/1.61 tff(1432,plain,
% 1.44/1.61 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(elem!1)))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1431])).
% 1.44/1.61 tff(1433,plain,
% 1.44/1.61 (s(s(z)) = s(s(s(elem!1)))),
% 1.44/1.61 inference(transitivity,[status(thm)],[103, 1432, 1280])).
% 1.44/1.61 tff(1434,plain,
% 1.44/1.61 (inj_0(s(s(z))) = inj_0(s(s(s(elem!1))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1433])).
% 1.44/1.61 tff(1435,plain,
% 1.44/1.61 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(z)))),
% 1.44/1.61 inference(symmetry,[status(thm)],[1434])).
% 1.44/1.61 tff(1436,plain,
% 1.44/1.61 (s(s(elem!1)) = s(z)),
% 1.44/1.61 inference(transitivity,[status(thm)],[140, 1435, 546])).
% 1.44/1.61 tff(1437,plain,
% 1.44/1.61 (s(s(s(s(z)))) = s(elem!1)),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1430])).
% 1.44/1.61 tff(1438,plain,
% 1.44/1.61 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1437])).
% 1.44/1.61 tff(1439,plain,
% 1.44/1.61 ((s(s(s(s(s(z))))) = s(z)) <=> (s(s(elem!1)) = s(z))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1438])).
% 1.44/1.61 tff(1440,plain,
% 1.44/1.61 ((~(s(s(s(s(s(z))))) = s(z))) <=> (~(s(s(elem!1)) = s(z)))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1439])).
% 1.44/1.61 tff(1441,plain,
% 1.44/1.61 (~(s(s(elem!1)) = s(z))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[500, 1440])).
% 1.44/1.61 tff(1442,plain,
% 1.44/1.61 ($false),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1441, 1436])).
% 1.44/1.61 tff(1443,plain,((~(elem!1 = s(s(s(s(elem!1)))))) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.61 tff(1444,plain,
% 1.44/1.61 (~(s(s(s(z))) = elem!1)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1443, 1428])).
% 1.44/1.61 tff(1445,plain,
% 1.44/1.61 ($false),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1444, 1422])).
% 1.44/1.61 tff(1446,plain,((~(s(s(elem!1)) = elem!1)) | b(elem!1, s(s(s(z)))) | (~r(s(s(s(z))), s(z))) | b(elem!1, s(z)) | (s(s(elem!1)) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.61 tff(1447,plain,
% 1.44/1.61 (s(s(elem!1)) = s(z)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1446, 1411, 3, 5, 114])).
% 1.44/1.61 tff(1448,plain,
% 1.44/1.61 (elem!1 = s(z)),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[1447, 1413])).
% 1.44/1.61 tff(1449,plain,
% 1.44/1.61 (s(z) = elem!1),
% 1.44/1.61 inference(symmetry,[status(thm)],[1448])).
% 1.44/1.61 tff(1450,plain,
% 1.44/1.61 (s(z) = s(s(elem!1))),
% 1.44/1.61 inference(transitivity,[status(thm)],[1449, 1412])).
% 1.44/1.61 tff(1451,plain,
% 1.44/1.61 (inj_0(s(z)) = inj_0(s(s(elem!1)))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1450])).
% 1.44/1.61 tff(1452,plain,
% 1.44/1.61 (inj_0(s(s(elem!1))) = inj_0(s(z))),
% 1.44/1.61 inference(symmetry,[status(thm)],[1451])).
% 1.44/1.61 tff(1453,plain,
% 1.44/1.61 (s(elem!1) = z),
% 1.44/1.61 inference(transitivity,[status(thm)],[67, 1452, 61])).
% 1.44/1.61 tff(1454,plain,
% 1.44/1.61 ($false),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[77, 1453])).
% 1.44/1.61 tff(1455,plain,(b(s(s(s(z))), s(z)) | b(elem!1, s(s(s(z)))) | b(elem!1, s(z)) | b(elem!1, z) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.61 tff(1456,plain,
% 1.44/1.61 (b(elem!1, s(s(s(z))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1455, 9, 5, 6, 2])).
% 1.44/1.61 tff(1457,plain,
% 1.44/1.61 (b(elem!1, s(s(s(z)))) <=> b(elem!1, elem!1)),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1430])).
% 1.44/1.61 tff(1458,plain,
% 1.44/1.61 (b(elem!1, elem!1) <=> b(elem!1, s(s(s(z))))),
% 1.44/1.61 inference(symmetry,[status(thm)],[1457])).
% 1.44/1.61 tff(1459,plain,
% 1.44/1.61 ((~b(elem!1, elem!1)) <=> (~b(elem!1, s(s(s(z)))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1458])).
% 1.44/1.61 tff(1460,plain,
% 1.44/1.61 (^[X: $i] : refl((~b(X, X)) <=> (~b(X, X)))),
% 1.44/1.61 inference(bind,[status(th)],[])).
% 1.44/1.61 tff(1461,plain,
% 1.44/1.61 (![X: $i] : (~b(X, X)) <=> ![X: $i] : (~b(X, X))),
% 1.44/1.61 inference(quant_intro,[status(thm)],[1460])).
% 1.44/1.61 tff(1462,plain,
% 1.44/1.61 (![X: $i] : (~b(X, X)) <=> ![X: $i] : (~b(X, X))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(1463,axiom,(![X: $i] : (~b(X, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bi')).
% 1.44/1.61 tff(1464,plain,
% 1.44/1.61 (![X: $i] : (~b(X, X))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[1463, 1462])).
% 1.44/1.61 tff(1465,plain,(
% 1.44/1.61 ![X: $i] : (~b(X, X))),
% 1.44/1.61 inference(skolemize,[status(sab)],[1464])).
% 1.44/1.61 tff(1466,plain,
% 1.44/1.61 (![X: $i] : (~b(X, X))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[1465, 1461])).
% 1.44/1.61 tff(1467,plain,
% 1.44/1.61 ((~![X: $i] : (~b(X, X))) | (~b(elem!1, elem!1))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(1468,plain,
% 1.44/1.61 (~b(elem!1, elem!1)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1467, 1466])).
% 1.44/1.61 tff(1469,plain,
% 1.44/1.61 (~b(elem!1, s(s(s(z))))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[1468, 1459])).
% 1.44/1.61 tff(1470,assumption,(b(elem!1, s(s(s(z))))), introduced(assumption)).
% 1.44/1.61 tff(1471,plain,
% 1.44/1.61 ($false),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1470, 1469])).
% 1.44/1.61 tff(1472,plain,((~(s(s(s(z))) = elem!1)) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.61 tff(1473,plain,
% 1.44/1.61 (~(s(s(s(z))) = elem!1)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1472, 1456])).
% 1.44/1.61 tff(1474,plain,
% 1.44/1.61 (r(elem!1, s(z))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[97, 83])).
% 1.44/1.61 tff(1475,plain,
% 1.44/1.61 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(1476,plain,
% 1.44/1.61 (((~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(1477,plain,
% 1.44/1.61 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z)))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1476])).
% 1.44/1.61 tff(1478,plain,
% 1.44/1.61 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))))),
% 1.44/1.61 inference(transitivity,[status(thm)],[1477, 1475])).
% 1.44/1.61 tff(1479,plain,
% 1.44/1.61 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(1480,plain,
% 1.44/1.61 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z)))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[1479, 1478])).
% 1.44/1.61 tff(1481,plain,
% 1.44/1.61 ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z)))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1480, 124])).
% 1.44/1.61 tff(1482,plain,
% 1.44/1.61 (~r(s(s(s(z))), elem!1)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1481, 1474, 114])).
% 1.44/1.61 tff(1483,assumption,(~(s(s(s(z))) = elem!1)), introduced(assumption)).
% 1.44/1.61 tff(1484,assumption,(~r(s(s(s(z))), elem!1)), introduced(assumption)).
% 1.44/1.61 tff(1485,plain,
% 1.44/1.61 (((~![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))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(1486,plain,
% 1.44/1.61 ((~![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))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(1487,plain,
% 1.44/1.61 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1)),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[1486, 1485])).
% 1.44/1.61 tff(1488,plain,
% 1.44/1.61 ($false),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1487, 43, 1, 1484, 1483])).
% 1.44/1.61 tff(1489,plain,(b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.61 tff(1490,plain,
% 1.44/1.61 (b(s(s(s(z))), elem!1)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1489, 1482, 1473])).
% 1.44/1.61 tff(1491,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(1492,plain,
% 1.44/1.61 (((~b(elem!1, s(s(s(z))))) | (~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), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(1493,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1492])).
% 1.44/1.61 tff(1494,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.44/1.61 inference(transitivity,[status(thm)],[1493, 1491])).
% 1.44/1.61 tff(1495,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~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)))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(1496,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[1495, 1494])).
% 1.44/1.61 tff(1497,plain,
% 1.44/1.61 (~b(s(z), elem!1)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1496, 306, 8, 1490, 1456])).
% 1.44/1.61 tff(1498,plain,
% 1.44/1.61 (((~![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))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(1499,plain,
% 1.44/1.61 ((~![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))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(1500,plain,
% 1.44/1.61 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1)),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[1499, 1498])).
% 1.44/1.61 tff(1501,plain,
% 1.44/1.61 (r(s(z), elem!1)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1500, 43, 1497, 90])).
% 1.44/1.61 tff(1502,assumption,(z = elem!1), introduced(assumption)).
% 1.44/1.61 tff(1503,plain,
% 1.44/1.61 (s(z) = s(elem!1)),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1502])).
% 1.44/1.61 tff(1504,plain,
% 1.44/1.61 (s(elem!1) = s(z)),
% 1.44/1.61 inference(symmetry,[status(thm)],[1503])).
% 1.44/1.61 tff(1505,assumption,(s(s(s(s(elem!1)))) = s(elem!1)), introduced(assumption)).
% 1.44/1.61 tff(1506,plain,
% 1.44/1.61 (s(s(z)) = s(s(elem!1))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1503])).
% 1.44/1.61 tff(1507,plain,
% 1.44/1.61 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1506])).
% 1.44/1.61 tff(1508,plain,
% 1.44/1.61 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1507])).
% 1.44/1.61 tff(1509,plain,
% 1.44/1.61 (s(s(s(s(z)))) = s(z)),
% 1.44/1.61 inference(transitivity,[status(thm)],[1508, 1505, 1504])).
% 1.44/1.61 tff(1510,plain,
% 1.44/1.61 ($false),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[324, 1509])).
% 1.44/1.61 tff(1511,plain,((~(s(s(s(s(elem!1)))) = s(elem!1))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.61 tff(1512,plain,
% 1.44/1.61 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1511, 1502])).
% 1.44/1.61 tff(1513,assumption,(elem!1 = s(s(s(elem!1)))), introduced(assumption)).
% 1.44/1.61 tff(1514,plain,
% 1.44/1.61 (s(elem!1) = s(s(s(s(elem!1))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1513])).
% 1.44/1.61 tff(1515,plain,
% 1.44/1.61 (s(s(s(s(elem!1)))) = s(elem!1)),
% 1.44/1.61 inference(symmetry,[status(thm)],[1514])).
% 1.44/1.61 tff(1516,assumption,(~(s(s(s(s(elem!1)))) = s(elem!1))), introduced(assumption)).
% 1.44/1.61 tff(1517,plain,
% 1.44/1.61 ($false),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1516, 1515])).
% 1.44/1.61 tff(1518,plain,((~(elem!1 = s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.61 tff(1519,plain,
% 1.44/1.61 (~(elem!1 = s(s(s(elem!1))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1518, 1512])).
% 1.44/1.61 tff(1520,plain,
% 1.44/1.61 (r(s(z), z) <=> r(s(z), elem!1)),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1502])).
% 1.44/1.61 tff(1521,plain,
% 1.44/1.61 (r(s(z), elem!1) <=> r(s(z), z)),
% 1.44/1.61 inference(symmetry,[status(thm)],[1520])).
% 1.44/1.61 tff(1522,plain,
% 1.44/1.61 (r(s(z), z)),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[4, 1521])).
% 1.44/1.61 tff(1523,plain,
% 1.44/1.61 ($false),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[214, 1522])).
% 1.44/1.61 tff(1524,plain,((~(z = elem!1)) | r(s(z), z) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.61 tff(1525,plain,
% 1.44/1.61 (r(s(z), z)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1524, 1502, 4])).
% 1.44/1.61 tff(1526,assumption,(~(s(s(s(elem!1))) = elem!1)), introduced(assumption)).
% 1.44/1.61 tff(1527,plain,
% 1.44/1.61 (~r(s(s(s(z))), z)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[211, 206, 204])).
% 1.44/1.61 tff(1528,plain,
% 1.44/1.61 (b(s(s(s(z))), z)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[202, 43, 169, 1527])).
% 1.44/1.61 tff(1529,plain,
% 1.44/1.61 (b(elem!1, z) <=> b(s(s(s(z))), z)),
% 1.44/1.61 inference(monotonicity,[status(thm)],[231])).
% 1.44/1.61 tff(1530,plain,
% 1.44/1.61 (b(s(s(s(z))), z) <=> b(elem!1, z)),
% 1.44/1.61 inference(symmetry,[status(thm)],[1529])).
% 1.44/1.61 tff(1531,assumption,(b(s(s(s(z))), z)), introduced(assumption)).
% 1.44/1.61 tff(1532,plain,
% 1.44/1.61 (b(elem!1, z)),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[1531, 1530])).
% 1.44/1.61 tff(1533,plain,
% 1.44/1.61 ($false),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[2, 1532])).
% 1.44/1.61 tff(1534,plain,((~(elem!1 = s(s(s(z))))) | b(elem!1, z) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.61 tff(1535,plain,
% 1.44/1.61 (~(elem!1 = s(s(s(z))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1534, 1528, 2])).
% 1.44/1.61 tff(1536,plain,
% 1.44/1.61 (~r(elem!1, s(s(s(z))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[127, 124, 206, 359])).
% 1.44/1.61 tff(1537,plain,
% 1.44/1.61 (b(elem!1, s(s(s(z))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[131, 43, 1536, 1535])).
% 1.44/1.61 tff(1538,plain,
% 1.44/1.61 ((~(elem!1 = s(s(s(z))))) <=> (~(s(s(s(z))) = elem!1))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1414])).
% 1.44/1.61 tff(1539,plain,
% 1.44/1.61 (~(s(s(s(z))) = elem!1)),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[1535, 1538])).
% 1.44/1.61 tff(1540,plain,
% 1.44/1.61 (~r(s(s(s(z))), elem!1)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1481, 359, 206])).
% 1.44/1.61 tff(1541,plain,
% 1.44/1.61 (b(s(s(s(z))), elem!1)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1489, 1540, 1539])).
% 1.44/1.61 tff(1542,plain,
% 1.44/1.61 ((s(s(s(s(elem!1)))) = elem!1) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.44/1.61 inference(commutativity,[status(thm)],[])).
% 1.44/1.61 tff(1543,plain,
% 1.44/1.61 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.44/1.61 inference(symmetry,[status(thm)],[1542])).
% 1.44/1.61 tff(1544,plain,
% 1.44/1.61 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1502])).
% 1.44/1.61 tff(1545,plain,
% 1.44/1.61 ((s(s(s(s(elem!1)))) = z) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.44/1.61 inference(transitivity,[status(thm)],[1544, 1542])).
% 1.44/1.61 tff(1546,plain,
% 1.44/1.61 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.44/1.61 inference(transitivity,[status(thm)],[1545, 1543])).
% 1.44/1.61 tff(1547,plain,
% 1.44/1.61 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1546])).
% 1.44/1.61 tff(1548,plain,
% 1.44/1.61 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(elem!1)))) = z))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(1549,plain,
% 1.44/1.61 (~(s(s(s(s(elem!1)))) = z)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1548, 75])).
% 1.44/1.61 tff(1550,plain,
% 1.44/1.61 (~(s(s(s(s(elem!1)))) = elem!1)),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[1549, 1547])).
% 1.44/1.61 tff(1551,plain,
% 1.44/1.61 (r(s(z), elem!1) <=> r(s(elem!1), elem!1)),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1503])).
% 1.44/1.61 tff(1552,plain,
% 1.44/1.61 (r(s(z), elem!1)),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[204, 1520])).
% 1.44/1.61 tff(1553,plain,
% 1.44/1.61 (r(s(elem!1), elem!1)),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[1552, 1551])).
% 1.44/1.61 tff(1554,plain,
% 1.44/1.61 ((s(s(s(elem!1))) = elem!1) <=> (elem!1 = s(s(s(elem!1))))),
% 1.44/1.61 inference(commutativity,[status(thm)],[])).
% 1.44/1.61 tff(1555,plain,
% 1.44/1.61 ((elem!1 = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 1.44/1.61 inference(symmetry,[status(thm)],[1554])).
% 1.44/1.61 tff(1556,plain,
% 1.44/1.61 (s(s(s(elem!1))) = s(elem!1)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1181, 188])).
% 1.44/1.61 tff(1557,plain,
% 1.44/1.61 ((elem!1 = s(s(s(elem!1)))) <=> (elem!1 = s(elem!1))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1556])).
% 1.44/1.61 tff(1558,plain,
% 1.44/1.61 ((elem!1 = s(s(s(elem!1)))) <=> (s(elem!1) = elem!1)),
% 1.44/1.61 inference(transitivity,[status(thm)],[1557, 1162])).
% 1.44/1.61 tff(1559,plain,
% 1.44/1.61 ((s(elem!1) = elem!1) <=> (elem!1 = s(s(s(elem!1))))),
% 1.44/1.61 inference(symmetry,[status(thm)],[1558])).
% 1.44/1.61 tff(1560,plain,
% 1.44/1.61 ((s(elem!1) = elem!1) <=> (s(s(s(elem!1))) = elem!1)),
% 1.44/1.61 inference(transitivity,[status(thm)],[1559, 1555])).
% 1.44/1.61 tff(1561,plain,
% 1.44/1.61 (s(elem!1) = elem!1),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[195, 188])).
% 1.44/1.61 tff(1562,plain,
% 1.44/1.61 (s(s(s(elem!1))) = elem!1),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[1561, 1560])).
% 1.44/1.61 tff(1563,plain,
% 1.44/1.61 ($false),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1526, 1562])).
% 1.44/1.61 tff(1564,plain,((~(s(s(elem!1)) = s(elem!1))) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.61 tff(1565,plain,
% 1.44/1.61 (~(s(s(elem!1)) = s(elem!1))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1564, 1526])).
% 1.44/1.61 tff(1566,plain,
% 1.44/1.61 (r(z, s(elem!1)) <=> r(elem!1, s(elem!1))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1502])).
% 1.44/1.61 tff(1567,plain,
% 1.44/1.61 (r(elem!1, s(elem!1)) <=> r(z, s(elem!1))),
% 1.44/1.61 inference(symmetry,[status(thm)],[1566])).
% 1.44/1.61 tff(1568,plain,
% 1.44/1.61 (r(elem!1, s(z)) <=> r(elem!1, s(elem!1))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1503])).
% 1.44/1.61 tff(1569,plain,
% 1.44/1.61 (r(elem!1, s(z)) <=> r(z, s(elem!1))),
% 1.44/1.61 inference(transitivity,[status(thm)],[1568, 1567])).
% 1.44/1.61 tff(1570,plain,
% 1.44/1.61 (r(z, s(elem!1))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[359, 1569])).
% 1.44/1.61 tff(1571,plain,
% 1.44/1.61 (r(s(s(s(z))), s(z)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1507, 1503])).
% 1.44/1.61 tff(1572,plain,
% 1.44/1.61 (r(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[206, 1571])).
% 1.44/1.61 tff(1573,plain,
% 1.44/1.61 ((s(elem!1) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.44/1.61 inference(commutativity,[status(thm)],[])).
% 1.44/1.61 tff(1574,plain,
% 1.44/1.61 ((s(z) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1503])).
% 1.44/1.61 tff(1575,plain,
% 1.44/1.61 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.44/1.61 inference(transitivity,[status(thm)],[1574, 1573])).
% 1.44/1.61 tff(1576,plain,
% 1.44/1.61 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1575])).
% 1.44/1.61 tff(1577,plain,
% 1.44/1.61 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[645, 1576])).
% 1.44/1.61 tff(1578,plain,
% 1.44/1.61 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[152, 1577])).
% 1.44/1.61 tff(1579,plain,
% 1.44/1.61 (b(z, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1502])).
% 1.44/1.61 tff(1580,plain,
% 1.44/1.61 (b(elem!1, s(s(s(elem!1)))) <=> b(z, s(s(s(elem!1))))),
% 1.44/1.61 inference(symmetry,[status(thm)],[1579])).
% 1.44/1.61 tff(1581,plain,
% 1.44/1.61 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1507])).
% 1.44/1.61 tff(1582,plain,
% 1.44/1.61 (b(elem!1, s(s(s(z)))) <=> b(z, s(s(s(elem!1))))),
% 1.44/1.61 inference(transitivity,[status(thm)],[1581, 1580])).
% 1.44/1.61 tff(1583,plain,
% 1.44/1.61 (b(z, s(s(s(elem!1))))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[1470, 1582])).
% 1.44/1.61 tff(1584,plain,
% 1.44/1.61 (~r(z, s(s(elem!1)))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[799, 244, 791])).
% 1.44/1.61 tff(1585,plain,
% 1.44/1.61 (b(z, s(s(elem!1)))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[460, 1584])).
% 1.44/1.61 tff(1586,plain,
% 1.44/1.61 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[659, 244, 654])).
% 1.44/1.61 tff(1587,plain,
% 1.44/1.61 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[610, 1586, 894])).
% 1.44/1.61 tff(1588,plain,
% 1.44/1.61 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[886, 244, 654])).
% 1.44/1.61 tff(1589,plain,
% 1.44/1.61 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[891, 1588, 157])).
% 1.44/1.61 tff(1590,assumption,(b(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 1.44/1.61 tff(1591,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(1592,plain,
% 1.44/1.61 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(1593,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1592])).
% 1.44/1.62 tff(1594,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.44/1.62 inference(transitivity,[status(thm)],[1593, 1591])).
% 1.44/1.62 tff(1595,plain,
% 1.44/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))),
% 1.44/1.62 inference(quant_inst,[status(thm)],[])).
% 1.44/1.62 tff(1596,plain,
% 1.44/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[1595, 1594])).
% 1.44/1.62 tff(1597,plain,
% 1.44/1.62 ($false),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1596, 306, 818, 1198, 1590, 601])).
% 1.44/1.62 tff(1598,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.62 tff(1599,plain,
% 1.44/1.62 ($false),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1598, 1589, 1587, 818, 1585])).
% 1.44/1.62 tff(1600,plain,((~r(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.62 tff(1601,plain,
% 1.44/1.62 (~r(s(s(elem!1)), s(elem!1))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1600, 1583, 1578, 1572, 1570])).
% 1.44/1.62 tff(1602,plain,
% 1.44/1.62 (b(s(s(elem!1)), s(elem!1))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[994, 1601, 1565])).
% 1.44/1.62 tff(1603,plain,
% 1.44/1.62 ((s(s(elem!1)) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.44/1.62 inference(commutativity,[status(thm)],[])).
% 1.44/1.62 tff(1604,plain,
% 1.44/1.62 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[1506, 1508])).
% 1.44/1.62 tff(1605,plain,
% 1.44/1.62 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.44/1.62 inference(transitivity,[status(thm)],[1604, 1603])).
% 1.44/1.62 tff(1606,plain,
% 1.44/1.62 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[1605])).
% 1.44/1.62 tff(1607,assumption,(s(s(z)) = s(s(s(s(z))))), introduced(assumption)).
% 1.44/1.62 tff(1608,plain,
% 1.44/1.62 (inj_0(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[1607])).
% 1.44/1.62 tff(1609,plain,
% 1.44/1.62 (inj_0(s(s(s(s(z))))) = inj_0(s(s(z)))),
% 1.44/1.62 inference(symmetry,[status(thm)],[1608])).
% 1.44/1.62 tff(1610,plain,
% 1.44/1.62 (s(s(s(z))) = s(z)),
% 1.44/1.62 inference(transitivity,[status(thm)],[321, 1609, 546])).
% 1.44/1.62 tff(1611,plain,
% 1.44/1.62 ($false),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[108, 1610])).
% 1.44/1.62 tff(1612,plain,(~(s(s(z)) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.62 tff(1613,plain,
% 1.44/1.62 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[1612, 1606])).
% 1.44/1.62 tff(1614,plain,
% 1.44/1.62 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[159, 1578])).
% 1.44/1.62 tff(1615,plain,
% 1.44/1.62 (elem!1 = z),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[1502, 162])).
% 1.44/1.62 tff(1616,assumption,(~(elem!1 = z)), introduced(assumption)).
% 1.44/1.62 tff(1617,plain,
% 1.44/1.62 ($false),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1616, 1615])).
% 1.44/1.62 tff(1618,plain,((~(z = elem!1)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.62 tff(1619,plain,
% 1.44/1.62 (elem!1 = z),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1618, 1502])).
% 1.44/1.62 tff(1620,assumption,(elem!1 = z), introduced(assumption)).
% 1.44/1.62 tff(1621,plain,
% 1.44/1.62 (s(elem!1) = s(z)),
% 1.44/1.62 inference(monotonicity,[status(thm)],[1620])).
% 1.44/1.62 tff(1622,plain,
% 1.44/1.62 (s(s(elem!1)) = s(s(z))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[1621])).
% 1.44/1.62 tff(1623,plain,
% 1.44/1.62 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[1622])).
% 1.44/1.62 tff(1624,plain,
% 1.44/1.62 (r(s(s(s(elem!1))), z) <=> r(s(s(s(z))), z)),
% 1.44/1.62 inference(monotonicity,[status(thm)],[1623])).
% 1.44/1.62 tff(1625,plain,
% 1.44/1.62 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), z)),
% 1.44/1.62 inference(monotonicity,[status(thm)],[1620])).
% 1.44/1.62 tff(1626,plain,
% 1.44/1.62 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(z))), z)),
% 1.44/1.62 inference(transitivity,[status(thm)],[1625, 1624])).
% 1.44/1.62 tff(1627,assumption,(r(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 1.44/1.62 tff(1628,plain,
% 1.44/1.62 (r(s(s(s(z))), z)),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[1627, 1626])).
% 1.44/1.62 tff(1629,assumption,(~r(s(s(s(z))), z)), introduced(assumption)).
% 1.44/1.62 tff(1630,plain,
% 1.44/1.62 ($false),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1629, 1628])).
% 1.44/1.62 tff(1631,plain,((~r(s(s(s(elem!1))), elem!1)) | r(s(s(s(z))), z) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.62 tff(1632,plain,
% 1.44/1.62 (~r(s(s(s(elem!1))), elem!1)),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1631, 1619, 1527])).
% 1.44/1.62 tff(1633,plain,
% 1.44/1.62 (((~![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))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(1634,plain,
% 1.44/1.62 ((~![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))),
% 1.44/1.62 inference(quant_inst,[status(thm)],[])).
% 1.44/1.62 tff(1635,plain,
% 1.44/1.62 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1)),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[1634, 1633])).
% 1.44/1.62 tff(1636,plain,
% 1.44/1.62 ((s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1)),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1635, 43])).
% 1.44/1.62 tff(1637,plain,
% 1.44/1.62 (b(s(s(s(elem!1))), elem!1)),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1636, 1632, 1526])).
% 1.44/1.62 tff(1638,plain,
% 1.44/1.62 (b(elem!1, s(s(s(elem!1))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[1470, 1581])).
% 1.44/1.62 tff(1639,plain,
% 1.44/1.62 (s(s(s(elem!1))) = elem!1),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[1513, 1555])).
% 1.44/1.62 tff(1640,plain,
% 1.44/1.62 ($false),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1526, 1639])).
% 1.44/1.62 tff(1641,plain,((~(elem!1 = s(s(s(elem!1))))) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.62 tff(1642,plain,
% 1.44/1.62 (~(elem!1 = s(s(s(elem!1))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1641, 1526])).
% 1.44/1.62 tff(1643,plain,
% 1.44/1.62 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1)))))),
% 1.44/1.62 inference(quant_inst,[status(thm)],[])).
% 1.44/1.62 tff(1644,plain,
% 1.44/1.62 (inj_0(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1643, 59])).
% 1.44/1.62 tff(1645,assumption,(s(s(elem!1)) = s(s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.44/1.62 tff(1646,plain,
% 1.44/1.62 (s(s(s(s(s(elem!1))))) = s(s(elem!1))),
% 1.44/1.62 inference(symmetry,[status(thm)],[1645])).
% 1.44/1.62 tff(1647,plain,
% 1.44/1.62 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(elem!1)))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[1646])).
% 1.44/1.62 tff(1648,plain,
% 1.44/1.62 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.44/1.62 inference(symmetry,[status(thm)],[1647])).
% 1.44/1.62 tff(1649,plain,
% 1.44/1.62 (s(elem!1) = s(s(s(s(elem!1))))),
% 1.44/1.62 inference(transitivity,[status(thm)],[67, 1648, 1644])).
% 1.44/1.62 tff(1650,plain,
% 1.44/1.62 (inj_0(s(elem!1)) = inj_0(s(s(s(s(elem!1)))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[1649])).
% 1.44/1.62 tff(1651,plain,
% 1.44/1.62 (elem!1 = inj_0(s(elem!1))),
% 1.44/1.62 inference(symmetry,[status(thm)],[135])).
% 1.44/1.62 tff(1652,plain,
% 1.44/1.62 (elem!1 = s(s(s(elem!1)))),
% 1.44/1.62 inference(transitivity,[status(thm)],[1651, 1650, 1280])).
% 1.44/1.62 tff(1653,assumption,(~(elem!1 = s(s(s(elem!1))))), introduced(assumption)).
% 1.44/1.62 tff(1654,plain,
% 1.44/1.62 ($false),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1653, 1652])).
% 1.44/1.62 tff(1655,plain,((~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))) | (elem!1 = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.62 tff(1656,plain,
% 1.44/1.62 (~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1655, 1642])).
% 1.44/1.62 tff(1657,plain,
% 1.44/1.62 ((s(s(elem!1)) = s(elem!1)) <=> (s(elem!1) = s(s(elem!1)))),
% 1.44/1.62 inference(symmetry,[status(thm)],[398])).
% 1.44/1.62 tff(1658,plain,
% 1.44/1.62 ((~(s(s(elem!1)) = s(elem!1))) <=> (~(s(elem!1) = s(s(elem!1))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[1657])).
% 1.44/1.62 tff(1659,plain,
% 1.44/1.62 (~(s(elem!1) = s(s(elem!1)))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[403, 1658])).
% 1.44/1.62 tff(1660,plain,
% 1.44/1.62 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 1.44/1.62 inference(monotonicity,[status(thm)],[1502])).
% 1.44/1.62 tff(1661,plain,
% 1.44/1.62 ((~(s(s(elem!1)) = z)) <=> (~(s(s(elem!1)) = elem!1))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[1660])).
% 1.44/1.62 tff(1662,plain,
% 1.44/1.62 (~(s(s(elem!1)) = elem!1)),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[454, 1661])).
% 1.44/1.62 tff(1663,assumption,(b(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 1.44/1.62 tff(1664,assumption,(b(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 1.44/1.62 tff(1665,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(1666,plain,
% 1.44/1.62 (((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(1667,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[1666])).
% 1.44/1.62 tff(1668,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.44/1.62 inference(transitivity,[status(thm)],[1667, 1665])).
% 1.44/1.62 tff(1669,plain,
% 1.44/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.44/1.62 inference(quant_inst,[status(thm)],[])).
% 1.44/1.62 tff(1670,plain,
% 1.44/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[1669, 1668])).
% 1.44/1.62 tff(1671,plain,
% 1.44/1.62 ($false),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1670, 306, 30, 1663, 1664, 601])).
% 1.44/1.62 tff(1672,plain,((~b(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(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.62 tff(1673,plain,
% 1.44/1.62 (~b(s(s(elem!1)), elem!1)),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1672, 601, 1664, 1663])).
% 1.44/1.62 tff(1674,plain,
% 1.44/1.62 (r(s(s(elem!1)), elem!1)),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[47, 1673, 1662])).
% 1.44/1.62 tff(1675,plain,
% 1.44/1.62 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(1676,plain,
% 1.44/1.62 (((~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(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(1677,plain,
% 1.44/1.62 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1))))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[1676])).
% 1.44/1.62 tff(1678,plain,
% 1.44/1.62 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.44/1.62 inference(transitivity,[status(thm)],[1677, 1675])).
% 1.44/1.62 tff(1679,plain,
% 1.44/1.62 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.44/1.62 inference(quant_inst,[status(thm)],[])).
% 1.44/1.62 tff(1680,plain,
% 1.44/1.62 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[1679, 1678])).
% 1.44/1.62 tff(1681,plain,
% 1.44/1.62 (~r(s(elem!1), s(s(elem!1)))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1680, 124, 802, 1674])).
% 1.44/1.62 tff(1682,plain,
% 1.44/1.62 (((~![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))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(1683,plain,
% 1.44/1.62 ((~![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))))),
% 1.44/1.62 inference(quant_inst,[status(thm)],[])).
% 1.44/1.62 tff(1684,plain,
% 1.44/1.62 ((~![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)))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[1683, 1682])).
% 1.44/1.62 tff(1685,plain,
% 1.44/1.62 ((s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1)))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1684, 43, 1681])).
% 1.44/1.62 tff(1686,plain,
% 1.44/1.62 (b(s(elem!1), s(s(elem!1)))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1685, 1659])).
% 1.44/1.62 tff(1687,plain,
% 1.44/1.62 ((s(s(elem!1)) = z) <=> (elem!1 = s(s(elem!1)))),
% 1.44/1.62 inference(transitivity,[status(thm)],[1660, 1170])).
% 1.44/1.62 tff(1688,plain,
% 1.44/1.62 ((~(s(s(elem!1)) = z)) <=> (~(elem!1 = s(s(elem!1))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[1687])).
% 1.44/1.62 tff(1689,plain,
% 1.44/1.62 (~(elem!1 = s(s(elem!1)))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[454, 1688])).
% 1.44/1.62 tff(1690,assumption,(b(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 1.44/1.62 tff(1691,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(1692,plain,
% 1.44/1.62 (((~b(s(elem!1), s(s(elem!1)))) | (~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(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(1693,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[1692])).
% 1.44/1.62 tff(1694,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.44/1.62 inference(transitivity,[status(thm)],[1693, 1691])).
% 1.44/1.62 tff(1695,plain,
% 1.44/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~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)))),
% 1.44/1.62 inference(quant_inst,[status(thm)],[])).
% 1.44/1.62 tff(1696,plain,
% 1.44/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[1695, 1694])).
% 1.44/1.62 tff(1697,plain,
% 1.44/1.62 ($false),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1696, 306, 1005, 1003, 1664, 601, 1690])).
% 1.44/1.62 tff(1698,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.62 tff(1699,plain,
% 1.44/1.62 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1698, 1003, 1690, 1664, 1005])).
% 1.44/1.62 tff(1700,plain,
% 1.44/1.62 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[610, 1699, 1614])).
% 1.44/1.62 tff(1701,plain,
% 1.44/1.62 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.44/1.62 inference(symmetry,[status(thm)],[1623])).
% 1.44/1.62 tff(1702,assumption,(s(s(s(s(z)))) = s(s(s(z)))), introduced(assumption)).
% 1.44/1.62 tff(1703,plain,
% 1.44/1.62 (s(s(s(s(s(z))))) = s(s(s(s(z))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[1702])).
% 1.44/1.62 tff(1704,plain,
% 1.44/1.62 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[1623])).
% 1.44/1.62 tff(1705,plain,
% 1.44/1.62 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[1704])).
% 1.44/1.62 tff(1706,plain,
% 1.44/1.62 (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))),
% 1.44/1.62 inference(transitivity,[status(thm)],[1705, 1703, 1702, 1701])).
% 1.44/1.62 tff(1707,plain,
% 1.44/1.62 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(z)))))),
% 1.44/1.62 inference(commutativity,[status(thm)],[])).
% 1.44/1.62 tff(1708,plain,
% 1.44/1.62 ((s(s(s(s(elem!1)))) = s(s(elem!1))) <=> (s(s(s(s(z)))) = s(s(z)))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[1704, 1622])).
% 1.44/1.62 tff(1709,plain,
% 1.44/1.62 ((s(s(s(s(elem!1)))) = s(s(elem!1))) <=> (s(s(z)) = s(s(s(s(z)))))),
% 1.44/1.62 inference(transitivity,[status(thm)],[1708, 1707])).
% 1.44/1.62 tff(1710,plain,
% 1.44/1.62 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.44/1.62 inference(symmetry,[status(thm)],[1709])).
% 1.44/1.62 tff(1711,plain,
% 1.44/1.62 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[1710])).
% 1.44/1.62 tff(1712,plain,
% 1.44/1.62 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[1612, 1711])).
% 1.44/1.62 tff(1713,assumption,(s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))), introduced(assumption)).
% 1.44/1.62 tff(1714,plain,
% 1.44/1.62 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(s(elem!1))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[1713])).
% 1.44/1.62 tff(1715,plain,
% 1.44/1.62 (s(s(s(s(elem!1)))) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.44/1.62 inference(symmetry,[status(thm)],[1644])).
% 1.44/1.62 tff(1716,plain,
% 1.44/1.62 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.44/1.62 inference(transitivity,[status(thm)],[1715, 1714, 139])).
% 1.44/1.62 tff(1717,assumption,(~(s(s(s(s(elem!1)))) = s(s(elem!1)))), introduced(assumption)).
% 1.44/1.62 tff(1718,plain,
% 1.44/1.62 ($false),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1717, 1716])).
% 1.44/1.62 tff(1719,plain,((~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.62 tff(1720,plain,
% 1.44/1.62 (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1719, 1712])).
% 1.44/1.62 tff(1721,plain,
% 1.44/1.62 ($false),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1720, 1706])).
% 1.44/1.62 tff(1722,plain,((~(s(s(s(s(z)))) = s(s(s(z))))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.62 tff(1723,plain,
% 1.44/1.62 (~(s(s(s(s(z)))) = s(s(s(z))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1722, 1619])).
% 1.44/1.62 tff(1724,plain,
% 1.44/1.62 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[1508])).
% 1.44/1.62 tff(1725,plain,
% 1.44/1.62 (b(s(s(s(s(elem!1)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.44/1.62 inference(symmetry,[status(thm)],[1724])).
% 1.44/1.62 tff(1726,plain,
% 1.44/1.62 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.44/1.62 inference(symmetry,[status(thm)],[1507])).
% 1.44/1.62 tff(1727,plain,
% 1.44/1.62 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[1726])).
% 1.44/1.62 tff(1728,plain,
% 1.44/1.62 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.44/1.62 inference(transitivity,[status(thm)],[1727, 1725])).
% 1.44/1.62 tff(1729,plain,
% 1.44/1.62 ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) <=> (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[1728])).
% 1.44/1.62 tff(1730,assumption,(r(s(s(elem!1)), elem!1)), introduced(assumption)).
% 1.44/1.62 tff(1731,assumption,(~(s(s(s(s(elem!1)))) = elem!1)), introduced(assumption)).
% 1.44/1.62 tff(1732,assumption,(~b(s(s(s(s(elem!1)))), elem!1)), introduced(assumption)).
% 1.44/1.62 tff(1733,plain,
% 1.44/1.62 (((~![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))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(1734,plain,
% 1.44/1.62 ((~![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))),
% 1.44/1.62 inference(quant_inst,[status(thm)],[])).
% 1.44/1.62 tff(1735,plain,
% 1.44/1.62 ((~![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)),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[1734, 1733])).
% 1.44/1.62 tff(1736,plain,
% 1.44/1.62 ((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)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1735, 43])).
% 1.44/1.63 tff(1737,plain,
% 1.44/1.63 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1736, 1732, 1731])).
% 1.44/1.63 tff(1738,plain,
% 1.44/1.63 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(1739,plain,
% 1.44/1.63 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(1740,plain,
% 1.44/1.63 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[1739, 1738])).
% 1.44/1.63 tff(1741,plain,
% 1.44/1.63 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1740, 124, 802, 1737])).
% 1.44/1.63 tff(1742,assumption,(~b(s(s(s(s(elem!1)))), s(s(elem!1)))), introduced(assumption)).
% 1.44/1.63 tff(1743,plain,
% 1.44/1.63 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1302, 1742, 1717])).
% 1.44/1.63 tff(1744,assumption,(s(s(s(s(elem!1)))) = elem!1), introduced(assumption)).
% 1.44/1.63 tff(1745,plain,
% 1.44/1.63 (b(s(s(s(s(elem!1)))), s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[1744])).
% 1.44/1.63 tff(1746,plain,
% 1.44/1.63 (b(elem!1, s(s(elem!1))) <=> b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.44/1.63 inference(symmetry,[status(thm)],[1745])).
% 1.44/1.63 tff(1747,plain,
% 1.44/1.63 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[1003, 1746])).
% 1.44/1.63 tff(1748,plain,
% 1.44/1.63 ($false),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1742, 1747])).
% 1.44/1.63 tff(1749,plain,((~(s(s(s(s(elem!1)))) = elem!1)) | b(s(s(s(s(elem!1)))), s(s(elem!1))) | (~b(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.63 tff(1750,plain,
% 1.44/1.63 (~(s(s(s(s(elem!1)))) = elem!1)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1749, 1742, 1003])).
% 1.44/1.63 tff(1751,plain,
% 1.44/1.63 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1736, 1750, 1732])).
% 1.44/1.63 tff(1752,plain,
% 1.44/1.63 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(1753,plain,
% 1.44/1.63 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(1754,plain,
% 1.44/1.63 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[1753, 1752])).
% 1.44/1.63 tff(1755,plain,
% 1.44/1.63 ($false),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1754, 124, 1730, 1751, 1743])).
% 1.44/1.63 tff(1756,plain,(b(s(s(s(s(elem!1)))), s(s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | b(s(s(s(s(elem!1)))), elem!1) | (~b(elem!1, s(s(elem!1)))) | (s(s(s(s(elem!1)))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.63 tff(1757,plain,
% 1.44/1.63 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1756, 1732, 1717, 1003, 1730])).
% 1.44/1.63 tff(1758,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(1759,plain,
% 1.44/1.63 (((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), 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(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(1760,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(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(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[1759])).
% 1.44/1.63 tff(1761,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(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(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.44/1.63 inference(transitivity,[status(thm)],[1760, 1758])).
% 1.44/1.63 tff(1762,plain,
% 1.44/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(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(s(s(elem!1)))), s(elem!1))))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(1763,plain,
% 1.44/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[1762, 1761])).
% 1.44/1.63 tff(1764,plain,
% 1.44/1.63 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1763, 306, 1005, 1757, 1690])).
% 1.44/1.63 tff(1765,plain,
% 1.44/1.63 (((~![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)))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(1766,plain,
% 1.44/1.63 ((~![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)))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(1767,plain,
% 1.44/1.63 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(elem!1)) | b(s(s(s(s(elem!1)))), s(elem!1)) | r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[1766, 1765])).
% 1.44/1.63 tff(1768,plain,
% 1.44/1.63 ($false),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1767, 43, 1516, 1764, 1741])).
% 1.44/1.63 tff(1769,plain,(b(s(s(s(s(elem!1)))), elem!1) | (s(s(s(s(elem!1)))) = s(elem!1)) | (~r(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (s(s(s(s(elem!1)))) = elem!1) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.63 tff(1770,plain,
% 1.44/1.63 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1769, 1003, 802, 1005, 1690, 1550, 1613, 1512, 1730])).
% 1.44/1.63 tff(1771,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(1772,plain,
% 1.44/1.63 (((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(1773,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[1772])).
% 1.44/1.63 tff(1774,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.44/1.63 inference(transitivity,[status(thm)],[1773, 1771])).
% 1.44/1.63 tff(1775,plain,
% 1.44/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(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))))))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(1776,plain,
% 1.44/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[1775, 1774])).
% 1.44/1.63 tff(1777,plain,
% 1.44/1.63 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1776, 306, 1663, 1664, 1770])).
% 1.44/1.63 tff(1778,plain,
% 1.44/1.63 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[1777, 1729])).
% 1.44/1.63 tff(1779,plain,
% 1.44/1.63 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[712, 1778, 1723])).
% 1.44/1.63 tff(1780,plain,
% 1.44/1.63 (s(s(z)) = s(s(elem!1))),
% 1.44/1.63 inference(symmetry,[status(thm)],[1622])).
% 1.44/1.63 tff(1781,plain,
% 1.44/1.63 (r(s(s(s(z))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[1701, 1780])).
% 1.44/1.63 tff(1782,plain,
% 1.44/1.63 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(z))), s(s(z)))),
% 1.44/1.63 inference(symmetry,[status(thm)],[1781])).
% 1.44/1.63 tff(1783,plain,
% 1.44/1.63 (r(s(s(s(z))), s(s(z)))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[653, 1782])).
% 1.44/1.63 tff(1784,plain,
% 1.44/1.63 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 1.44/1.63 inference(symmetry,[status(thm)],[1704])).
% 1.44/1.63 tff(1785,plain,
% 1.44/1.63 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[1784, 1780])).
% 1.44/1.63 tff(1786,plain,
% 1.44/1.63 (r(s(s(s(s(elem!1)))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(z)))),
% 1.44/1.63 inference(symmetry,[status(thm)],[1785])).
% 1.44/1.63 tff(1787,plain,
% 1.44/1.63 (r(s(s(s(s(z)))), s(s(z)))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[1288, 1786])).
% 1.44/1.63 tff(1788,plain,
% 1.44/1.63 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(1789,plain,
% 1.44/1.63 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(1790,plain,
% 1.44/1.63 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[1789, 1788])).
% 1.44/1.63 tff(1791,plain,
% 1.44/1.63 ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1790, 124, 1033])).
% 1.44/1.63 tff(1792,plain,
% 1.44/1.63 ($false),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1791, 1787, 1783])).
% 1.44/1.63 tff(1793,plain,((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~(elem!1 = z)) | (~r(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.63 tff(1794,plain,
% 1.44/1.63 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1793, 1779, 1619, 1700])).
% 1.44/1.63 tff(1795,plain,
% 1.44/1.63 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1302, 1794, 1613])).
% 1.44/1.63 tff(1796,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(1797,plain,
% 1.44/1.63 (((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), 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(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(1798,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[1797])).
% 1.44/1.63 tff(1799,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.44/1.63 inference(transitivity,[status(thm)],[1798, 1796])).
% 1.44/1.63 tff(1800,plain,
% 1.44/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), 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)))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(1801,plain,
% 1.44/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[1800, 1799])).
% 1.44/1.63 tff(1802,plain,
% 1.44/1.63 ($false),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1801, 306, 1005, 1003, 1770, 1795, 1690])).
% 1.44/1.63 tff(1803,plain,((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~(z = elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.63 tff(1804,plain,
% 1.44/1.63 (~b(elem!1, s(s(elem!1)))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1803, 1686, 1005, 1502, 1663, 1664, 802, 1674])).
% 1.44/1.63 tff(1805,plain,
% 1.44/1.63 (r(elem!1, s(s(elem!1)))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[516, 1804, 1689])).
% 1.44/1.63 tff(1806,plain,
% 1.44/1.63 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[1545])).
% 1.44/1.63 tff(1807,plain,
% 1.44/1.63 (~(elem!1 = s(s(s(s(elem!1)))))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[1549, 1806])).
% 1.44/1.63 tff(1808,plain,
% 1.44/1.63 ((s(s(s(s(s(elem!1))))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(s(s(elem!1))))))),
% 1.44/1.63 inference(commutativity,[status(thm)],[])).
% 1.44/1.63 tff(1809,plain,
% 1.44/1.63 ((s(s(elem!1)) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 1.44/1.63 inference(symmetry,[status(thm)],[1808])).
% 1.44/1.63 tff(1810,plain,
% 1.44/1.63 ((~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))) <=> (~(s(s(s(s(s(elem!1))))) = s(s(elem!1))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[1809])).
% 1.44/1.63 tff(1811,assumption,(~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.44/1.63 tff(1812,plain,
% 1.44/1.63 (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[1811, 1810])).
% 1.44/1.63 tff(1813,plain,
% 1.44/1.63 (s(s(s(s(s(z))))) = s(s(s(s(s(elem!1)))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[1508])).
% 1.44/1.63 tff(1814,plain,
% 1.44/1.63 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))),
% 1.44/1.63 inference(symmetry,[status(thm)],[1813])).
% 1.44/1.63 tff(1815,plain,
% 1.44/1.63 ((s(s(s(s(s(elem!1))))) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(z))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[1814, 1504])).
% 1.44/1.63 tff(1816,plain,
% 1.44/1.63 ((s(s(s(s(s(z))))) = s(z)) <=> (s(s(s(s(s(elem!1))))) = s(elem!1))),
% 1.44/1.63 inference(symmetry,[status(thm)],[1815])).
% 1.44/1.63 tff(1817,plain,
% 1.44/1.63 ((~(s(s(s(s(s(z))))) = s(z))) <=> (~(s(s(s(s(s(elem!1))))) = s(elem!1)))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[1816])).
% 1.44/1.63 tff(1818,plain,
% 1.44/1.63 (~(s(s(s(s(s(elem!1))))) = s(elem!1))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[500, 1817])).
% 1.44/1.63 tff(1819,plain,
% 1.44/1.63 ((s(s(s(s(s(elem!1))))) = z) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 1.44/1.63 inference(monotonicity,[status(thm)],[1502])).
% 1.44/1.63 tff(1820,plain,
% 1.44/1.63 ((~(s(s(s(s(s(elem!1))))) = z)) <=> (~(s(s(s(s(s(elem!1))))) = elem!1))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[1819])).
% 1.44/1.63 tff(1821,plain,
% 1.44/1.63 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(elem!1))))) = z))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(1822,plain,
% 1.44/1.63 (~(s(s(s(s(s(elem!1))))) = z)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1821, 75])).
% 1.44/1.63 tff(1823,plain,
% 1.44/1.63 (~(s(s(s(s(s(elem!1))))) = elem!1)),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[1822, 1820])).
% 1.44/1.63 tff(1824,assumption,(r(s(s(s(s(s(elem!1))))), elem!1)), introduced(assumption)).
% 1.44/1.63 tff(1825,plain,
% 1.44/1.63 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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)))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(1826,plain,
% 1.44/1.63 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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)))))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(1827,plain,
% 1.44/1.63 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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))))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[1826, 1825])).
% 1.44/1.63 tff(1828,plain,
% 1.44/1.63 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1827, 124, 1730, 1824])).
% 1.44/1.63 tff(1829,plain,
% 1.44/1.63 (((~![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))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(1830,plain,
% 1.44/1.63 ((~![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))))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(1831,plain,
% 1.44/1.63 ((~![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)))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[1830, 1829])).
% 1.44/1.63 tff(1832,plain,
% 1.44/1.63 ((s(s(s(s(s(elem!1))))) = s(s(elem!1))) | b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1831, 43, 1828])).
% 1.44/1.63 tff(1833,plain,
% 1.44/1.63 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1832, 1812])).
% 1.44/1.63 tff(1834,plain,
% 1.44/1.63 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(1835,plain,
% 1.44/1.63 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(1836,plain,
% 1.44/1.63 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[1835, 1834])).
% 1.44/1.63 tff(1837,plain,
% 1.44/1.63 (~r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1836, 124, 802, 1824])).
% 1.44/1.63 tff(1838,plain,
% 1.44/1.63 (((~![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)))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(1839,plain,
% 1.44/1.63 ((~![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)))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(1840,plain,
% 1.44/1.64 ((~![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))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[1839, 1838])).
% 1.44/1.64 tff(1841,plain,
% 1.44/1.64 ((s(s(s(s(s(elem!1))))) = s(elem!1)) | b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1840, 43, 1837])).
% 1.44/1.64 tff(1842,plain,
% 1.44/1.64 (b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1841, 1818])).
% 1.44/1.64 tff(1843,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(1844,plain,
% 1.44/1.64 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), 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))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(1845,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), 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)))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[1844])).
% 1.44/1.64 tff(1846,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), 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))))),
% 1.44/1.64 inference(transitivity,[status(thm)],[1845, 1843])).
% 1.44/1.64 tff(1847,plain,
% 1.44/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(1848,plain,
% 1.44/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[1847, 1846])).
% 1.44/1.64 tff(1849,plain,
% 1.44/1.64 ($false),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1848, 306, 1005, 1690, 1842, 1833])).
% 1.44/1.64 tff(1850,plain,((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(s(s(elem!1)))))) | (~(z = elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.64 tff(1851,plain,
% 1.44/1.64 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1850, 1686, 1005, 1811, 1502, 1674, 802])).
% 1.44/1.64 tff(1852,plain,
% 1.44/1.64 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = elem!1) | b(s(s(s(s(s(elem!1))))), elem!1) | r(s(s(s(s(s(elem!1))))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = elem!1) | b(s(s(s(s(s(elem!1))))), elem!1) | r(s(s(s(s(s(elem!1))))), elem!1))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(1853,plain,
% 1.44/1.64 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = elem!1) | b(s(s(s(s(s(elem!1))))), elem!1) | r(s(s(s(s(s(elem!1))))), elem!1))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(1854,plain,
% 1.44/1.64 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = elem!1) | b(s(s(s(s(s(elem!1))))), elem!1) | r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[1853, 1852])).
% 1.44/1.64 tff(1855,plain,
% 1.44/1.64 ((s(s(s(s(s(elem!1))))) = elem!1) | b(s(s(s(s(s(elem!1))))), elem!1) | r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1854, 43])).
% 1.44/1.64 tff(1856,plain,
% 1.44/1.64 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1855, 1851, 1823])).
% 1.44/1.64 tff(1857,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(1858,plain,
% 1.44/1.64 (((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(1859,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[1858])).
% 1.44/1.64 tff(1860,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.44/1.64 inference(transitivity,[status(thm)],[1859, 1857])).
% 1.44/1.64 tff(1861,plain,
% 1.44/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(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))))))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(1862,plain,
% 1.44/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[1861, 1860])).
% 1.44/1.64 tff(1863,plain,
% 1.44/1.64 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1862, 306, 1663, 1664, 1856])).
% 1.44/1.64 tff(1864,plain,
% 1.44/1.64 (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1719, 1613])).
% 1.44/1.64 tff(1865,plain,
% 1.44/1.64 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) | r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) | r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(1866,plain,
% 1.44/1.64 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) | r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(1867,plain,
% 1.44/1.64 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) | r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[1866, 1865])).
% 1.44/1.64 tff(1868,plain,
% 1.44/1.64 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1867, 43, 1864, 1863])).
% 1.44/1.64 tff(1869,plain,
% 1.44/1.64 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(elem!1) = s(s(s(elem!1))))),
% 1.44/1.64 inference(symmetry,[status(thm)],[1573])).
% 1.44/1.64 tff(1870,plain,
% 1.44/1.64 ((~(s(s(s(elem!1))) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(elem!1)))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[1869])).
% 1.44/1.64 tff(1871,plain,
% 1.44/1.64 (~(s(elem!1) = s(s(s(elem!1))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[1577, 1870])).
% 1.44/1.64 tff(1872,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(1873,plain,
% 1.44/1.64 (((~b(s(elem!1), s(s(elem!1)))) | (~b(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(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(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(1874,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(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(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1)))))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[1873])).
% 1.44/1.64 tff(1875,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(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(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.44/1.64 inference(transitivity,[status(thm)],[1874, 1872])).
% 1.44/1.64 tff(1876,plain,
% 1.44/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(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(elem!1), s(s(s(elem!1))))))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(1877,plain,
% 1.44/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1)))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[1876, 1875])).
% 1.44/1.64 tff(1878,plain,
% 1.44/1.64 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1877, 306, 1005, 601, 1686])).
% 1.44/1.64 tff(1879,plain,
% 1.44/1.64 (((~![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)))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(1880,plain,
% 1.44/1.64 ((~![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)))))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(1881,plain,
% 1.44/1.64 ((~![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))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[1880, 1879])).
% 1.44/1.64 tff(1882,plain,
% 1.44/1.64 ((s(elem!1) = s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1881, 43, 1878])).
% 1.44/1.64 tff(1883,plain,
% 1.44/1.64 (r(s(elem!1), s(s(s(elem!1))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1882, 1871])).
% 1.44/1.64 tff(1884,plain,
% 1.44/1.64 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), 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))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(1885,plain,
% 1.44/1.64 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(1886,plain,
% 1.44/1.64 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[1885, 1884])).
% 1.44/1.64 tff(1887,plain,
% 1.44/1.64 (~r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1886, 124, 1883, 1868])).
% 1.44/1.64 tff(1888,plain,
% 1.44/1.64 ((s(s(s(s(s(elem!1))))) = s(elem!1)) | b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1840, 43, 1887])).
% 1.44/1.64 tff(1889,plain,
% 1.44/1.64 (b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1888, 1818])).
% 1.44/1.64 tff(1890,plain,
% 1.44/1.64 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1848, 306, 1005, 1686, 1889])).
% 1.44/1.64 tff(1891,plain,
% 1.44/1.64 ((s(s(s(s(s(elem!1))))) = s(s(elem!1))) | r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1831, 43, 1890])).
% 1.44/1.64 tff(1892,plain,
% 1.44/1.64 (r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1891, 1812])).
% 1.44/1.64 tff(1893,assumption,(s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1))))), introduced(assumption)).
% 1.44/1.64 tff(1894,plain,
% 1.44/1.64 (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))),
% 1.44/1.64 inference(symmetry,[status(thm)],[1893])).
% 1.44/1.64 tff(1895,plain,
% 1.44/1.64 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[1894])).
% 1.44/1.64 tff(1896,plain,
% 1.44/1.64 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(s(s(elem!1)))))),
% 1.44/1.64 inference(symmetry,[status(thm)],[1895])).
% 1.44/1.64 tff(1897,plain,
% 1.44/1.64 (s(s(s(s(elem!1)))) = s(s(s(z)))),
% 1.44/1.64 inference(transitivity,[status(thm)],[1715, 1896, 1280, 1726])).
% 1.44/1.64 tff(1898,plain,
% 1.44/1.64 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 1.44/1.64 inference(symmetry,[status(thm)],[1508])).
% 1.44/1.64 tff(1899,plain,
% 1.44/1.64 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[1898])).
% 1.44/1.64 tff(1900,plain,
% 1.44/1.64 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(s(z))))),
% 1.44/1.64 inference(symmetry,[status(thm)],[1899])).
% 1.44/1.64 tff(1901,plain,
% 1.44/1.64 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(s(elem!1)))) = s(s(s(z)))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[1900])).
% 1.44/1.64 tff(1902,plain,
% 1.44/1.64 (~(s(s(s(s(elem!1)))) = s(s(s(z))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[1723, 1901])).
% 1.44/1.64 tff(1903,plain,
% 1.44/1.64 ($false),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1902, 1897])).
% 1.44/1.64 tff(1904,plain,((~(s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1)))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.64 tff(1905,plain,
% 1.44/1.64 (~(s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1)))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1904, 1502])).
% 1.44/1.64 tff(1906,assumption,(b(s(s(s(s(s(elem!1))))), elem!1)), introduced(assumption)).
% 1.44/1.64 tff(1907,plain,
% 1.44/1.64 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1297, 1288, 970])).
% 1.44/1.64 tff(1908,plain,
% 1.44/1.64 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1736, 1907, 1731])).
% 1.44/1.64 tff(1909,assumption,(~(elem!1 = s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.44/1.64 tff(1910,assumption,(r(elem!1, s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.44/1.64 tff(1911,plain,
% 1.44/1.64 (((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(1912,plain,
% 1.44/1.64 (((~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(elem!1, s(s(s(s(elem!1)))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(1913,plain,
% 1.44/1.64 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1))))))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[1912])).
% 1.44/1.64 tff(1914,plain,
% 1.44/1.64 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.44/1.64 inference(transitivity,[status(thm)],[1913, 1911])).
% 1.44/1.64 tff(1915,plain,
% 1.44/1.64 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(1916,plain,
% 1.44/1.64 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1))))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[1915, 1914])).
% 1.44/1.64 tff(1917,plain,
% 1.44/1.64 ($false),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1916, 124, 1910, 970, 1288])).
% 1.44/1.64 tff(1918,plain,((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.64 tff(1919,plain,
% 1.44/1.64 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1918, 1288, 970])).
% 1.44/1.64 tff(1920,plain,
% 1.44/1.64 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(elem!1))))) | b(elem!1, s(s(s(s(elem!1))))) | r(elem!1, s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(elem!1))))) | b(elem!1, s(s(s(s(elem!1))))) | r(elem!1, s(s(s(s(elem!1))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(1921,plain,
% 1.44/1.64 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(elem!1))))) | b(elem!1, s(s(s(s(elem!1))))) | r(elem!1, s(s(s(s(elem!1))))))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(1922,plain,
% 1.44/1.64 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(elem!1))))) | b(elem!1, s(s(s(s(elem!1))))) | r(elem!1, s(s(s(s(elem!1)))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[1921, 1920])).
% 1.44/1.64 tff(1923,plain,
% 1.44/1.64 ((elem!1 = s(s(s(s(elem!1))))) | b(elem!1, s(s(s(s(elem!1))))) | r(elem!1, s(s(s(s(elem!1)))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1922, 43])).
% 1.44/1.64 tff(1924,plain,
% 1.44/1.64 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1923, 1919, 1909])).
% 1.44/1.64 tff(1925,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, 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(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(1926,plain,
% 1.44/1.64 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(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))))))) <=> ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, 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(s(s(elem!1)))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(1927,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[1926])).
% 1.44/1.64 tff(1928,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.44/1.64 inference(transitivity,[status(thm)],[1927, 1925])).
% 1.44/1.64 tff(1929,plain,
% 1.44/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(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)))))))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(1930,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, 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(s(s(elem!1))))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[1929, 1928])).
% 1.44/1.65 tff(1931,plain,
% 1.44/1.65 (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1930, 306, 1924, 1908, 1906])).
% 1.44/1.65 tff(1932,assumption,(r(s(s(s(s(s(elem!1))))), s(s(elem!1)))), introduced(assumption)).
% 1.44/1.65 tff(1933,plain,
% 1.44/1.65 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(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(s(elem!1)))))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(1934,plain,
% 1.44/1.65 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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))))), s(s(s(s(elem!1)))))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(1935,plain,
% 1.44/1.65 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(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))))), s(s(s(s(elem!1))))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[1934, 1933])).
% 1.44/1.65 tff(1936,plain,
% 1.44/1.65 (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1935, 124, 1288, 1932])).
% 1.44/1.65 tff(1937,assumption,(~(s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.44/1.65 tff(1938,plain,
% 1.44/1.65 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1))))) | b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))) | r(s(s(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(s(s(elem!1))))) = s(s(s(s(elem!1))))) | b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(1939,plain,
% 1.44/1.65 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1))))) | b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(1940,plain,
% 1.44/1.65 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1))))) | b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[1939, 1938])).
% 1.44/1.65 tff(1941,plain,
% 1.44/1.65 ($false),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1940, 43, 1937, 1936, 1931])).
% 1.44/1.65 tff(1942,plain,((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (s(s(s(s(elem!1)))) = elem!1) | (elem!1 = s(s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.65 tff(1943,plain,
% 1.44/1.65 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1942, 1856, 1905, 1892, 1550, 1807, 1805])).
% 1.44/1.65 tff(1944,plain,
% 1.44/1.65 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1302, 1943, 1613])).
% 1.44/1.65 tff(1945,plain,
% 1.44/1.65 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1763, 306, 1005, 1944, 1686])).
% 1.44/1.65 tff(1946,plain,
% 1.44/1.65 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1767, 43, 1512, 1945])).
% 1.44/1.65 tff(1947,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(1948,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(1949,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[1948, 1947])).
% 1.44/1.65 tff(1950,plain,
% 1.44/1.65 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1949, 306, 1005, 601, 1944, 1686])).
% 1.44/1.65 tff(1951,assumption,(s(s(s(s(elem!1)))) = s(s(s(elem!1)))), introduced(assumption)).
% 1.44/1.65 tff(1952,plain,
% 1.44/1.65 (s(s(s(s(elem!1)))) = s(s(s(z)))),
% 1.44/1.65 inference(transitivity,[status(thm)],[1951, 1726])).
% 1.44/1.65 tff(1953,plain,
% 1.44/1.65 ($false),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1902, 1952])).
% 1.44/1.65 tff(1954,plain,((~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.65 tff(1955,plain,
% 1.44/1.65 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1954, 1502])).
% 1.44/1.65 tff(1956,plain,
% 1.44/1.65 (((~![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)))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(1957,plain,
% 1.44/1.65 ((~![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)))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(1958,plain,
% 1.44/1.65 ((~![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))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[1957, 1956])).
% 1.44/1.65 tff(1959,plain,
% 1.44/1.65 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1958, 43, 1955, 1950])).
% 1.44/1.65 tff(1960,plain,
% 1.44/1.65 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(1961,plain,
% 1.44/1.65 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(1962,plain,
% 1.44/1.65 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[1961, 1960])).
% 1.44/1.65 tff(1963,plain,
% 1.44/1.65 ($false),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1962, 124, 654, 1959, 1946])).
% 1.44/1.65 tff(1964,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (s(s(elem!1)) = s(s(s(s(s(elem!1)))))) | (~(z = elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (s(s(elem!1)) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.65 tff(1965,plain,
% 1.44/1.65 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1964, 1572, 1602, 1656, 1502, 1638, 1637, 1553, 1565])).
% 1.44/1.65 tff(1966,plain,
% 1.44/1.65 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[610, 1965, 1614])).
% 1.44/1.65 tff(1967,assumption,(b(s(s(s(z))), elem!1)), introduced(assumption)).
% 1.44/1.65 tff(1968,assumption,(s(s(s(z))) = s(s(s(s(z))))), introduced(assumption)).
% 1.44/1.65 tff(1969,plain,
% 1.44/1.65 (s(s(s(s(z)))) = s(s(s(z)))),
% 1.44/1.65 inference(symmetry,[status(thm)],[1968])).
% 1.44/1.65 tff(1970,plain,
% 1.44/1.65 ($false),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[342, 1969])).
% 1.44/1.65 tff(1971,plain,((~(s(s(s(z))) = s(s(s(s(z)))))) | (s(s(s(s(z)))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.65 tff(1972,plain,
% 1.44/1.65 (~(s(s(s(z))) = s(s(s(s(z)))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1971, 1723])).
% 1.44/1.65 tff(1973,assumption,(b(s(s(s(s(elem!1)))), s(s(elem!1)))), introduced(assumption)).
% 1.44/1.65 tff(1974,plain,
% 1.44/1.65 ((s(elem!1) = s(s(s(s(elem!1))))) <=> (s(z) = s(s(s(s(z)))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[1504, 1898])).
% 1.44/1.65 tff(1975,plain,
% 1.44/1.65 ((s(elem!1) = s(s(s(s(elem!1))))) <=> (s(s(s(s(z)))) = s(z))),
% 1.44/1.65 inference(transitivity,[status(thm)],[1974, 667])).
% 1.44/1.65 tff(1976,plain,
% 1.44/1.65 ((s(s(s(s(z)))) = s(z)) <=> (s(elem!1) = s(s(s(s(elem!1)))))),
% 1.44/1.65 inference(symmetry,[status(thm)],[1975])).
% 1.44/1.65 tff(1977,plain,
% 1.44/1.65 ((~(s(s(s(s(z)))) = s(z))) <=> (~(s(elem!1) = s(s(s(s(elem!1))))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[1976])).
% 1.44/1.65 tff(1978,plain,
% 1.44/1.65 (~(s(elem!1) = s(s(s(s(elem!1)))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[324, 1977])).
% 1.44/1.65 tff(1979,plain,
% 1.44/1.65 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(1980,plain,
% 1.44/1.65 (((~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(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(1981,plain,
% 1.44/1.65 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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))))))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[1980])).
% 1.44/1.65 tff(1982,plain,
% 1.44/1.65 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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)))))))),
% 1.44/1.65 inference(transitivity,[status(thm)],[1981, 1979])).
% 1.44/1.65 tff(1983,plain,
% 1.44/1.65 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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)))))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(1984,plain,
% 1.44/1.65 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1))))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[1983, 1982])).
% 1.44/1.65 tff(1985,plain,
% 1.44/1.65 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1984, 124, 802, 1289])).
% 1.44/1.65 tff(1986,plain,
% 1.44/1.65 (((~![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))))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(1987,plain,
% 1.44/1.65 ((~![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))))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(1988,plain,
% 1.44/1.65 ((~![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)))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[1987, 1986])).
% 1.44/1.65 tff(1989,plain,
% 1.44/1.65 ((s(elem!1) = s(s(s(s(elem!1))))) | b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1988, 43, 1985])).
% 1.44/1.65 tff(1990,plain,
% 1.44/1.65 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1989, 1978])).
% 1.44/1.65 tff(1991,plain,
% 1.44/1.65 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1740, 124, 802, 1289])).
% 1.44/1.65 tff(1992,plain,
% 1.44/1.65 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1767, 43, 1512, 1991])).
% 1.44/1.65 tff(1993,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(1994,plain,
% 1.44/1.65 (((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(1995,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[1994])).
% 1.44/1.65 tff(1996,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.44/1.65 inference(transitivity,[status(thm)],[1995, 1993])).
% 1.44/1.65 tff(1997,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(1998,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[1997, 1996])).
% 1.44/1.65 tff(1999,plain,
% 1.44/1.65 ($false),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1998, 306, 1005, 1973, 1992, 1990])).
% 1.44/1.65 tff(2000,plain,((~r(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~(z = elem!1)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.65 tff(2001,plain,
% 1.44/1.65 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2000, 1973, 1005, 1502, 802])).
% 1.44/1.65 tff(2002,plain,
% 1.44/1.65 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1736, 2001, 1550])).
% 1.44/1.65 tff(2003,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(2004,plain,
% 1.44/1.65 (((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(2005,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[2004])).
% 1.44/1.65 tff(2006,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.44/1.65 inference(transitivity,[status(thm)],[2005, 2003])).
% 1.44/1.65 tff(2007,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(2008,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[2007, 2006])).
% 1.44/1.65 tff(2009,plain,
% 1.44/1.65 ($false),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2008, 306, 30, 1663, 1664, 2002, 1973])).
% 1.44/1.65 tff(2010,plain,((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~(z = elem!1)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.65 tff(2011,plain,
% 1.44/1.65 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2010, 30, 1663, 1664, 1005, 1502, 802])).
% 1.44/1.65 tff(2012,plain,
% 1.44/1.65 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1302, 2011, 1613])).
% 1.44/1.65 tff(2013,assumption,(r(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 1.44/1.65 tff(2014,plain,
% 1.44/1.65 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(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)))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(2015,plain,
% 1.44/1.65 (((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(2016,plain,
% 1.44/1.65 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[2015])).
% 1.44/1.65 tff(2017,plain,
% 1.44/1.65 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.44/1.65 inference(transitivity,[status(thm)],[2016, 2014])).
% 1.44/1.65 tff(2018,plain,
% 1.44/1.65 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(2019,plain,
% 1.44/1.65 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[2018, 2017])).
% 1.44/1.65 tff(2020,plain,
% 1.44/1.65 ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2019, 124, 2013])).
% 1.44/1.65 tff(2021,plain,
% 1.44/1.65 ($false),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2020, 1787, 1783])).
% 1.44/1.65 tff(2022,plain,((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~(elem!1 = z)) | (~r(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.65 tff(2023,plain,
% 1.44/1.65 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2022, 2012, 1619, 653])).
% 1.44/1.65 tff(2024,assumption,(~r(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 1.44/1.65 tff(2025,assumption,(~(s(s(s(z))) = s(s(s(s(z)))))), introduced(assumption)).
% 1.44/1.65 tff(2026,plain,
% 1.44/1.65 ($false),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[350, 43, 347, 2025, 2024])).
% 1.44/1.65 tff(2027,plain,(r(s(s(s(z))), s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | (s(s(s(z))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.65 tff(2028,plain,
% 1.44/1.65 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2027, 2023, 1972])).
% 1.44/1.65 tff(2029,plain,
% 1.44/1.65 (b(s(s(z)), z) <=> b(s(s(z)), elem!1)),
% 1.44/1.65 inference(monotonicity,[status(thm)],[1502])).
% 1.44/1.65 tff(2030,plain,
% 1.44/1.65 (b(s(s(z)), elem!1) <=> b(s(s(z)), z)),
% 1.44/1.65 inference(symmetry,[status(thm)],[2029])).
% 1.44/1.65 tff(2031,plain,
% 1.44/1.65 (b(s(s(z)), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 1.44/1.65 inference(monotonicity,[status(thm)],[1506])).
% 1.44/1.66 tff(2032,plain,
% 1.44/1.66 (b(s(s(elem!1)), elem!1) <=> b(s(s(z)), elem!1)),
% 1.44/1.66 inference(symmetry,[status(thm)],[2031])).
% 1.44/1.66 tff(2033,plain,
% 1.44/1.66 (b(s(s(elem!1)), elem!1) <=> b(s(s(z)), z)),
% 1.44/1.66 inference(transitivity,[status(thm)],[2032, 2030])).
% 1.44/1.66 tff(2034,plain,
% 1.44/1.66 (b(s(s(z)), z)),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[30, 2033])).
% 1.44/1.66 tff(2035,plain,
% 1.44/1.66 (b(z, s(s(z))) <=> b(elem!1, s(s(z)))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[1502])).
% 1.44/1.66 tff(2036,plain,
% 1.44/1.66 (b(elem!1, s(s(z))) <=> b(z, s(s(z)))),
% 1.44/1.66 inference(symmetry,[status(thm)],[2035])).
% 1.44/1.66 tff(2037,plain,
% 1.44/1.66 (b(elem!1, s(s(z))) <=> b(elem!1, s(s(elem!1)))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[1506])).
% 1.44/1.66 tff(2038,plain,
% 1.44/1.66 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(z)))),
% 1.44/1.66 inference(symmetry,[status(thm)],[2037])).
% 1.44/1.66 tff(2039,plain,
% 1.44/1.66 (b(elem!1, s(s(elem!1))) <=> b(z, s(s(z)))),
% 1.44/1.66 inference(transitivity,[status(thm)],[2038, 2036])).
% 1.44/1.66 tff(2040,plain,
% 1.44/1.66 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[1736, 1907, 1550])).
% 1.44/1.66 tff(2041,plain,
% 1.44/1.66 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[1923, 1919, 1807])).
% 1.44/1.66 tff(2042,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(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(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(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(elem!1, s(s(s(s(elem!1)))))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(2043,plain,
% 1.44/1.66 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(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(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(2044,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1))))))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[2043])).
% 1.44/1.66 tff(2045,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.44/1.66 inference(transitivity,[status(thm)],[2044, 2042])).
% 1.44/1.66 tff(2046,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(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))))))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(2047,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[2046, 2045])).
% 1.44/1.66 tff(2048,plain,
% 1.44/1.66 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2047, 306, 2041, 1664, 2040])).
% 1.44/1.66 tff(2049,plain,
% 1.44/1.66 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[2048, 1729])).
% 1.44/1.66 tff(2050,plain,
% 1.44/1.66 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[1793, 1288, 1619, 653])).
% 1.44/1.66 tff(2051,plain,
% 1.44/1.66 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[712, 2050, 1723])).
% 1.44/1.66 tff(2052,plain,
% 1.44/1.66 ($false),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2051, 2049])).
% 1.44/1.66 tff(2053,plain,((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~(z = elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.66 tff(2054,plain,
% 1.44/1.66 (~r(elem!1, s(s(elem!1)))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2053, 2012, 1664, 653, 1502])).
% 1.44/1.66 tff(2055,plain,
% 1.44/1.66 (b(elem!1, s(s(elem!1)))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[516, 2054, 1689])).
% 1.44/1.66 tff(2056,plain,
% 1.44/1.66 (b(z, s(s(z)))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[2055, 2039])).
% 1.44/1.66 tff(2057,plain,
% 1.44/1.66 (z = elem!1),
% 1.44/1.66 inference(symmetry,[status(thm)],[1620])).
% 1.44/1.66 tff(2058,plain,
% 1.44/1.66 (b(s(s(s(z))), z) <=> b(s(s(s(z))), elem!1)),
% 1.44/1.66 inference(monotonicity,[status(thm)],[2057])).
% 1.44/1.66 tff(2059,plain,
% 1.44/1.66 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), z)),
% 1.44/1.66 inference(symmetry,[status(thm)],[2058])).
% 1.44/1.66 tff(2060,plain,
% 1.44/1.66 (b(s(s(s(z))), z)),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[1967, 2059])).
% 1.44/1.66 tff(2061,assumption,(b(s(s(z)), z)), introduced(assumption)).
% 1.44/1.66 tff(2062,assumption,(b(z, s(s(z)))), introduced(assumption)).
% 1.44/1.66 tff(2063,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(2064,plain,
% 1.44/1.66 (((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(2065,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[2064])).
% 1.44/1.66 tff(2066,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 1.44/1.66 inference(transitivity,[status(thm)],[2065, 2063])).
% 1.44/1.66 tff(2067,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(2068,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[2067, 2066])).
% 1.44/1.66 tff(2069,plain,
% 1.44/1.66 (~b(s(s(s(z))), z)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2068, 306, 393, 942, 2062, 2061])).
% 1.44/1.66 tff(2070,plain,
% 1.44/1.66 ($false),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2069, 2060])).
% 1.44/1.66 tff(2071,plain,((~b(s(s(s(z))), elem!1)) | (~(elem!1 = z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.66 tff(2072,plain,
% 1.44/1.66 (~b(s(s(s(s(z)))), z)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2071, 2056, 1967, 2034, 2028, 1619])).
% 1.44/1.66 tff(2073,plain,
% 1.44/1.66 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(s(z)))), z)),
% 1.44/1.66 inference(monotonicity,[status(thm)],[1704])).
% 1.44/1.66 tff(2074,plain,
% 1.44/1.66 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(elem!1)))), z)),
% 1.44/1.66 inference(monotonicity,[status(thm)],[1620])).
% 1.44/1.66 tff(2075,plain,
% 1.44/1.66 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(z)))), z)),
% 1.44/1.66 inference(transitivity,[status(thm)],[2074, 2073])).
% 1.44/1.66 tff(2076,assumption,(b(s(s(s(s(elem!1)))), elem!1)), introduced(assumption)).
% 1.44/1.66 tff(2077,plain,
% 1.44/1.66 (b(s(s(s(s(z)))), z)),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[2076, 2075])).
% 1.44/1.66 tff(2078,plain,
% 1.44/1.66 ($false),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[693, 2077])).
% 1.44/1.66 tff(2079,plain,((~b(s(s(s(s(elem!1)))), elem!1)) | b(s(s(s(s(z)))), z) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.66 tff(2080,plain,
% 1.44/1.66 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2079, 2072, 1619])).
% 1.44/1.66 tff(2081,plain,
% 1.44/1.66 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[1736, 2080, 1550])).
% 1.44/1.66 tff(2082,plain,
% 1.44/1.66 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[1984, 124, 802, 2081])).
% 1.44/1.66 tff(2083,plain,
% 1.44/1.66 ((s(elem!1) = s(s(s(s(elem!1))))) | b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[1988, 43, 2082])).
% 1.44/1.66 tff(2084,plain,
% 1.44/1.66 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2083, 1978])).
% 1.44/1.66 tff(2085,plain,
% 1.44/1.66 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[1740, 124, 802, 2081])).
% 1.44/1.66 tff(2086,plain,
% 1.44/1.66 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[1767, 43, 1512, 2085])).
% 1.44/1.66 tff(2087,plain,
% 1.44/1.66 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[1726, 1898])).
% 1.44/1.66 tff(2088,plain,
% 1.44/1.66 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.44/1.66 inference(symmetry,[status(thm)],[2087])).
% 1.44/1.66 tff(2089,plain,
% 1.44/1.66 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[2028, 2088])).
% 1.44/1.66 tff(2090,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(2091,plain,
% 1.44/1.66 (((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(2092,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[2091])).
% 1.44/1.66 tff(2093,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.44/1.66 inference(transitivity,[status(thm)],[2092, 2090])).
% 1.44/1.66 tff(2094,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(2095,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[2094, 2093])).
% 1.44/1.66 tff(2096,plain,
% 1.44/1.66 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2095, 306, 2089, 2086, 2084])).
% 1.44/1.66 tff(2097,plain,
% 1.44/1.66 ((s(elem!1) = s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[1881, 43, 2096])).
% 1.44/1.66 tff(2098,plain,
% 1.44/1.66 (r(s(elem!1), s(s(s(elem!1))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2097, 1871])).
% 1.44/1.66 tff(2099,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(2100,plain,
% 1.44/1.66 (((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(2101,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[2100])).
% 1.44/1.66 tff(2102,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.44/1.66 inference(transitivity,[status(thm)],[2101, 2099])).
% 1.44/1.66 tff(2103,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(2104,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[2103, 2102])).
% 1.44/1.66 tff(2105,plain,
% 1.44/1.66 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2104, 306, 30, 1663, 1664])).
% 1.44/1.66 tff(2106,plain,
% 1.44/1.66 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[891, 2105, 1578])).
% 1.44/1.66 tff(2107,plain,
% 1.44/1.66 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(2108,plain,
% 1.44/1.66 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(2109,plain,
% 1.44/1.66 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[2108, 2107])).
% 1.44/1.66 tff(2110,plain,
% 1.44/1.66 (~r(s(elem!1), s(s(elem!1)))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2109, 124, 2106, 2098])).
% 1.44/1.66 tff(2111,plain,
% 1.44/1.66 ((s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1)))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[1684, 43, 2110])).
% 1.44/1.66 tff(2112,plain,
% 1.44/1.66 (b(s(elem!1), s(s(elem!1)))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2111, 1659])).
% 1.44/1.66 tff(2113,plain,
% 1.44/1.66 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(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(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(2114,plain,
% 1.44/1.66 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(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(s(elem!1)))))))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(2115,plain,
% 1.44/1.66 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(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(s(elem!1))))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[2114, 2113])).
% 1.44/1.66 tff(2116,plain,
% 1.44/1.66 (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2115, 124, 1289, 1824])).
% 1.44/1.66 tff(2117,plain,
% 1.44/1.66 (b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[1940, 43, 1905, 2116])).
% 1.44/1.66 tff(2118,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(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(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(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(s(s(elem!1)))))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(2119,plain,
% 1.44/1.66 (((~b(s(elem!1), 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)))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))) <=> ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(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(s(s(elem!1)))))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(2120,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(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)))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(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(s(s(elem!1))))))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[2119])).
% 1.44/1.66 tff(2121,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(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)))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(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(s(s(elem!1)))))))),
% 1.44/1.66 inference(transitivity,[status(thm)],[2120, 2118])).
% 1.44/1.66 tff(2122,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(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)))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(2123,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[2122, 2121])).
% 1.44/1.66 tff(2124,plain,
% 1.44/1.66 (~b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2123, 306, 1690, 1992, 1990, 2117])).
% 1.44/1.66 tff(2125,plain,
% 1.44/1.66 ($false),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[1841, 2124, 1818])).
% 1.44/1.66 tff(2126,plain,((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~(z = elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.66 tff(2127,plain,
% 1.44/1.66 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2126, 2112, 1502, 2081, 802])).
% 1.44/1.66 tff(2128,plain,
% 1.44/1.66 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[1855, 2127, 1823])).
% 1.44/1.66 tff(2129,plain,
% 1.44/1.66 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1862, 306, 1663, 1664, 2128])).
% 1.44/1.67 tff(2130,plain,
% 1.44/1.67 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1867, 43, 1864, 2129])).
% 1.44/1.67 tff(2131,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(2132,plain,
% 1.44/1.67 (((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1)))))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(2133,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1)))))))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[2132])).
% 1.44/1.67 tff(2134,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.44/1.67 inference(transitivity,[status(thm)],[2133, 2131])).
% 1.44/1.67 tff(2135,plain,
% 1.44/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(2136,plain,
% 1.44/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1)))))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[2135, 2134])).
% 1.44/1.67 tff(2137,plain,
% 1.44/1.67 (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2136, 306, 30, 1663, 1664, 2128])).
% 1.44/1.67 tff(2138,plain,
% 1.44/1.67 (((~![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)))))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(2139,plain,
% 1.44/1.67 ((~![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)))))))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(2140,plain,
% 1.44/1.67 ((~![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))))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[2139, 2138])).
% 1.44/1.67 tff(2141,plain,
% 1.44/1.67 (r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2140, 43, 1811, 2137])).
% 1.44/1.67 tff(2142,plain,
% 1.44/1.67 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(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))))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(2143,plain,
% 1.44/1.67 (((~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))))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(2144,plain,
% 1.44/1.67 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[2143])).
% 1.44/1.67 tff(2145,plain,
% 1.44/1.67 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.44/1.67 inference(transitivity,[status(thm)],[2144, 2142])).
% 1.44/1.67 tff(2146,plain,
% 1.44/1.67 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(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))))))))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(2147,plain,
% 1.44/1.67 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[2146, 2145])).
% 1.44/1.67 tff(2148,plain,
% 1.44/1.67 ($false),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2147, 124, 2106, 2141, 2130])).
% 1.44/1.67 tff(2149,plain,((~b(s(s(elem!1)), elem!1)) | (s(s(elem!1)) = s(s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~(z = elem!1)) | (~r(s(elem!1), elem!1)) | (s(s(elem!1)) = s(elem!1)) | (~b(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.67 tff(2150,plain,
% 1.44/1.67 (~b(s(s(elem!1)), elem!1)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2149, 1638, 1656, 1637, 1502, 1553, 1565, 1967, 1966, 1602])).
% 1.44/1.67 tff(2151,plain,
% 1.44/1.67 (r(s(s(elem!1)), elem!1)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[47, 2150, 1662])).
% 1.44/1.67 tff(2152,plain,
% 1.44/1.67 (~(s(elem!1) = s(s(elem!1)))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[1565, 1658])).
% 1.44/1.67 tff(2153,plain,
% 1.44/1.67 (~r(s(elem!1), s(s(elem!1)))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1680, 124, 1553, 2151])).
% 1.44/1.67 tff(2154,plain,
% 1.44/1.67 ((s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1)))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1684, 43, 2153])).
% 1.44/1.67 tff(2155,plain,
% 1.44/1.67 (b(s(elem!1), s(s(elem!1)))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2154, 2152])).
% 1.44/1.67 tff(2156,plain,
% 1.44/1.67 (~b(elem!1, s(s(elem!1)))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1803, 2155, 1602, 1502, 1638, 1637, 1553, 2151])).
% 1.44/1.67 tff(2157,plain,
% 1.44/1.67 (r(elem!1, s(s(elem!1)))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[516, 2156, 1689])).
% 1.44/1.67 tff(2158,plain,
% 1.44/1.67 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2053, 2157, 1637, 1966, 1502])).
% 1.44/1.67 tff(2159,plain,
% 1.44/1.67 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1302, 2158, 1613])).
% 1.44/1.67 tff(2160,plain,
% 1.44/1.67 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2000, 2159, 1602, 1502, 1553])).
% 1.44/1.67 tff(2161,plain,
% 1.44/1.67 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1736, 2160, 1550])).
% 1.44/1.67 tff(2162,plain,
% 1.44/1.67 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1776, 306, 1638, 1637, 2161])).
% 1.44/1.67 tff(2163,plain,
% 1.44/1.67 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1958, 43, 1955, 2162])).
% 1.44/1.67 tff(2164,plain,
% 1.44/1.67 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1763, 306, 1602, 2159, 2155])).
% 1.44/1.67 tff(2165,plain,
% 1.44/1.67 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1767, 43, 1512, 2164])).
% 1.44/1.67 tff(2166,plain,
% 1.44/1.67 ($false),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1962, 124, 1572, 2165, 2163])).
% 1.44/1.67 tff(2167,plain,((~(z = elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), z)) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.67 tff(2168,plain,
% 1.44/1.67 (~(z = elem!1)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2167, 1541, 1537, 206, 359, 204, 1526])).
% 1.44/1.67 tff(2169,plain,
% 1.44/1.67 (z = elem!1),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[1620, 161])).
% 1.44/1.67 tff(2170,assumption,(~(z = elem!1)), introduced(assumption)).
% 1.44/1.67 tff(2171,plain,
% 1.44/1.67 ($false),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2170, 2169])).
% 1.44/1.67 tff(2172,plain,((~(elem!1 = z)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.67 tff(2173,plain,
% 1.44/1.67 (~(elem!1 = z)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2172, 2168])).
% 1.44/1.67 tff(2174,plain,
% 1.44/1.67 (r(elem!1, z)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[174, 2173, 2])).
% 1.44/1.67 tff(2175,plain,
% 1.44/1.67 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(2176,plain,
% 1.44/1.67 (((~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(2177,plain,
% 1.44/1.67 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z)))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[2176])).
% 1.44/1.67 tff(2178,plain,
% 1.44/1.67 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z))))),
% 1.44/1.67 inference(transitivity,[status(thm)],[2177, 2175])).
% 1.44/1.67 tff(2179,plain,
% 1.44/1.67 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(2180,plain,
% 1.44/1.67 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z)))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[2179, 2178])).
% 1.44/1.67 tff(2181,plain,
% 1.44/1.67 ($false),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2180, 124, 2174, 359, 204])).
% 1.44/1.67 tff(2182,plain,((~r(elem!1, s(z))) | (~r(s(z), z)) | b(elem!1, z) | (~r(s(s(s(z))), s(z))) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.67 tff(2183,plain,
% 1.44/1.67 (s(s(s(elem!1))) = elem!1),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2182, 1525, 206, 2, 359])).
% 1.44/1.67 tff(2184,assumption,(s(s(s(elem!1))) = elem!1), introduced(assumption)).
% 1.44/1.67 tff(2185,plain,
% 1.44/1.67 (elem!1 = s(s(s(elem!1)))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[2184, 1554])).
% 1.44/1.67 tff(2186,plain,
% 1.44/1.67 ($false),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1653, 2185])).
% 1.44/1.67 tff(2187,plain,((~(s(s(s(elem!1))) = elem!1)) | (elem!1 = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.67 tff(2188,plain,
% 1.44/1.67 ($false),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2187, 2183, 1519])).
% 1.44/1.67 tff(2189,plain,((~(z = elem!1)) | (~r(s(s(s(z))), s(z))) | b(elem!1, z) | (~r(elem!1, s(z))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.67 tff(2190,plain,
% 1.44/1.67 (~(z = elem!1)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2189, 114, 2, 1474, 1501])).
% 1.44/1.67 tff(2191,plain,
% 1.44/1.67 (b(z, elem!1)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[835, 2190, 7])).
% 1.44/1.67 tff(2192,plain,
% 1.44/1.67 (~(elem!1 = z)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2172, 2190])).
% 1.44/1.67 tff(2193,plain,
% 1.44/1.67 (r(elem!1, z)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[174, 2192, 2])).
% 1.44/1.67 tff(2194,plain,
% 1.44/1.67 (~r(s(s(s(z))), z)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[211, 204, 114])).
% 1.44/1.67 tff(2195,assumption,(~b(s(s(s(z))), z)), introduced(assumption)).
% 1.44/1.67 tff(2196,plain,
% 1.44/1.67 ($false),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[202, 43, 169, 1629, 2195])).
% 1.44/1.67 tff(2197,plain,(r(s(s(s(z))), z) | b(s(s(s(z))), z)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.67 tff(2198,plain,
% 1.44/1.67 (b(s(s(s(z))), z)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2197, 2194])).
% 1.44/1.67 tff(2199,plain,
% 1.44/1.67 (s(s(s(z))) = elem!1),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1489, 1, 1484])).
% 1.44/1.67 tff(2200,plain,
% 1.44/1.67 (r(s(s(s(z))), z) <=> r(elem!1, z)),
% 1.44/1.67 inference(monotonicity,[status(thm)],[1430])).
% 1.44/1.67 tff(2201,plain,
% 1.44/1.67 (r(elem!1, z) <=> r(s(s(s(z))), z)),
% 1.44/1.67 inference(symmetry,[status(thm)],[2200])).
% 1.44/1.67 tff(2202,plain,
% 1.44/1.67 (r(s(s(s(z))), z)),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[246, 2201])).
% 1.44/1.67 tff(2203,plain,
% 1.44/1.67 ($false),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1629, 2202])).
% 1.44/1.67 tff(2204,plain,((~(s(s(s(z))) = elem!1)) | r(s(s(s(z))), z) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.67 tff(2205,plain,
% 1.44/1.67 (~r(elem!1, z)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2204, 2199, 1629])).
% 1.44/1.67 tff(2206,plain,
% 1.44/1.67 (elem!1 = z),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[174, 2205, 2])).
% 1.44/1.67 tff(2207,plain,
% 1.44/1.67 (z = elem!1),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2172, 2206])).
% 1.44/1.67 tff(2208,plain,
% 1.44/1.67 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1511, 2207])).
% 1.44/1.67 tff(2209,plain,
% 1.44/1.67 (~(elem!1 = s(s(s(elem!1))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1518, 2208])).
% 1.44/1.67 tff(2210,plain,
% 1.44/1.67 (~r(s(s(s(elem!1))), elem!1)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1631, 2206, 1629])).
% 1.44/1.67 tff(2211,plain,
% 1.44/1.67 (b(s(s(s(z))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 1.44/1.67 inference(monotonicity,[status(thm)],[1507])).
% 1.44/1.67 tff(2212,plain,
% 1.44/1.67 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(z))), elem!1)),
% 1.44/1.67 inference(symmetry,[status(thm)],[2211])).
% 1.44/1.67 tff(2213,plain,
% 1.44/1.67 (b(s(s(s(z))), elem!1)),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[1664, 2212])).
% 1.44/1.67 tff(2214,plain,
% 1.44/1.67 ($false),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1, 2213])).
% 1.44/1.67 tff(2215,plain,((~b(s(s(s(elem!1))), elem!1)) | b(s(s(s(z))), elem!1) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.67 tff(2216,plain,
% 1.44/1.67 (~b(s(s(s(elem!1))), elem!1)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2215, 2207, 1])).
% 1.44/1.67 tff(2217,plain,
% 1.44/1.67 (s(s(s(elem!1))) = elem!1),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1636, 2216, 2210])).
% 1.44/1.67 tff(2218,plain,
% 1.44/1.67 ($false),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2187, 2217, 2209])).
% 1.44/1.67 tff(2219,plain,(b(s(s(s(z))), elem!1) | r(s(s(s(z))), z) | b(elem!1, z) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.67 tff(2220,plain,
% 1.44/1.67 (b(s(s(s(z))), elem!1)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2219, 2194, 2, 1484])).
% 1.44/1.67 tff(2221,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(2222,plain,
% 1.44/1.67 (((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z))) <=> ((~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(2223,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[2222])).
% 1.44/1.67 tff(2224,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 1.44/1.67 inference(transitivity,[status(thm)],[2223, 2221])).
% 1.44/1.67 tff(2225,plain,
% 1.44/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(2226,plain,
% 1.44/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[2225, 2224])).
% 1.44/1.67 tff(2227,plain,
% 1.44/1.67 ($false),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2226, 306, 838, 1967, 1531, 1470])).
% 1.44/1.67 tff(2228,plain,((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.67 tff(2229,plain,
% 1.44/1.67 (~b(elem!1, s(s(s(z))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2228, 2220, 838, 2198])).
% 1.44/1.67 tff(2230,plain,
% 1.44/1.67 (b(elem!1, s(z))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1455, 2229, 9, 6, 2])).
% 1.44/1.67 tff(2231,plain,
% 1.44/1.67 (b(s(s(s(z))), s(z)) <=> b(s(s(s(z))), elem!1)),
% 1.44/1.67 inference(monotonicity,[status(thm)],[85])).
% 1.44/1.67 tff(2232,plain,
% 1.44/1.67 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(z))),
% 1.44/1.67 inference(symmetry,[status(thm)],[2231])).
% 1.44/1.67 tff(2233,plain,
% 1.44/1.67 (b(s(s(s(z))), s(z))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[1967, 2232])).
% 1.44/1.67 tff(2234,plain,
% 1.44/1.67 ($false),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[9, 2233])).
% 1.44/1.67 tff(2235,plain,((~(s(z) = elem!1)) | b(s(s(s(z))), s(z)) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.67 tff(2236,plain,
% 1.44/1.67 (~(s(z) = elem!1)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2235, 2220, 9])).
% 1.44/1.67 tff(2237,plain,
% 1.44/1.67 (~r(s(z), elem!1)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1049, 204, 246])).
% 1.44/1.67 tff(2238,plain,
% 1.44/1.67 (b(s(z), elem!1)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1500, 43, 2237, 2236])).
% 1.44/1.67 tff(2239,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(2240,plain,
% 1.44/1.67 (((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z))) <=> ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(2241,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[2240])).
% 1.44/1.67 tff(2242,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.44/1.67 inference(transitivity,[status(thm)],[2241, 2239])).
% 1.44/1.67 tff(2243,plain,
% 1.44/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(2244,plain,
% 1.44/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[2243, 2242])).
% 1.44/1.67 tff(2245,plain,
% 1.44/1.67 ($false),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2244, 306, 838, 2238, 2220, 2230, 2198])).
% 1.44/1.67 tff(2246,plain,((~r(s(z), z)) | (~b(z, elem!1)) | b(s(s(s(z))), s(z)) | r(s(s(elem!1)), elem!1) | b(elem!1, z) | r(s(s(s(z))), elem!1) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.67 tff(2247,plain,
% 1.44/1.67 (~r(s(z), z)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2246, 2193, 9, 6, 2, 1482, 2191])).
% 1.44/1.67 tff(2248,plain,
% 1.44/1.67 (b(s(z), z)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[221, 2247])).
% 1.44/1.67 tff(2249,assumption,(~(s(elem!1) = s(z))), introduced(assumption)).
% 1.44/1.67 tff(2250,plain,
% 1.44/1.67 ($false),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2249, 1504])).
% 1.44/1.67 tff(2251,plain,((~(z = elem!1)) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.67 tff(2252,plain,
% 1.44/1.67 (~(z = elem!1)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2251, 2249])).
% 1.44/1.67 tff(2253,plain,
% 1.44/1.67 (~(elem!1 = z)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2172, 2252])).
% 1.44/1.67 tff(2254,plain,
% 1.44/1.67 (r(elem!1, z)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[174, 2253, 2])).
% 1.44/1.67 tff(2255,plain,
% 1.44/1.67 (b(z, elem!1)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[835, 2252, 7])).
% 1.44/1.67 tff(2256,assumption,(~b(z, s(z))), introduced(assumption)).
% 1.44/1.67 tff(2257,assumption,(z = s(z)), introduced(assumption)).
% 1.44/1.67 tff(2258,plain,
% 1.44/1.67 (s(z) = z),
% 1.44/1.67 inference(symmetry,[status(thm)],[2257])).
% 1.44/1.67 tff(2259,plain,
% 1.44/1.67 ($false),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[216, 2258])).
% 1.44/1.67 tff(2260,plain,(~(z = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.67 tff(2261,assumption,(~r(z, s(z))), introduced(assumption)).
% 1.44/1.67 tff(2262,plain,
% 1.44/1.67 ($false),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[389, 43, 2261, 2256, 2260])).
% 1.44/1.67 tff(2263,plain,(r(z, s(z)) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.67 tff(2264,plain,
% 1.44/1.68 (r(z, s(z))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2263, 2256])).
% 1.44/1.68 tff(2265,assumption,(r(z, s(z))), introduced(assumption)).
% 1.44/1.68 tff(2266,plain,
% 1.44/1.68 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(z))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(z))) | (~r(elem!1, s(z))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(2267,plain,
% 1.44/1.68 (((~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z))) <=> ((~r(elem!1, z)) | (~r(z, s(z))) | (~r(elem!1, s(z))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(2268,plain,
% 1.44/1.68 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(z))) | (~r(elem!1, s(z)))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[2267])).
% 1.44/1.68 tff(2269,plain,
% 1.44/1.68 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(z))) | (~r(elem!1, s(z))))),
% 1.44/1.68 inference(transitivity,[status(thm)],[2268, 2266])).
% 1.44/1.68 tff(2270,plain,
% 1.44/1.68 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z)))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(2271,plain,
% 1.44/1.68 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(z))) | (~r(elem!1, s(z)))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[2270, 2269])).
% 1.44/1.68 tff(2272,plain,
% 1.44/1.68 ($false),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2271, 124, 246, 2265, 359])).
% 1.44/1.68 tff(2273,plain,((~r(z, s(z))) | (~r(elem!1, z)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.68 tff(2274,plain,
% 1.44/1.68 (~r(elem!1, s(z))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2273, 2264, 246])).
% 1.44/1.68 tff(2275,plain,
% 1.44/1.68 (elem!1 = s(z)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[97, 2274])).
% 1.44/1.68 tff(2276,plain,
% 1.44/1.68 (b(z, elem!1) <=> b(z, s(z))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[2275])).
% 1.44/1.68 tff(2277,plain,
% 1.44/1.68 (b(z, s(z)) <=> b(z, elem!1)),
% 1.44/1.68 inference(symmetry,[status(thm)],[2276])).
% 1.44/1.68 tff(2278,plain,
% 1.44/1.68 ((~b(z, s(z))) <=> (~b(z, elem!1))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[2277])).
% 1.44/1.68 tff(2279,plain,
% 1.44/1.68 (~b(z, elem!1)),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[2256, 2278])).
% 1.44/1.68 tff(2280,plain,
% 1.44/1.68 ($false),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[838, 2279])).
% 1.44/1.68 tff(2281,plain,(b(z, s(z)) | (~b(z, elem!1)) | b(elem!1, s(z)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.68 tff(2282,plain,
% 1.44/1.68 (b(z, s(z))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2281, 838, 5, 246])).
% 1.44/1.68 tff(2283,plain,
% 1.44/1.68 (b(s(s(s(z))), s(z))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1455, 3, 5, 6, 2])).
% 1.44/1.68 tff(2284,assumption,(b(s(s(s(z))), s(z))), introduced(assumption)).
% 1.44/1.68 tff(2285,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(2286,plain,
% 1.44/1.68 (((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(2287,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(z))), z)) | (~b(z, s(z)))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[2286])).
% 1.44/1.68 tff(2288,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(z))), z)) | (~b(z, s(z))))),
% 1.44/1.68 inference(transitivity,[status(thm)],[2287, 2285])).
% 1.44/1.68 tff(2289,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(2290,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(z)))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[2289, 2288])).
% 1.44/1.68 tff(2291,plain,
% 1.44/1.68 (~b(s(s(s(z))), z)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2290, 306, 2284, 8, 485])).
% 1.44/1.68 tff(2292,plain,
% 1.44/1.68 (r(s(s(s(z))), z)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2197, 2291])).
% 1.44/1.68 tff(2293,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(2294,plain,
% 1.44/1.68 (((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z)))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(2295,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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)))))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[2294])).
% 1.44/1.68 tff(2296,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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))))))),
% 1.44/1.68 inference(transitivity,[status(thm)],[2295, 2293])).
% 1.44/1.68 tff(2297,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(2298,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z)))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[2297, 2296])).
% 1.44/1.68 tff(2299,plain,
% 1.44/1.68 (~b(z, s(s(s(z))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2298, 306, 2284, 8, 485])).
% 1.44/1.68 tff(2300,plain,
% 1.44/1.68 (~(elem!1 = s(s(s(z))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[842, 2299, 838])).
% 1.44/1.68 tff(2301,assumption,(~(elem!1 = s(s(s(z))))), introduced(assumption)).
% 1.44/1.68 tff(2302,assumption,(~r(elem!1, s(s(s(z))))), introduced(assumption)).
% 1.44/1.68 tff(2303,plain,
% 1.44/1.68 ($false),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[131, 43, 2302, 3, 2301])).
% 1.44/1.68 tff(2304,plain,(b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z)))) | (elem!1 = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.68 tff(2305,plain,
% 1.44/1.68 (r(elem!1, s(s(s(z))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2304, 2300, 3])).
% 1.44/1.68 tff(2306,plain,
% 1.44/1.68 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(2307,plain,
% 1.44/1.68 (((~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(z)))))) <=> ((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(2308,plain,
% 1.44/1.68 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z)))))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[2307])).
% 1.44/1.68 tff(2309,plain,
% 1.44/1.68 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))),
% 1.44/1.68 inference(transitivity,[status(thm)],[2308, 2306])).
% 1.44/1.68 tff(2310,plain,
% 1.44/1.68 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(2311,plain,
% 1.44/1.68 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z)))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[2310, 2309])).
% 1.44/1.68 tff(2312,plain,
% 1.44/1.68 ((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z)))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2311, 124])).
% 1.44/1.68 tff(2313,plain,
% 1.44/1.68 ($false),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2312, 2305, 2292, 246])).
% 1.44/1.68 tff(2314,plain,((~b(z, s(z))) | (~r(elem!1, z)) | b(elem!1, s(s(s(z)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.68 tff(2315,plain,
% 1.44/1.68 ($false),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2314, 2283, 3, 246, 838, 2282, 8])).
% 1.44/1.68 tff(2316,plain,(b(elem!1, s(s(s(z)))) | (~r(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), s(s(s(z))))) | b(elem!1, s(z)) | r(s(s(elem!1)), elem!1) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.68 tff(2317,plain,
% 1.44/1.68 (b(elem!1, s(s(s(z))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2316, 2254, 2255, 8, 5, 6, 2])).
% 1.44/1.68 tff(2318,plain,
% 1.44/1.68 (~(s(s(s(z))) = elem!1)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1472, 2317])).
% 1.44/1.68 tff(2319,plain,
% 1.44/1.68 (b(z, s(z))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2281, 2255, 5, 2254])).
% 1.44/1.68 tff(2320,plain,
% 1.44/1.68 (b(elem!1, s(s(s(z))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2316, 246, 838, 8, 5, 6, 2])).
% 1.44/1.68 tff(2321,plain,
% 1.44/1.68 (~(s(s(s(z))) = elem!1)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1472, 2320])).
% 1.44/1.68 tff(2322,plain,
% 1.44/1.68 (b(s(s(s(z))), elem!1)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1489, 1482, 2321])).
% 1.44/1.68 tff(2323,plain,
% 1.44/1.68 (b(s(elem!1), elem!1)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[813, 193, 808])).
% 1.44/1.68 tff(2324,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(2325,plain,
% 1.44/1.68 (((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1))))) <=> ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(2326,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[2325])).
% 1.44/1.68 tff(2327,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.44/1.68 inference(transitivity,[status(thm)],[2326, 2324])).
% 1.44/1.68 tff(2328,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(2329,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[2328, 2327])).
% 1.44/1.68 tff(2330,plain,
% 1.44/1.68 (~b(z, s(s(elem!1)))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2329, 306, 838, 92, 1967, 1470])).
% 1.44/1.68 tff(2331,plain,
% 1.44/1.68 (r(z, s(s(elem!1)))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[460, 2330])).
% 1.44/1.68 tff(2332,plain,
% 1.44/1.68 (~r(elem!1, s(s(elem!1)))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[978, 2331, 246])).
% 1.44/1.68 tff(2333,plain,
% 1.44/1.68 (b(elem!1, s(s(elem!1)))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[516, 2332, 187])).
% 1.44/1.68 tff(2334,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(2335,plain,
% 1.44/1.68 (((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1)))) <=> ((~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(2336,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[2335])).
% 1.44/1.68 tff(2337,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 1.44/1.68 inference(transitivity,[status(thm)],[2336, 2334])).
% 1.44/1.68 tff(2338,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(2339,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[2338, 2337])).
% 1.44/1.68 tff(2340,plain,
% 1.44/1.68 ($false),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2339, 306, 838, 30, 817, 1003, 816])).
% 1.44/1.68 tff(2341,plain,((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.68 tff(2342,plain,
% 1.44/1.68 (~b(z, s(elem!1))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2341, 2333, 838, 816, 92])).
% 1.44/1.68 tff(2343,plain,
% 1.44/1.68 (r(z, s(elem!1))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[275, 2342])).
% 1.44/1.68 tff(2344,plain,
% 1.44/1.68 (~b(s(s(elem!1)), s(elem!1))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1024, 2333, 816, 92])).
% 1.44/1.68 tff(2345,plain,
% 1.44/1.68 (r(s(s(elem!1)), s(elem!1))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[994, 2344, 403])).
% 1.44/1.68 tff(2346,plain,
% 1.44/1.68 ($false),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[799, 2345, 2343, 2331])).
% 1.44/1.68 tff(2347,plain,((s(s(elem!1)) = elem!1) | (s(s(elem!1)) = s(elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~r(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.68 tff(2348,plain,
% 1.44/1.68 (s(s(elem!1)) = elem!1),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2347, 392, 2323, 838, 246, 1967, 1470, 6])).
% 1.44/1.68 tff(2349,assumption,(s(elem!1) = s(s(s(z)))), introduced(assumption)).
% 1.44/1.68 tff(2350,plain,
% 1.44/1.68 (s(s(s(z))) = s(elem!1)),
% 1.44/1.68 inference(symmetry,[status(thm)],[2349])).
% 1.44/1.68 tff(2351,plain,
% 1.44/1.68 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[2350])).
% 1.44/1.68 tff(2352,plain,
% 1.44/1.68 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.44/1.68 inference(symmetry,[status(thm)],[2351])).
% 1.44/1.68 tff(2353,plain,
% 1.44/1.68 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[2350])).
% 1.44/1.68 tff(2354,plain,
% 1.44/1.68 (s(s(z)) = s(s(s(s(z))))),
% 1.44/1.68 inference(transitivity,[status(thm)],[103, 2353, 135, 1427, 2352])).
% 1.44/1.68 tff(2355,plain,
% 1.44/1.68 ($false),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1612, 2354])).
% 1.44/1.68 tff(2356,plain,((~(s(elem!1) = s(s(s(z))))) | (~(s(s(elem!1)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.68 tff(2357,plain,
% 1.44/1.68 (~(s(elem!1) = s(s(s(z))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2356, 2348])).
% 1.44/1.68 tff(2358,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(2359,plain,
% 1.44/1.68 (((~b(s(s(s(z))), elem!1)) | (~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), s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(2360,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[2359])).
% 1.44/1.68 tff(2361,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.44/1.68 inference(transitivity,[status(thm)],[2360, 2358])).
% 1.44/1.68 tff(2362,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~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))))))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(2363,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[2362, 2361])).
% 1.44/1.68 tff(2364,plain,
% 1.44/1.68 (~b(s(elem!1), s(s(s(z))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2363, 306, 2323, 1967, 1470])).
% 1.44/1.68 tff(2365,plain,
% 1.44/1.68 (((~![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)))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(2366,plain,
% 1.44/1.68 ((~![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)))))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(2367,plain,
% 1.44/1.68 ((~![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))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[2366, 2365])).
% 1.44/1.68 tff(2368,plain,
% 1.44/1.68 (r(s(elem!1), s(s(s(z))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2367, 43, 2364, 2357])).
% 1.44/1.68 tff(2369,plain,
% 1.44/1.68 (~b(s(s(s(z))), z)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2228, 1967, 838, 1470])).
% 1.44/1.68 tff(2370,plain,
% 1.44/1.68 (r(s(s(s(z))), z)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2197, 2369])).
% 1.44/1.68 tff(2371,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(2372,plain,
% 1.44/1.68 (((~b(s(s(s(z))), elem!1)) | (~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(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(2373,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[2372])).
% 1.44/1.69 tff(2374,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.44/1.69 inference(transitivity,[status(thm)],[2373, 2371])).
% 1.44/1.69 tff(2375,plain,
% 1.44/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(2376,plain,
% 1.44/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[2375, 2374])).
% 1.44/1.69 tff(2377,plain,
% 1.44/1.69 (~b(s(elem!1), z)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2376, 306, 838, 2323, 1967, 1470])).
% 1.44/1.69 tff(2378,assumption,(~b(s(elem!1), z)), introduced(assumption)).
% 1.44/1.69 tff(2379,plain,
% 1.44/1.69 ($false),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[1185, 43, 77, 408, 2378])).
% 1.44/1.69 tff(2380,plain,(b(s(elem!1), z) | r(s(elem!1), z)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.69 tff(2381,plain,
% 1.44/1.69 (r(s(elem!1), z)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2380, 2377])).
% 1.44/1.69 tff(2382,plain,
% 1.44/1.69 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), s(s(s(z))))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(2383,plain,
% 1.44/1.69 (((~r(s(s(s(z))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(z)))))) <=> ((~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), s(s(s(z))))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(2384,plain,
% 1.44/1.69 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), s(s(s(z)))))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[2383])).
% 1.44/1.69 tff(2385,plain,
% 1.44/1.69 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), s(s(s(z))))))),
% 1.44/1.69 inference(transitivity,[status(thm)],[2384, 2382])).
% 1.44/1.69 tff(2386,plain,
% 1.44/1.69 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(z))))))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(2387,plain,
% 1.44/1.69 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), s(s(s(z)))))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[2386, 2385])).
% 1.44/1.69 tff(2388,plain,
% 1.44/1.69 ($false),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2387, 124, 2381, 2370, 2368])).
% 1.44/1.69 tff(2389,plain,((s(elem!1) = elem!1) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~r(elem!1, z)) | r(s(s(elem!1)), elem!1) | r(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.69 tff(2390,plain,
% 1.44/1.69 (s(elem!1) = elem!1),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2389, 2322, 2320, 838, 246, 6, 808])).
% 1.44/1.69 tff(2391,plain,
% 1.44/1.69 (elem!1 = s(elem!1)),
% 1.44/1.69 inference(symmetry,[status(thm)],[176])).
% 1.44/1.69 tff(2392,assumption,(s(s(z)) = elem!1), introduced(assumption)).
% 1.44/1.69 tff(2393,plain,
% 1.44/1.69 (s(s(z)) = s(elem!1)),
% 1.44/1.69 inference(transitivity,[status(thm)],[2392, 2391])).
% 1.44/1.69 tff(2394,plain,
% 1.44/1.69 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[2393])).
% 1.44/1.69 tff(2395,plain,
% 1.44/1.69 (inj_0(s(elem!1)) = inj_0(s(s(z)))),
% 1.44/1.69 inference(symmetry,[status(thm)],[2394])).
% 1.44/1.69 tff(2396,plain,
% 1.44/1.69 (elem!1 = s(z)),
% 1.44/1.69 inference(transitivity,[status(thm)],[1651, 2395, 546])).
% 1.44/1.69 tff(2397,plain,
% 1.44/1.69 ($false),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[87, 2396])).
% 1.44/1.69 tff(2398,plain,((~(s(s(z)) = elem!1)) | (elem!1 = s(z)) | (~(s(elem!1) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.69 tff(2399,plain,
% 1.44/1.69 (~(s(s(z)) = elem!1)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2398, 2390, 83])).
% 1.44/1.69 tff(2400,plain,
% 1.44/1.69 (~r(s(z), z)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2246, 1482, 246, 6, 2, 9, 838])).
% 1.44/1.69 tff(2401,plain,
% 1.44/1.69 (b(s(z), z)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[221, 2400])).
% 1.44/1.69 tff(2402,assumption,(z = s(s(s(z)))), introduced(assumption)).
% 1.44/1.69 tff(2403,plain,
% 1.44/1.69 (s(s(s(z))) = z),
% 1.44/1.69 inference(symmetry,[status(thm)],[2402])).
% 1.44/1.69 tff(2404,plain,
% 1.44/1.69 ($false),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[169, 2403])).
% 1.44/1.69 tff(2405,plain,(~(z = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.69 tff(2406,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(2407,plain,
% 1.44/1.69 (((~b(s(s(s(z))), elem!1)) | (~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(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(2408,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z)))))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[2407])).
% 1.44/1.69 tff(2409,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))))),
% 1.44/1.69 inference(transitivity,[status(thm)],[2408, 2406])).
% 1.44/1.69 tff(2410,plain,
% 1.44/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(2411,plain,
% 1.44/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z)))))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[2410, 2409])).
% 1.44/1.69 tff(2412,plain,
% 1.44/1.69 (~b(z, s(s(s(z))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2411, 306, 838, 2322, 2320])).
% 1.44/1.69 tff(2413,plain,
% 1.44/1.69 (((~![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)))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(2414,plain,
% 1.44/1.69 ((~![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)))))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(2415,plain,
% 1.44/1.69 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z))))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[2414, 2413])).
% 1.44/1.69 tff(2416,plain,
% 1.44/1.69 (r(z, s(s(s(z))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2415, 43, 2412, 2405])).
% 1.44/1.69 tff(2417,plain,
% 1.44/1.69 (b(s(elem!1), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[176])).
% 1.44/1.69 tff(2418,plain,
% 1.44/1.69 (b(elem!1, s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 1.44/1.69 inference(symmetry,[status(thm)],[2417])).
% 1.44/1.69 tff(2419,plain,
% 1.44/1.69 (b(s(elem!1), s(s(s(z))))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[1470, 2418])).
% 1.44/1.69 tff(2420,assumption,(~b(s(elem!1), s(s(s(z))))), introduced(assumption)).
% 1.44/1.69 tff(2421,plain,
% 1.44/1.69 ($false),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2420, 2419])).
% 1.44/1.69 tff(2422,plain,((~b(elem!1, s(s(s(z))))) | b(s(elem!1), s(s(s(z)))) | (~(s(elem!1) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.69 tff(2423,plain,
% 1.44/1.69 (b(s(elem!1), s(s(s(z))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2422, 2390, 2320])).
% 1.44/1.69 tff(2424,plain,
% 1.44/1.69 (s(s(elem!1)) = elem!1),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[180, 2390])).
% 1.44/1.69 tff(2425,plain,
% 1.44/1.69 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 1.44/1.69 inference(symmetry,[status(thm)],[154])).
% 1.44/1.69 tff(2426,plain,
% 1.44/1.69 (s(s(elem!1)) = elem!1),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[180, 176])).
% 1.44/1.69 tff(2427,plain,
% 1.44/1.69 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[2426])).
% 1.44/1.69 tff(2428,plain,
% 1.44/1.69 ((elem!1 = s(s(s(elem!1)))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 1.44/1.69 inference(symmetry,[status(thm)],[2427])).
% 1.44/1.69 tff(2429,plain,
% 1.44/1.69 ((elem!1 = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 1.44/1.69 inference(transitivity,[status(thm)],[2428, 2425])).
% 1.44/1.69 tff(2430,plain,
% 1.44/1.69 (elem!1 = s(s(elem!1))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[1174, 2426])).
% 1.44/1.69 tff(2431,plain,
% 1.44/1.69 (s(s(s(elem!1))) = s(elem!1)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[1168, 2430])).
% 1.44/1.69 tff(2432,plain,
% 1.44/1.69 (s(elem!1) = s(s(s(elem!1)))),
% 1.44/1.69 inference(symmetry,[status(thm)],[2431])).
% 1.44/1.69 tff(2433,plain,
% 1.44/1.69 (elem!1 = s(s(s(elem!1)))),
% 1.44/1.69 inference(transitivity,[status(thm)],[2391, 2432])).
% 1.44/1.69 tff(2434,plain,
% 1.44/1.69 (s(s(s(elem!1))) = s(s(elem!1))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[2433, 2429])).
% 1.44/1.69 tff(2435,plain,
% 1.44/1.69 ($false),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[739, 2434])).
% 1.44/1.69 tff(2436,plain,((~(s(elem!1) = elem!1)) | (s(s(s(elem!1))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.69 tff(2437,plain,
% 1.44/1.69 (s(s(s(elem!1))) = s(s(elem!1))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2436, 2390])).
% 1.44/1.69 tff(2438,plain,
% 1.44/1.69 (elem!1 = s(s(elem!1))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[1174, 2424])).
% 1.44/1.69 tff(2439,plain,
% 1.44/1.69 (s(s(s(elem!1))) = s(elem!1)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[1168, 2438])).
% 1.44/1.69 tff(2440,plain,
% 1.44/1.69 (s(elem!1) = s(s(s(elem!1)))),
% 1.44/1.69 inference(symmetry,[status(thm)],[2439])).
% 1.44/1.69 tff(2441,plain,
% 1.44/1.69 (s(elem!1) = elem!1),
% 1.44/1.69 inference(transitivity,[status(thm)],[2440, 2437, 2424])).
% 1.44/1.69 tff(2442,plain,
% 1.44/1.69 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(z))), elem!1)),
% 1.44/1.69 inference(monotonicity,[status(thm)],[2441])).
% 1.44/1.69 tff(2443,plain,
% 1.44/1.69 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(elem!1))),
% 1.44/1.69 inference(symmetry,[status(thm)],[2442])).
% 1.44/1.69 tff(2444,plain,
% 1.44/1.69 (b(s(s(s(z))), s(elem!1))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[2322, 2443])).
% 1.44/1.69 tff(2445,plain,
% 1.44/1.69 ((s(s(z)) = s(elem!1)) <=> (s(s(z)) = elem!1)),
% 1.44/1.69 inference(monotonicity,[status(thm)],[176])).
% 1.44/1.69 tff(2446,plain,
% 1.44/1.69 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(elem!1))),
% 1.44/1.69 inference(symmetry,[status(thm)],[2445])).
% 1.44/1.69 tff(2447,plain,
% 1.44/1.69 ((~(s(s(z)) = elem!1)) <=> (~(s(s(z)) = s(elem!1)))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[2446])).
% 1.44/1.69 tff(2448,assumption,(~(s(s(z)) = elem!1)), introduced(assumption)).
% 1.44/1.69 tff(2449,plain,
% 1.44/1.69 (~(s(s(z)) = s(elem!1))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[2448, 2447])).
% 1.44/1.69 tff(2450,plain,
% 1.44/1.69 (r(s(s(z)), s(elem!1)) <=> r(s(s(z)), elem!1)),
% 1.44/1.69 inference(monotonicity,[status(thm)],[176])).
% 1.44/1.69 tff(2451,plain,
% 1.44/1.69 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(elem!1))),
% 1.44/1.69 inference(symmetry,[status(thm)],[2450])).
% 1.44/1.69 tff(2452,plain,
% 1.44/1.69 ((~r(s(s(z)), elem!1)) <=> (~r(s(s(z)), s(elem!1)))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[2451])).
% 1.44/1.69 tff(2453,assumption,(b(s(s(s(z))), s(elem!1))), introduced(assumption)).
% 1.44/1.69 tff(2454,assumption,(b(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 1.44/1.69 tff(2455,assumption,(b(s(elem!1), s(s(s(z))))), introduced(assumption)).
% 1.44/1.69 tff(2456,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(z)), s(z))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(2457,plain,
% 1.44/1.69 (((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(z)), s(z))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(2458,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(z)), s(z)))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[2457])).
% 1.44/1.69 tff(2459,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(z)), s(z))))),
% 1.44/1.69 inference(transitivity,[status(thm)],[2458, 2456])).
% 1.44/1.69 tff(2460,plain,
% 1.44/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(2461,plain,
% 1.44/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(z)), s(z)))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[2460, 2459])).
% 1.44/1.69 tff(2462,plain,
% 1.44/1.69 (~b(s(s(z)), s(z))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2461, 306, 8, 2455, 2454, 2453])).
% 1.44/1.69 tff(2463,assumption,(~r(s(s(z)), s(z))), introduced(assumption)).
% 1.44/1.69 tff(2464,assumption,(s(s(z)) = s(z)), introduced(assumption)).
% 1.44/1.69 tff(2465,plain,
% 1.44/1.69 (s(z) = s(s(z))),
% 1.44/1.69 inference(symmetry,[status(thm)],[2464])).
% 1.44/1.69 tff(2466,plain,
% 1.44/1.69 (inj_0(s(z)) = inj_0(s(s(z)))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[2465])).
% 1.44/1.69 tff(2467,plain,
% 1.44/1.69 (inj_0(s(s(z))) = inj_0(s(z))),
% 1.44/1.69 inference(symmetry,[status(thm)],[2466])).
% 1.44/1.69 tff(2468,plain,
% 1.44/1.69 (s(z) = z),
% 1.44/1.69 inference(transitivity,[status(thm)],[547, 2467, 61])).
% 1.44/1.69 tff(2469,plain,
% 1.44/1.69 ($false),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[216, 2468])).
% 1.44/1.69 tff(2470,plain,(~(s(s(z)) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.69 tff(2471,assumption,(~b(s(s(z)), s(z))), introduced(assumption)).
% 1.44/1.69 tff(2472,plain,
% 1.44/1.69 (((~![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)))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(2473,plain,
% 1.44/1.69 ((~![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)))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(2474,plain,
% 1.44/1.69 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[2473, 2472])).
% 1.44/1.69 tff(2475,plain,
% 1.44/1.69 ($false),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2474, 43, 2471, 2470, 2463])).
% 1.44/1.69 tff(2476,plain,(r(s(s(z)), s(z)) | b(s(s(z)), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.69 tff(2477,plain,
% 1.44/1.69 (r(s(s(z)), s(z))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2476, 2462])).
% 1.44/1.69 tff(2478,assumption,(r(s(s(z)), elem!1)), introduced(assumption)).
% 1.44/1.69 tff(2479,assumption,(r(s(s(z)), s(z))), introduced(assumption)).
% 1.44/1.69 tff(2480,plain,
% 1.44/1.69 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(2481,plain,
% 1.44/1.69 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(2482,plain,
% 1.44/1.69 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[2481, 2480])).
% 1.44/1.69 tff(2483,plain,
% 1.44/1.69 ($false),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2482, 124, 359, 2479, 2478])).
% 1.44/1.69 tff(2484,plain,((~r(s(s(z)), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.69 tff(2485,plain,
% 1.44/1.69 (~r(s(s(z)), elem!1)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2484, 2477, 359])).
% 1.44/1.69 tff(2486,plain,
% 1.44/1.69 (~r(s(s(z)), s(elem!1))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[2485, 2452])).
% 1.44/1.69 tff(2487,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(z)), s(elem!1))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(2488,plain,
% 1.44/1.69 (((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(elem!1)))) <=> ((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(z)), s(elem!1))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(2489,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(z)), s(elem!1)))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[2488])).
% 1.44/1.69 tff(2490,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(z)), s(elem!1))))),
% 1.44/1.69 inference(transitivity,[status(thm)],[2489, 2487])).
% 1.44/1.69 tff(2491,plain,
% 1.44/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(elem!1))))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(2492,plain,
% 1.44/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(z)), s(elem!1)))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[2491, 2490])).
% 1.44/1.69 tff(2493,plain,
% 1.44/1.69 (~b(s(s(z)), s(elem!1))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2492, 306, 2455, 2454, 2453])).
% 1.44/1.69 tff(2494,plain,
% 1.44/1.69 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(elem!1)) | b(s(s(z)), s(elem!1)) | r(s(s(z)), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(elem!1)) | b(s(s(z)), s(elem!1)) | r(s(s(z)), s(elem!1)))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(2495,plain,
% 1.44/1.69 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(elem!1)) | b(s(s(z)), s(elem!1)) | r(s(s(z)), s(elem!1)))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(2496,plain,
% 1.44/1.69 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(elem!1)) | b(s(s(z)), s(elem!1)) | r(s(s(z)), s(elem!1))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[2495, 2494])).
% 1.44/1.69 tff(2497,plain,
% 1.44/1.69 ((s(s(z)) = s(elem!1)) | r(s(s(z)), s(elem!1))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2496, 43, 2493])).
% 1.44/1.69 tff(2498,plain,
% 1.44/1.69 ($false),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2497, 2486, 2449])).
% 1.44/1.69 tff(2499,plain,((~b(s(s(z)), s(s(s(z))))) | (~(s(elem!1) = elem!1)) | (s(s(z)) = elem!1) | (~r(elem!1, s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.69 tff(2500,plain,
% 1.44/1.69 (~b(s(s(z)), s(s(s(z))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2499, 2444, 8, 1474, 2399, 2390, 2423])).
% 1.44/1.69 tff(2501,assumption,(~r(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 1.44/1.69 tff(2502,assumption,(s(s(z)) = s(s(s(z)))), introduced(assumption)).
% 1.44/1.69 tff(2503,plain,
% 1.44/1.69 (inj_0(s(s(z))) = inj_0(s(s(s(z))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[2502])).
% 1.44/1.69 tff(2504,plain,
% 1.44/1.69 (inj_0(s(s(s(z)))) = inj_0(s(s(z)))),
% 1.44/1.69 inference(symmetry,[status(thm)],[2503])).
% 1.44/1.69 tff(2505,plain,
% 1.44/1.69 (s(s(s(z))) = s(s(z))),
% 1.44/1.69 inference(symmetry,[status(thm)],[2502])).
% 1.44/1.69 tff(2506,plain,
% 1.44/1.69 (s(s(s(z))) = s(z)),
% 1.44/1.69 inference(transitivity,[status(thm)],[2505, 103, 2504, 546])).
% 1.44/1.69 tff(2507,plain,
% 1.44/1.69 ($false),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[108, 2506])).
% 1.44/1.69 tff(2508,plain,(~(s(s(z)) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.70 tff(2509,assumption,(~b(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 1.54/1.70 tff(2510,plain,
% 1.54/1.70 (((~![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)))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(2511,plain,
% 1.54/1.70 ((~![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)))))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(2512,plain,
% 1.54/1.70 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z))))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[2511, 2510])).
% 1.54/1.70 tff(2513,plain,
% 1.54/1.70 ($false),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2512, 43, 2509, 2508, 2501])).
% 1.54/1.70 tff(2514,plain,(b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.70 tff(2515,plain,
% 1.54/1.70 (r(s(s(z)), s(s(s(z))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2514, 2500])).
% 1.54/1.70 tff(2516,assumption,(r(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 1.54/1.70 tff(2517,assumption,(r(s(s(z)), z)), introduced(assumption)).
% 1.54/1.70 tff(2518,assumption,(r(z, s(s(s(z))))), introduced(assumption)).
% 1.54/1.70 tff(2519,plain,
% 1.54/1.70 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(2520,plain,
% 1.54/1.70 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(2521,plain,
% 1.54/1.70 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[2520, 2519])).
% 1.54/1.70 tff(2522,plain,
% 1.54/1.70 ($false),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2521, 124, 2518, 2517, 2516])).
% 1.54/1.70 tff(2523,plain,((~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.70 tff(2524,plain,
% 1.54/1.70 (~r(s(s(z)), z)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2523, 2515, 2416])).
% 1.54/1.70 tff(2525,assumption,(~r(s(s(z)), z)), introduced(assumption)).
% 1.54/1.70 tff(2526,assumption,(~b(s(s(z)), z)), introduced(assumption)).
% 1.54/1.70 tff(2527,plain,
% 1.54/1.70 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(2528,plain,
% 1.54/1.70 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(2529,plain,
% 1.54/1.70 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z)),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[2528, 2527])).
% 1.54/1.70 tff(2530,plain,
% 1.54/1.70 ($false),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2529, 43, 106, 2526, 2525])).
% 1.54/1.70 tff(2531,plain,(r(s(s(z)), z) | b(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.70 tff(2532,plain,
% 1.54/1.70 (b(s(s(z)), z)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2531, 2524])).
% 1.54/1.70 tff(2533,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(2534,plain,
% 1.54/1.70 (((~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))) <=> ((~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(2535,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z)))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[2534])).
% 1.54/1.70 tff(2536,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))))),
% 1.54/1.70 inference(transitivity,[status(thm)],[2535, 2533])).
% 1.54/1.70 tff(2537,plain,
% 1.54/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(2538,plain,
% 1.54/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z)))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[2537, 2536])).
% 1.54/1.70 tff(2539,plain,
% 1.54/1.70 (~b(s(s(z)), s(z))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2538, 306, 838, 2532, 2401, 2320])).
% 1.54/1.70 tff(2540,plain,
% 1.54/1.70 (r(s(s(z)), s(z))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2476, 2539])).
% 1.54/1.70 tff(2541,plain,
% 1.54/1.70 (~r(s(s(z)), elem!1)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2484, 2540, 1474])).
% 1.54/1.70 tff(2542,plain,
% 1.54/1.70 (((~![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))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(2543,plain,
% 1.54/1.70 ((~![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))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(2544,plain,
% 1.54/1.70 ((~![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)),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[2543, 2542])).
% 1.54/1.70 tff(2545,plain,
% 1.54/1.70 ((s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2544, 43])).
% 1.54/1.70 tff(2546,plain,
% 1.54/1.70 (b(s(s(z)), elem!1)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2545, 2541, 2399])).
% 1.54/1.70 tff(2547,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(2548,plain,
% 1.54/1.70 (((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z))) <=> ((~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(2549,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[2548])).
% 1.54/1.70 tff(2550,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))),
% 1.54/1.70 inference(transitivity,[status(thm)],[2549, 2547])).
% 1.54/1.70 tff(2551,plain,
% 1.54/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(2552,plain,
% 1.54/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[2551, 2550])).
% 1.54/1.70 tff(2553,plain,
% 1.54/1.70 ($false),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2552, 306, 838, 2322, 2532, 2320, 2546])).
% 1.54/1.70 tff(2554,plain,(b(s(s(s(z))), s(z)) | (~b(z, elem!1)) | (~b(s(z), s(s(s(z))))) | (~r(elem!1, z)) | r(s(s(elem!1)), elem!1) | r(s(elem!1), elem!1) | b(elem!1, z) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.70 tff(2555,plain,
% 1.54/1.70 (b(s(s(s(z))), s(z))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2554, 2255, 8, 2254, 6, 808, 2, 5])).
% 1.54/1.70 tff(2556,plain,
% 1.54/1.70 (~b(s(s(s(z))), z)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2290, 306, 2555, 8, 2319])).
% 1.54/1.70 tff(2557,plain,
% 1.54/1.70 (r(s(s(s(z))), z)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2197, 2556])).
% 1.54/1.70 tff(2558,plain,
% 1.54/1.70 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(2559,plain,
% 1.54/1.70 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(2560,plain,
% 1.54/1.70 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[2559, 2558])).
% 1.54/1.70 tff(2561,plain,
% 1.54/1.70 ((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2560, 124])).
% 1.54/1.70 tff(2562,plain,
% 1.54/1.70 (~r(s(s(s(z))), elem!1)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2561, 2557, 2254])).
% 1.54/1.70 tff(2563,plain,
% 1.54/1.70 (b(s(s(s(z))), elem!1)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[1489, 2562, 2318])).
% 1.54/1.70 tff(2564,plain,
% 1.54/1.70 (s(elem!1) = elem!1),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2389, 2563, 2317, 2255, 2254, 6, 808])).
% 1.54/1.70 tff(2565,plain,
% 1.54/1.70 ((s(elem!1) = s(z)) <=> (elem!1 = s(z))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[2564])).
% 1.54/1.70 tff(2566,plain,
% 1.54/1.70 ((~(s(elem!1) = s(z))) <=> (~(elem!1 = s(z)))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[2565])).
% 1.54/1.70 tff(2567,plain,
% 1.54/1.70 (~(elem!1 = s(z))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[2249, 2566])).
% 1.54/1.70 tff(2568,plain,
% 1.54/1.70 (~(s(s(z)) = elem!1)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2398, 2567, 2564])).
% 1.54/1.70 tff(2569,plain,
% 1.54/1.70 (elem!1 = s(elem!1)),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[176, 1163])).
% 1.54/1.70 tff(2570,plain,
% 1.54/1.70 ($false),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[366, 2569])).
% 1.54/1.70 tff(2571,plain,((~(s(elem!1) = elem!1)) | (elem!1 = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.70 tff(2572,plain,
% 1.54/1.70 (elem!1 = s(elem!1)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2571, 2564])).
% 1.54/1.70 tff(2573,plain,
% 1.54/1.70 (b(s(elem!1), s(z)) <=> b(elem!1, s(z))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[2564])).
% 1.54/1.70 tff(2574,plain,
% 1.54/1.70 (b(elem!1, s(z)) <=> b(s(elem!1), s(z))),
% 1.54/1.70 inference(symmetry,[status(thm)],[2573])).
% 1.54/1.70 tff(2575,plain,
% 1.54/1.70 ((~b(elem!1, s(z))) <=> (~b(s(elem!1), s(z)))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[2574])).
% 1.54/1.70 tff(2576,plain,
% 1.54/1.70 (~b(s(elem!1), s(z))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[5, 2575])).
% 1.54/1.70 tff(2577,plain,
% 1.54/1.70 (s(elem!1) = elem!1),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[364, 361])).
% 1.54/1.70 tff(2578,plain,
% 1.54/1.70 (s(s(elem!1)) = elem!1),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[180, 2577])).
% 1.54/1.70 tff(2579,plain,
% 1.54/1.70 (elem!1 = s(s(elem!1))),
% 1.54/1.70 inference(symmetry,[status(thm)],[2578])).
% 1.54/1.70 tff(2580,plain,
% 1.54/1.70 (s(elem!1) = s(s(elem!1))),
% 1.54/1.70 inference(transitivity,[status(thm)],[362, 2579])).
% 1.54/1.70 tff(2581,plain,
% 1.54/1.70 ((s(elem!1) = s(z)) <=> (s(s(elem!1)) = s(z))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[2580])).
% 1.54/1.70 tff(2582,plain,
% 1.54/1.70 ((s(s(elem!1)) = s(z)) <=> (s(elem!1) = s(z))),
% 1.54/1.70 inference(symmetry,[status(thm)],[2581])).
% 1.54/1.70 tff(2583,plain,
% 1.54/1.70 ((~(s(s(elem!1)) = s(z))) <=> (~(s(elem!1) = s(z)))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[2582])).
% 1.54/1.70 tff(2584,plain,
% 1.54/1.70 (s(s(elem!1)) = s(elem!1)),
% 1.54/1.70 inference(transitivity,[status(thm)],[2578, 361])).
% 1.54/1.70 tff(2585,plain,
% 1.54/1.70 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[2584])).
% 1.54/1.70 tff(2586,plain,
% 1.54/1.70 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.54/1.70 inference(transitivity,[status(thm)],[2585, 1573])).
% 1.54/1.70 tff(2587,plain,
% 1.54/1.70 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 1.54/1.70 inference(symmetry,[status(thm)],[2586])).
% 1.54/1.70 tff(2588,plain,
% 1.54/1.70 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 1.54/1.70 inference(transitivity,[status(thm)],[2587, 2425])).
% 1.54/1.70 tff(2589,plain,
% 1.54/1.70 (elem!1 = s(s(elem!1))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[1174, 2578])).
% 1.54/1.70 tff(2590,plain,
% 1.54/1.70 (s(s(s(elem!1))) = s(elem!1)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[1168, 2589])).
% 1.54/1.70 tff(2591,plain,
% 1.54/1.70 (s(s(s(elem!1))) = s(s(elem!1))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[2590, 2588])).
% 1.54/1.70 tff(2592,assumption,(s(s(elem!1)) = s(z)), introduced(assumption)).
% 1.54/1.70 tff(2593,plain,
% 1.54/1.70 (s(z) = s(s(elem!1))),
% 1.54/1.70 inference(symmetry,[status(thm)],[2592])).
% 1.54/1.70 tff(2594,plain,
% 1.54/1.70 (inj_0(s(z)) = inj_0(s(s(elem!1)))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[2593])).
% 1.54/1.70 tff(2595,plain,
% 1.54/1.70 (inj_0(s(s(elem!1))) = inj_0(s(z))),
% 1.54/1.70 inference(symmetry,[status(thm)],[2594])).
% 1.54/1.70 tff(2596,plain,
% 1.54/1.70 (s(s(elem!1)) = s(s(s(elem!1)))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[159, 155])).
% 1.54/1.70 tff(2597,plain,
% 1.54/1.70 (s(s(s(elem!1))) = s(elem!1)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[152, 2596])).
% 1.54/1.70 tff(2598,plain,
% 1.54/1.70 (s(s(elem!1)) = s(s(s(elem!1)))),
% 1.54/1.70 inference(symmetry,[status(thm)],[155])).
% 1.54/1.70 tff(2599,plain,
% 1.54/1.70 (s(s(elem!1)) = z),
% 1.54/1.70 inference(transitivity,[status(thm)],[2598, 2597, 67, 2595, 61])).
% 1.54/1.70 tff(2600,plain,
% 1.54/1.70 ($false),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[454, 2599])).
% 1.54/1.70 tff(2601,plain,((~(s(s(elem!1)) = s(z))) | (~(s(s(s(elem!1))) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.70 tff(2602,plain,
% 1.54/1.70 (~(s(s(elem!1)) = s(z))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2601, 2591])).
% 1.54/1.70 tff(2603,plain,
% 1.54/1.70 (~(s(elem!1) = s(z))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[2602, 2583])).
% 1.54/1.70 tff(2604,plain,
% 1.54/1.70 (r(s(elem!1), s(z)) <=> r(elem!1, s(z))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[362])).
% 1.54/1.70 tff(2605,plain,
% 1.54/1.70 (r(elem!1, s(z)) <=> r(s(elem!1), s(z))),
% 1.54/1.70 inference(symmetry,[status(thm)],[2604])).
% 1.54/1.70 tff(2606,plain,
% 1.54/1.70 ((~r(elem!1, s(z))) <=> (~r(s(elem!1), s(z)))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[2605])).
% 1.54/1.70 tff(2607,assumption,(~r(elem!1, s(z))), introduced(assumption)).
% 1.54/1.70 tff(2608,plain,
% 1.54/1.70 (~r(s(elem!1), s(z))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[2607, 2606])).
% 1.54/1.70 tff(2609,assumption,(~b(s(elem!1), s(z))), introduced(assumption)).
% 1.54/1.70 tff(2610,plain,
% 1.54/1.70 (((~![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)))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(2611,plain,
% 1.54/1.70 ((~![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)))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(2612,plain,
% 1.54/1.70 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(z)) | b(s(elem!1), s(z)) | r(s(elem!1), s(z))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[2611, 2610])).
% 1.54/1.70 tff(2613,plain,
% 1.54/1.70 ((s(elem!1) = s(z)) | r(s(elem!1), s(z))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2612, 43, 2609])).
% 1.54/1.70 tff(2614,plain,
% 1.54/1.70 ($false),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2613, 2608, 2603])).
% 1.54/1.70 tff(2615,plain,(r(elem!1, s(z)) | b(s(elem!1), s(z)) | (~(elem!1 = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.70 tff(2616,plain,
% 1.54/1.70 (r(elem!1, s(z))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2615, 2576, 2572])).
% 1.54/1.70 tff(2617,plain,
% 1.54/1.70 (b(s(s(elem!1)), s(z)) <=> b(elem!1, s(z))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[2426])).
% 1.54/1.70 tff(2618,plain,
% 1.54/1.70 (b(elem!1, s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.54/1.70 inference(symmetry,[status(thm)],[2617])).
% 1.54/1.70 tff(2619,plain,
% 1.54/1.70 ((~b(elem!1, s(z))) <=> (~b(s(s(elem!1)), s(z)))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[2618])).
% 1.54/1.70 tff(2620,plain,
% 1.54/1.70 (~b(s(s(elem!1)), s(z))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[5, 2619])).
% 1.54/1.70 tff(2621,plain,
% 1.54/1.70 (elem!1 = s(elem!1)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2571, 176])).
% 1.54/1.70 tff(2622,plain,
% 1.54/1.70 (r(elem!1, s(z))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2615, 2569, 2609])).
% 1.54/1.70 tff(2623,plain,
% 1.54/1.70 (r(s(elem!1), z) <=> r(elem!1, z)),
% 1.54/1.70 inference(monotonicity,[status(thm)],[176])).
% 1.54/1.70 tff(2624,plain,
% 1.54/1.70 (r(elem!1, z) <=> r(s(elem!1), z)),
% 1.54/1.70 inference(symmetry,[status(thm)],[2623])).
% 1.54/1.70 tff(2625,plain,
% 1.54/1.70 (r(s(elem!1), z)),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[246, 2624])).
% 1.54/1.70 tff(2626,assumption,(r(s(elem!1), s(z))), introduced(assumption)).
% 1.54/1.70 tff(2627,plain,
% 1.54/1.70 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(2628,plain,
% 1.54/1.70 (((~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z)))) <=> ((~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(2629,plain,
% 1.54/1.70 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), s(z)))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[2628])).
% 1.54/1.70 tff(2630,plain,
% 1.54/1.70 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))),
% 1.54/1.70 inference(transitivity,[status(thm)],[2629, 2627])).
% 1.54/1.70 tff(2631,plain,
% 1.54/1.70 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(2632,plain,
% 1.54/1.70 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), s(z)))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[2631, 2630])).
% 1.54/1.70 tff(2633,plain,
% 1.54/1.70 ($false),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2632, 124, 466, 204, 2626])).
% 1.54/1.70 tff(2634,plain,((~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.70 tff(2635,plain,
% 1.54/1.70 (~r(s(elem!1), s(z))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2634, 2625, 204])).
% 1.54/1.70 tff(2636,plain,
% 1.54/1.70 (r(s(elem!1), s(z))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[359, 2605])).
% 1.54/1.70 tff(2637,assumption,(~r(s(elem!1), s(z))), introduced(assumption)).
% 1.54/1.70 tff(2638,plain,
% 1.54/1.70 ($false),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2637, 2636])).
% 1.54/1.70 tff(2639,plain,(r(s(elem!1), s(z)) | (~r(elem!1, s(z))) | (~(elem!1 = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.70 tff(2640,plain,
% 1.54/1.70 ($false),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2639, 2635, 2622, 2569])).
% 1.54/1.70 tff(2641,plain,((~(s(elem!1) = elem!1)) | (~r(s(z), z)) | b(s(elem!1), s(z)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.70 tff(2642,plain,
% 1.54/1.70 (b(s(elem!1), s(z))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2641, 176, 246, 204])).
% 1.54/1.70 tff(2643,plain,
% 1.54/1.70 (b(s(s(elem!1)), s(z)) <=> b(elem!1, s(z))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[2578])).
% 1.54/1.70 tff(2644,plain,
% 1.54/1.70 (b(elem!1, s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.54/1.70 inference(symmetry,[status(thm)],[2643])).
% 1.54/1.70 tff(2645,plain,
% 1.54/1.70 (b(s(elem!1), s(z)) <=> b(elem!1, s(z))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[362])).
% 1.54/1.70 tff(2646,plain,
% 1.54/1.70 (b(s(elem!1), s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.54/1.70 inference(transitivity,[status(thm)],[2645, 2644])).
% 1.54/1.70 tff(2647,assumption,(b(s(elem!1), s(z))), introduced(assumption)).
% 1.54/1.70 tff(2648,plain,
% 1.54/1.70 (b(s(s(elem!1)), s(z))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[2647, 2646])).
% 1.54/1.70 tff(2649,assumption,(~b(s(s(elem!1)), s(z))), introduced(assumption)).
% 1.54/1.70 tff(2650,plain,
% 1.54/1.70 ($false),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2649, 2648])).
% 1.54/1.70 tff(2651,plain,((~b(s(elem!1), s(z))) | b(s(s(elem!1)), s(z)) | (~(elem!1 = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.70 tff(2652,plain,
% 1.54/1.70 (b(s(s(elem!1)), s(z))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2651, 2642, 2621])).
% 1.54/1.70 tff(2653,plain,
% 1.54/1.70 ($false),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2652, 2620])).
% 1.54/1.70 tff(2654,plain,((~(s(elem!1) = elem!1)) | b(elem!1, s(z)) | (~r(elem!1, z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.70 tff(2655,plain,
% 1.54/1.70 (~r(s(z), z)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2654, 2564, 2254, 5])).
% 1.54/1.70 tff(2656,plain,
% 1.54/1.70 (b(s(z), z)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[221, 2655])).
% 1.54/1.70 tff(2657,plain,
% 1.54/1.70 (~b(z, s(s(s(z))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2298, 306, 2555, 8, 2319])).
% 1.54/1.70 tff(2658,plain,
% 1.54/1.70 (r(z, s(s(s(z))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2415, 43, 2657, 2405])).
% 1.54/1.70 tff(2659,plain,
% 1.54/1.70 (b(s(elem!1), s(s(s(z))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2422, 2564, 2317])).
% 1.54/1.70 tff(2660,plain,
% 1.54/1.70 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(z))), elem!1)),
% 1.54/1.70 inference(monotonicity,[status(thm)],[2564])).
% 1.54/1.70 tff(2661,plain,
% 1.54/1.70 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(elem!1))),
% 1.54/1.70 inference(symmetry,[status(thm)],[2660])).
% 1.54/1.70 tff(2662,plain,
% 1.54/1.70 (b(s(s(s(z))), s(elem!1))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[2563, 2661])).
% 1.54/1.70 tff(2663,plain,
% 1.54/1.70 (~b(s(s(z)), s(s(s(z))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2499, 2662, 8, 2616, 2568, 2564, 2659])).
% 1.54/1.70 tff(2664,plain,
% 1.54/1.70 (r(s(s(z)), s(s(s(z))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2514, 2663])).
% 1.54/1.70 tff(2665,plain,
% 1.54/1.70 (~r(s(s(z)), z)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2523, 2664, 2658])).
% 1.54/1.70 tff(2666,plain,
% 1.54/1.70 (b(s(s(z)), z)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2531, 2665])).
% 1.54/1.70 tff(2667,plain,
% 1.54/1.70 (~b(s(s(z)), s(z))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2538, 306, 2255, 2666, 2656, 2317])).
% 1.54/1.70 tff(2668,plain,
% 1.54/1.70 (r(s(s(z)), s(z))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2476, 2667])).
% 1.54/1.70 tff(2669,plain,
% 1.54/1.70 (~r(s(s(z)), elem!1)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2484, 2668, 2616])).
% 1.54/1.70 tff(2670,plain,
% 1.54/1.70 (b(s(s(z)), elem!1)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2545, 2669, 2568])).
% 1.54/1.71 tff(2671,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(2672,plain,
% 1.54/1.71 (((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z))) <=> ((~b(z, elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(2673,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[2672])).
% 1.54/1.71 tff(2674,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))),
% 1.54/1.71 inference(transitivity,[status(thm)],[2673, 2671])).
% 1.54/1.71 tff(2675,plain,
% 1.54/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(2676,plain,
% 1.54/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[2675, 2674])).
% 1.54/1.71 tff(2677,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2676, 306, 2255, 2555, 2666, 2317, 2670])).
% 1.54/1.71 tff(2678,plain,((s(elem!1) = s(z)) | (~b(s(z), s(s(s(z))))) | b(elem!1, s(z)) | r(s(s(elem!1)), elem!1) | r(s(elem!1), elem!1) | b(elem!1, z) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(2679,plain,
% 1.54/1.71 (s(elem!1) = s(z)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2678, 808, 5, 6, 8, 2, 7])).
% 1.54/1.71 tff(2680,plain,
% 1.54/1.71 (s(s(elem!1)) = s(s(z))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[2679])).
% 1.54/1.71 tff(2681,plain,
% 1.54/1.71 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[2680])).
% 1.54/1.71 tff(2682,plain,
% 1.54/1.71 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(z))), elem!1)),
% 1.54/1.71 inference(monotonicity,[status(thm)],[2681])).
% 1.54/1.71 tff(2683,assumption,(s(elem!1) = s(z)), introduced(assumption)).
% 1.54/1.71 tff(2684,plain,
% 1.54/1.71 (inj_0(s(elem!1)) = inj_0(s(z))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[2683])).
% 1.54/1.71 tff(2685,plain,
% 1.54/1.71 (inj_0(s(z)) = inj_0(s(elem!1))),
% 1.54/1.71 inference(symmetry,[status(thm)],[2684])).
% 1.54/1.71 tff(2686,plain,
% 1.54/1.71 (z = inj_0(s(z))),
% 1.54/1.71 inference(symmetry,[status(thm)],[61])).
% 1.54/1.71 tff(2687,plain,
% 1.54/1.71 (z = elem!1),
% 1.54/1.71 inference(transitivity,[status(thm)],[2686, 2685, 135])).
% 1.54/1.71 tff(2688,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2170, 2687])).
% 1.54/1.71 tff(2689,plain,((~(s(elem!1) = s(z))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(2690,plain,
% 1.54/1.71 (z = elem!1),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2689, 2679])).
% 1.54/1.71 tff(2691,plain,
% 1.54/1.71 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[1511, 2690])).
% 1.54/1.71 tff(2692,plain,
% 1.54/1.71 (~(elem!1 = s(s(s(elem!1))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[1518, 2691])).
% 1.54/1.71 tff(2693,plain,
% 1.54/1.71 (~(s(s(s(elem!1))) = elem!1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2187, 2692])).
% 1.54/1.71 tff(2694,plain,
% 1.54/1.71 (elem!1 = z),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[1618, 2690])).
% 1.54/1.71 tff(2695,plain,
% 1.54/1.71 (elem!1 = z),
% 1.54/1.71 inference(symmetry,[status(thm)],[1502])).
% 1.54/1.71 tff(2696,plain,
% 1.54/1.71 (s(elem!1) = z),
% 1.54/1.71 inference(transitivity,[status(thm)],[176, 2695])).
% 1.54/1.71 tff(2697,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[77, 2696])).
% 1.54/1.71 tff(2698,plain,((~(s(elem!1) = elem!1)) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(2699,plain,
% 1.54/1.71 (~(s(elem!1) = elem!1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2698, 2690])).
% 1.54/1.71 tff(2700,plain,
% 1.54/1.71 (b(s(elem!1), elem!1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[813, 2699, 808])).
% 1.54/1.71 tff(2701,plain,
% 1.54/1.71 (z = elem!1),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2689, 2683])).
% 1.54/1.71 tff(2702,plain,
% 1.54/1.71 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 1.54/1.71 inference(monotonicity,[status(thm)],[2701])).
% 1.54/1.71 tff(2703,plain,
% 1.54/1.71 ((~(s(s(s(z))) = z)) <=> (~(s(s(s(z))) = elem!1))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[2702])).
% 1.54/1.71 tff(2704,plain,
% 1.54/1.71 (~(s(s(s(z))) = elem!1)),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[169, 2703])).
% 1.54/1.71 tff(2705,plain,
% 1.54/1.71 (b(s(elem!1), z) <=> b(s(elem!1), elem!1)),
% 1.54/1.71 inference(monotonicity,[status(thm)],[1502])).
% 1.54/1.71 tff(2706,plain,
% 1.54/1.71 ((~b(s(elem!1), z)) <=> (~b(s(elem!1), elem!1))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[2705])).
% 1.54/1.71 tff(2707,plain,
% 1.54/1.71 (~b(s(elem!1), elem!1)),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[2378, 2706])).
% 1.54/1.71 tff(2708,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[816, 2707])).
% 1.54/1.71 tff(2709,plain,((~b(s(elem!1), elem!1)) | b(s(elem!1), z) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(2710,plain,
% 1.54/1.71 (b(s(elem!1), z)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2709, 816, 2701])).
% 1.54/1.71 tff(2711,plain,
% 1.54/1.71 (b(s(elem!1), elem!1) <=> b(s(elem!1), z)),
% 1.54/1.71 inference(symmetry,[status(thm)],[2705])).
% 1.54/1.71 tff(2712,plain,
% 1.54/1.71 (b(s(z), elem!1) <=> b(s(elem!1), elem!1)),
% 1.54/1.71 inference(monotonicity,[status(thm)],[1503])).
% 1.54/1.71 tff(2713,plain,
% 1.54/1.71 (b(s(z), elem!1) <=> b(s(elem!1), z)),
% 1.54/1.71 inference(transitivity,[status(thm)],[2712, 2711])).
% 1.54/1.71 tff(2714,plain,
% 1.54/1.71 ((~b(s(z), elem!1)) <=> (~b(s(elem!1), z))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[2713])).
% 1.54/1.71 tff(2715,assumption,(~b(s(z), elem!1)), introduced(assumption)).
% 1.54/1.71 tff(2716,plain,
% 1.54/1.71 (~b(s(elem!1), z)),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[2715, 2714])).
% 1.54/1.71 tff(2717,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[1199, 2716])).
% 1.54/1.71 tff(2718,plain,(b(s(z), elem!1) | (~b(s(elem!1), z)) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(2719,plain,
% 1.54/1.71 (b(s(z), elem!1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2718, 2710, 2701])).
% 1.54/1.71 tff(2720,plain,
% 1.54/1.71 (s(elem!1) = s(s(s(elem!1)))),
% 1.54/1.71 inference(symmetry,[status(thm)],[136])).
% 1.54/1.71 tff(2721,plain,
% 1.54/1.71 (s(z) = s(elem!1)),
% 1.54/1.71 inference(symmetry,[status(thm)],[2683])).
% 1.54/1.71 tff(2722,plain,
% 1.54/1.71 (s(z) = s(s(s(elem!1)))),
% 1.54/1.71 inference(transitivity,[status(thm)],[2721, 2720])).
% 1.54/1.71 tff(2723,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[645, 2722])).
% 1.54/1.71 tff(2724,plain,((~(s(elem!1) = s(z))) | (~(s(s(s(elem!1))) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(2725,plain,
% 1.54/1.71 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2724, 2683])).
% 1.54/1.71 tff(2726,plain,
% 1.54/1.71 (~(elem!1 = s(s(elem!1)))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[1168, 2725])).
% 1.54/1.71 tff(2727,plain,
% 1.54/1.71 (~(s(s(elem!1)) = elem!1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[1174, 2726])).
% 1.54/1.71 tff(2728,plain,
% 1.54/1.71 (b(s(s(elem!1)), elem!1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[47, 2727, 6])).
% 1.54/1.71 tff(2729,plain,
% 1.54/1.71 (~(s(elem!1) = elem!1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2698, 2701])).
% 1.54/1.71 tff(2730,plain,
% 1.54/1.71 (~(elem!1 = s(elem!1))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[364, 2729])).
% 1.54/1.71 tff(2731,plain,
% 1.54/1.71 (b(elem!1, s(elem!1)) <=> b(elem!1, s(z))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[2683])).
% 1.54/1.71 tff(2732,plain,
% 1.54/1.71 (b(elem!1, s(z)) <=> b(elem!1, s(elem!1))),
% 1.54/1.71 inference(symmetry,[status(thm)],[2731])).
% 1.54/1.71 tff(2733,plain,
% 1.54/1.71 ((~b(elem!1, s(z))) <=> (~b(elem!1, s(elem!1)))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[2732])).
% 1.54/1.71 tff(2734,plain,
% 1.54/1.71 (~b(elem!1, s(elem!1))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[5, 2733])).
% 1.54/1.71 tff(2735,plain,
% 1.54/1.71 (r(elem!1, s(elem!1))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[372, 2734, 2730])).
% 1.54/1.71 tff(2736,plain,
% 1.54/1.71 (~(s(s(elem!1)) = s(elem!1))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[1181, 2725])).
% 1.54/1.71 tff(2737,plain,
% 1.54/1.71 (b(z, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[2701])).
% 1.54/1.71 tff(2738,plain,
% 1.54/1.71 (b(elem!1, s(s(s(elem!1)))) <=> b(z, s(s(s(elem!1))))),
% 1.54/1.71 inference(symmetry,[status(thm)],[2737])).
% 1.54/1.71 tff(2739,plain,
% 1.54/1.71 (s(s(elem!1)) = s(s(z))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[2683])).
% 1.54/1.71 tff(2740,plain,
% 1.54/1.71 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[2739])).
% 1.54/1.71 tff(2741,plain,
% 1.54/1.71 (b(elem!1, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(z))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[2740])).
% 1.54/1.71 tff(2742,plain,
% 1.54/1.71 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.54/1.71 inference(symmetry,[status(thm)],[2741])).
% 1.54/1.71 tff(2743,plain,
% 1.54/1.71 (b(elem!1, s(s(s(z)))) <=> b(z, s(s(s(elem!1))))),
% 1.54/1.71 inference(transitivity,[status(thm)],[2742, 2738])).
% 1.54/1.71 tff(2744,plain,
% 1.54/1.71 ((~b(elem!1, s(s(s(z))))) <=> (~b(z, s(s(s(elem!1)))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[2743])).
% 1.54/1.71 tff(2745,plain,
% 1.54/1.71 (~b(z, s(s(s(elem!1))))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[3, 2744])).
% 1.54/1.71 tff(2746,plain,
% 1.54/1.71 (r(z, s(s(s(elem!1))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[585, 2745])).
% 1.54/1.71 tff(2747,plain,
% 1.54/1.71 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(z)))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[2740, 2739])).
% 1.54/1.71 tff(2748,plain,
% 1.54/1.71 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[152, 2725])).
% 1.54/1.71 tff(2749,plain,
% 1.54/1.71 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[159, 2748])).
% 1.54/1.71 tff(2750,plain,
% 1.54/1.71 (~b(elem!1, s(s(elem!1)))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[1024, 1005, 816, 30])).
% 1.54/1.71 tff(2751,plain,
% 1.54/1.71 (b(z, s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[1502])).
% 1.54/1.71 tff(2752,plain,
% 1.54/1.71 (b(elem!1, s(s(elem!1))) <=> b(z, s(s(elem!1)))),
% 1.54/1.71 inference(symmetry,[status(thm)],[2751])).
% 1.54/1.71 tff(2753,plain,
% 1.54/1.71 ((~b(elem!1, s(s(elem!1)))) <=> (~b(z, s(s(elem!1))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[2752])).
% 1.54/1.71 tff(2754,assumption,(~b(elem!1, s(s(elem!1)))), introduced(assumption)).
% 1.54/1.71 tff(2755,plain,
% 1.54/1.71 (~b(z, s(s(elem!1)))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[2754, 2753])).
% 1.54/1.71 tff(2756,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[1198, 2755])).
% 1.54/1.71 tff(2757,plain,((~(z = elem!1)) | (~b(z, s(s(elem!1)))) | b(elem!1, s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(2758,plain,
% 1.54/1.71 (~b(z, s(s(elem!1)))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2757, 2750, 2701])).
% 1.54/1.71 tff(2759,plain,
% 1.54/1.71 (r(z, s(s(elem!1)))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[460, 2758])).
% 1.54/1.71 tff(2760,plain,
% 1.54/1.71 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[950, 2759, 564])).
% 1.54/1.71 tff(2761,plain,
% 1.54/1.71 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[610, 2760, 2749])).
% 1.54/1.71 tff(2762,plain,
% 1.54/1.71 (b(s(s(s(z))), s(s(z)))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[2761, 2747])).
% 1.54/1.71 tff(2763,plain,
% 1.54/1.71 (s(s(z)) = s(s(elem!1))),
% 1.54/1.71 inference(symmetry,[status(thm)],[2739])).
% 1.54/1.71 tff(2764,plain,
% 1.54/1.71 (b(s(s(z)), s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[2763])).
% 1.54/1.71 tff(2765,plain,
% 1.54/1.71 (b(s(s(elem!1)), s(z)) <=> b(s(s(z)), s(z))),
% 1.54/1.71 inference(symmetry,[status(thm)],[2764])).
% 1.54/1.71 tff(2766,plain,
% 1.54/1.71 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(elem!1)), s(z))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[2683])).
% 1.54/1.71 tff(2767,plain,
% 1.54/1.71 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(z)), s(z))),
% 1.54/1.71 inference(transitivity,[status(thm)],[2766, 2765])).
% 1.54/1.71 tff(2768,plain,
% 1.54/1.71 (b(s(s(z)), s(z))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[1005, 2767])).
% 1.54/1.71 tff(2769,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(2770,plain,
% 1.54/1.71 (((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(2771,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(z)), s(z))) | (~b(s(s(s(z))), s(s(z))))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[2770])).
% 1.54/1.71 tff(2772,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.54/1.71 inference(transitivity,[status(thm)],[2771, 2769])).
% 1.54/1.71 tff(2773,plain,
% 1.54/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(2774,plain,
% 1.54/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z))))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[2773, 2772])).
% 1.54/1.71 tff(2775,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2774, 306, 2284, 8, 2768, 2762])).
% 1.54/1.71 tff(2776,plain,((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~(s(elem!1) = s(z))) | (~r(z, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(2777,plain,
% 1.54/1.71 (~b(s(s(elem!1)), s(elem!1))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2776, 2283, 8, 2683, 2746, 816, 2728])).
% 1.54/1.71 tff(2778,plain,
% 1.54/1.71 (r(s(s(elem!1)), s(elem!1))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[994, 2777, 2736])).
% 1.54/1.71 tff(2779,plain,
% 1.54/1.71 (~r(elem!1, s(s(elem!1)))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[1238, 2778, 2735])).
% 1.54/1.71 tff(2780,plain,
% 1.54/1.71 (b(elem!1, s(s(elem!1)))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[516, 2779, 2726])).
% 1.54/1.71 tff(2781,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(2782,plain,
% 1.54/1.71 (((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(2783,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[2782])).
% 1.54/1.71 tff(2784,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)))),
% 1.54/1.71 inference(transitivity,[status(thm)],[2783, 2781])).
% 1.54/1.71 tff(2785,plain,
% 1.54/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(2786,plain,
% 1.54/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[2785, 2784])).
% 1.54/1.71 tff(2787,plain,
% 1.54/1.71 ((~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2786, 306])).
% 1.54/1.71 tff(2788,plain,
% 1.54/1.71 (~b(s(s(s(z))), elem!1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2787, 2780, 2728, 2719, 2283])).
% 1.54/1.71 tff(2789,plain,
% 1.54/1.71 ((s(elem!1) = elem!1) <=> (s(z) = elem!1)),
% 1.54/1.71 inference(monotonicity,[status(thm)],[2683])).
% 1.54/1.71 tff(2790,plain,
% 1.54/1.71 ((s(elem!1) = elem!1) <=> (elem!1 = s(z))),
% 1.54/1.71 inference(transitivity,[status(thm)],[2789, 84])).
% 1.54/1.71 tff(2791,plain,
% 1.54/1.71 ((~(s(elem!1) = elem!1)) <=> (~(elem!1 = s(z)))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[2790])).
% 1.54/1.71 tff(2792,plain,
% 1.54/1.71 (~(elem!1 = s(z))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[2729, 2791])).
% 1.54/1.71 tff(2793,plain,
% 1.54/1.71 (r(elem!1, s(z))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[97, 2792])).
% 1.54/1.71 tff(2794,plain,
% 1.54/1.71 ((s(s(s(s(s(s(z)))))) = z) <=> (s(s(s(s(s(s(z)))))) = elem!1)),
% 1.54/1.71 inference(monotonicity,[status(thm)],[2701])).
% 1.54/1.71 tff(2795,plain,
% 1.54/1.71 ((~(s(s(s(s(s(s(z)))))) = z)) <=> (~(s(s(s(s(s(s(z)))))) = elem!1))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[2794])).
% 1.54/1.71 tff(2796,plain,
% 1.54/1.71 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[554, 2795])).
% 1.54/1.71 tff(2797,plain,
% 1.54/1.71 (b(z, s(elem!1)) <=> b(z, s(z))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[2683])).
% 1.54/1.71 tff(2798,plain,
% 1.54/1.71 (b(z, s(z)) <=> b(z, s(elem!1))),
% 1.54/1.71 inference(symmetry,[status(thm)],[2797])).
% 1.54/1.71 tff(2799,plain,
% 1.54/1.71 (b(z, s(z)) <=> b(elem!1, s(z))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[2701])).
% 1.54/1.71 tff(2800,plain,
% 1.54/1.71 (b(elem!1, s(z)) <=> b(z, s(z))),
% 1.54/1.71 inference(symmetry,[status(thm)],[2799])).
% 1.54/1.71 tff(2801,plain,
% 1.54/1.71 (b(elem!1, s(z)) <=> b(z, s(elem!1))),
% 1.54/1.71 inference(transitivity,[status(thm)],[2800, 2798])).
% 1.54/1.71 tff(2802,plain,
% 1.54/1.71 ((~b(elem!1, s(z))) <=> (~b(z, s(elem!1)))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[2801])).
% 1.54/1.71 tff(2803,plain,
% 1.54/1.71 (~b(z, s(elem!1))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[5, 2802])).
% 1.54/1.71 tff(2804,plain,
% 1.54/1.71 (r(z, s(elem!1))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[275, 2803])).
% 1.54/1.71 tff(2805,plain,
% 1.54/1.71 (b(s(s(elem!1)), elem!1) <=> b(s(s(z)), elem!1)),
% 1.54/1.71 inference(monotonicity,[status(thm)],[2739])).
% 1.54/1.71 tff(2806,plain,
% 1.54/1.71 (b(s(s(z)), elem!1)),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[2728, 2805])).
% 1.54/1.71 tff(2807,plain,
% 1.54/1.71 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(z)))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[2739])).
% 1.54/1.71 tff(2808,plain,
% 1.54/1.71 (b(z, s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[2701])).
% 1.54/1.71 tff(2809,plain,
% 1.54/1.71 (b(z, s(s(elem!1))) <=> b(elem!1, s(s(z)))),
% 1.54/1.71 inference(transitivity,[status(thm)],[2808, 2807])).
% 1.54/1.71 tff(2810,plain,
% 1.54/1.71 (b(elem!1, s(s(z)))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[1585, 2809])).
% 1.54/1.71 tff(2811,assumption,(b(s(s(z)), elem!1)), introduced(assumption)).
% 1.54/1.71 tff(2812,assumption,(b(s(s(s(s(s(s(z)))))), elem!1)), introduced(assumption)).
% 1.54/1.71 tff(2813,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(2814,plain,
% 1.54/1.71 (((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(2815,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[2814])).
% 1.54/1.71 tff(2816,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.54/1.71 inference(transitivity,[status(thm)],[2815, 2813])).
% 1.54/1.71 tff(2817,plain,
% 1.54/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(2818,plain,
% 1.54/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[2817, 2816])).
% 1.54/1.71 tff(2819,plain,
% 1.54/1.71 (~b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2818, 306, 2812, 2811, 2810])).
% 1.54/1.71 tff(2820,assumption,(s(s(z)) = s(s(s(s(s(s(z))))))), introduced(assumption)).
% 1.54/1.71 tff(2821,plain,
% 1.54/1.71 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[2820])).
% 1.54/1.72 tff(2822,plain,
% 1.54/1.72 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(z)))),
% 1.54/1.72 inference(symmetry,[status(thm)],[2821])).
% 1.54/1.72 tff(2823,plain,
% 1.54/1.72 (s(s(s(s(s(z))))) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.54/1.72 inference(symmetry,[status(thm)],[540])).
% 1.54/1.72 tff(2824,plain,
% 1.54/1.72 (s(s(s(s(s(z))))) = s(z)),
% 1.54/1.72 inference(transitivity,[status(thm)],[2823, 2822, 546])).
% 1.54/1.72 tff(2825,plain,
% 1.54/1.72 ($false),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[500, 2824])).
% 1.54/1.72 tff(2826,plain,(~(s(s(z)) = s(s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.72 tff(2827,plain,
% 1.54/1.72 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(s(s(z))))))) | b(s(s(z)), s(s(s(s(s(s(z))))))) | r(s(s(z)), s(s(s(s(s(s(z))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(s(s(z))))))) | b(s(s(z)), s(s(s(s(s(s(z))))))) | r(s(s(z)), s(s(s(s(s(s(z))))))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(2828,plain,
% 1.54/1.72 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(s(s(z))))))) | b(s(s(z)), s(s(s(s(s(s(z))))))) | r(s(s(z)), s(s(s(s(s(s(z))))))))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(2829,plain,
% 1.54/1.72 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(s(s(z))))))) | b(s(s(z)), s(s(s(s(s(s(z))))))) | r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[2828, 2827])).
% 1.54/1.72 tff(2830,plain,
% 1.54/1.72 (r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2829, 43, 2826, 2819])).
% 1.54/1.72 tff(2831,assumption,(b(s(z), elem!1)), introduced(assumption)).
% 1.54/1.72 tff(2832,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(2833,plain,
% 1.54/1.72 (((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(2834,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[2833])).
% 1.54/1.72 tff(2835,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.54/1.72 inference(transitivity,[status(thm)],[2834, 2832])).
% 1.54/1.72 tff(2836,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(2837,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[2836, 2835])).
% 1.54/1.72 tff(2838,plain,
% 1.54/1.72 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2837, 306, 2831, 2812, 2811, 2810])).
% 1.54/1.72 tff(2839,plain,
% 1.54/1.72 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(z))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[637])).
% 1.54/1.72 tff(2840,plain,
% 1.54/1.72 (s(s(s(s(s(z))))) = z),
% 1.54/1.72 inference(transitivity,[status(thm)],[2823, 2839, 61])).
% 1.54/1.72 tff(2841,plain,
% 1.54/1.72 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(z))))) = z))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(2842,plain,
% 1.54/1.72 (~(s(s(s(s(s(z))))) = z)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2841, 75])).
% 1.54/1.72 tff(2843,plain,
% 1.54/1.72 ($false),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2842, 2840])).
% 1.54/1.72 tff(2844,plain,(~(s(s(s(s(s(s(z)))))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.72 tff(2845,plain,
% 1.54/1.72 (r(s(s(s(s(s(s(z)))))), s(z))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[651, 43, 2844, 2838])).
% 1.54/1.72 tff(2846,plain,
% 1.54/1.72 (r(s(s(z)), s(z)) <=> r(s(s(elem!1)), s(z))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[2763])).
% 1.54/1.72 tff(2847,plain,
% 1.54/1.72 (r(s(s(elem!1)), s(z)) <=> r(s(s(z)), s(z))),
% 1.54/1.72 inference(symmetry,[status(thm)],[2846])).
% 1.54/1.72 tff(2848,plain,
% 1.54/1.72 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(elem!1)), s(z))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[2683])).
% 1.54/1.72 tff(2849,plain,
% 1.54/1.72 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(z)), s(z))),
% 1.54/1.72 inference(transitivity,[status(thm)],[2848, 2847])).
% 1.54/1.72 tff(2850,plain,
% 1.54/1.72 (r(s(s(z)), s(z))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[244, 2849])).
% 1.54/1.72 tff(2851,plain,
% 1.54/1.72 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(2852,plain,
% 1.54/1.72 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(2853,plain,
% 1.54/1.72 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[2852, 2851])).
% 1.54/1.72 tff(2854,plain,
% 1.54/1.72 ($false),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2853, 124, 2850, 2845, 2830])).
% 1.54/1.72 tff(2855,plain,((~r(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~(s(elem!1) = s(z))) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.72 tff(2856,plain,
% 1.54/1.72 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2855, 2778, 2806, 2719, 2683, 2804])).
% 1.54/1.72 tff(2857,plain,
% 1.54/1.72 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[1144, 2856, 2796])).
% 1.54/1.72 tff(2858,assumption,(r(s(s(s(s(s(s(z)))))), elem!1)), introduced(assumption)).
% 1.54/1.72 tff(2859,assumption,(r(s(s(s(z))), elem!1)), introduced(assumption)).
% 1.54/1.72 tff(2860,plain,
% 1.54/1.72 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(2861,plain,
% 1.54/1.72 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(2862,plain,
% 1.54/1.72 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[2861, 2860])).
% 1.54/1.72 tff(2863,plain,
% 1.54/1.72 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2862, 124, 2859, 2858])).
% 1.54/1.72 tff(2864,plain,
% 1.54/1.72 ((s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))) <=> (s(s(s(s(s(s(z)))))) = s(s(s(z))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[1726])).
% 1.54/1.72 tff(2865,plain,
% 1.54/1.72 ((s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))) <=> (s(s(s(z))) = s(s(s(s(s(s(z)))))))),
% 1.54/1.72 inference(transitivity,[status(thm)],[2864, 1122])).
% 1.54/1.72 tff(2866,plain,
% 1.54/1.72 ((s(s(s(z))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = s(s(s(elem!1))))),
% 1.54/1.72 inference(symmetry,[status(thm)],[2865])).
% 1.54/1.72 tff(2867,plain,
% 1.54/1.72 ((~(s(s(s(z))) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[2866])).
% 1.54/1.72 tff(2868,plain,
% 1.54/1.72 (~(s(s(s(s(s(s(z)))))) = s(s(s(elem!1))))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[556, 2867])).
% 1.54/1.72 tff(2869,plain,
% 1.54/1.72 (r(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))) <=> r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[1726])).
% 1.54/1.72 tff(2870,plain,
% 1.54/1.72 (r(s(s(s(s(s(s(z)))))), s(s(s(z)))) <=> r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))),
% 1.54/1.72 inference(symmetry,[status(thm)],[2869])).
% 1.54/1.72 tff(2871,plain,
% 1.54/1.72 ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) <=> (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[2870])).
% 1.54/1.72 tff(2872,assumption,(~r(s(s(s(s(s(s(z)))))), s(s(s(z))))), introduced(assumption)).
% 1.54/1.72 tff(2873,plain,
% 1.54/1.72 (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[2872, 2871])).
% 1.54/1.72 tff(2874,assumption,(~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))), introduced(assumption)).
% 1.54/1.72 tff(2875,plain,
% 1.54/1.72 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))) | r(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))) | r(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(2876,plain,
% 1.54/1.72 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))) | r(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(2877,plain,
% 1.54/1.72 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))) | r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[2876, 2875])).
% 1.54/1.72 tff(2878,plain,
% 1.54/1.72 ((s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))) | r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2877, 43, 2874])).
% 1.54/1.72 tff(2879,plain,
% 1.54/1.72 ($false),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2878, 2873, 2868])).
% 1.54/1.72 tff(2880,plain,(b(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))) | r(s(s(s(s(s(s(z)))))), s(s(s(z)))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.72 tff(2881,plain,
% 1.54/1.72 (b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2880, 2863, 1502])).
% 1.54/1.72 tff(2882,plain,
% 1.54/1.72 (b(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[1726])).
% 1.54/1.72 tff(2883,plain,
% 1.54/1.72 (b(s(s(s(s(s(s(z)))))), s(s(s(z)))) <=> b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))),
% 1.54/1.72 inference(symmetry,[status(thm)],[2882])).
% 1.54/1.72 tff(2884,plain,
% 1.54/1.72 ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) <=> (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[2883])).
% 1.54/1.72 tff(2885,assumption,(~b(s(s(s(s(s(s(z)))))), s(s(s(z))))), introduced(assumption)).
% 1.54/1.72 tff(2886,plain,
% 1.54/1.72 (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[2885, 2884])).
% 1.54/1.72 tff(2887,assumption,(b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))), introduced(assumption)).
% 1.54/1.72 tff(2888,plain,
% 1.54/1.72 ($false),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2887, 2886])).
% 1.54/1.72 tff(2889,plain,((~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | b(s(s(s(s(s(s(z)))))), s(s(s(z)))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.72 tff(2890,plain,
% 1.54/1.72 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2889, 2881, 1502])).
% 1.54/1.72 tff(2891,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(2892,plain,
% 1.54/1.72 (((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(2893,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[2892])).
% 1.54/1.72 tff(2894,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.54/1.72 inference(transitivity,[status(thm)],[2893, 2891])).
% 1.54/1.72 tff(2895,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(2896,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[2895, 2894])).
% 1.54/1.72 tff(2897,plain,
% 1.54/1.72 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2896, 306, 2284, 8, 2890])).
% 1.54/1.72 tff(2898,plain,
% 1.54/1.72 (r(s(s(s(s(s(s(z)))))), s(z))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[651, 43, 2844, 2897])).
% 1.54/1.72 tff(2899,plain,
% 1.54/1.72 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(2900,plain,
% 1.54/1.72 (((~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), elem!1))) <=> ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(2901,plain,
% 1.54/1.72 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(z)))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[2900])).
% 1.54/1.72 tff(2902,plain,
% 1.54/1.72 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 1.54/1.72 inference(transitivity,[status(thm)],[2901, 2899])).
% 1.54/1.72 tff(2903,plain,
% 1.54/1.72 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(2904,plain,
% 1.54/1.72 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(z)))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[2903, 2902])).
% 1.54/1.72 tff(2905,plain,
% 1.54/1.72 ($false),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2904, 124, 359, 2858, 2898])).
% 1.54/1.72 tff(2906,plain,((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~(z = elem!1)) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.72 tff(2907,plain,
% 1.54/1.72 (~r(s(s(s(z))), elem!1)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2906, 2857, 2283, 8, 2701, 2793])).
% 1.54/1.72 tff(2908,plain,
% 1.54/1.72 ($false),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[1489, 2907, 2788, 2704])).
% 1.54/1.72 tff(2909,plain,(b(elem!1, s(s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~(s(elem!1) = s(z))) | (~b(s(elem!1), elem!1)) | b(elem!1, s(z)) | r(s(s(elem!1)), elem!1) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.72 tff(2910,plain,
% 1.54/1.72 (b(elem!1, s(s(s(z))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2909, 2679, 8, 2700, 5, 6, 2])).
% 1.54/1.72 tff(2911,plain,
% 1.54/1.72 (b(s(elem!1), z)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2709, 2700, 2690])).
% 1.54/1.72 tff(2912,plain,
% 1.54/1.72 (b(s(z), elem!1)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2718, 2911, 2690])).
% 1.54/1.72 tff(2913,plain,
% 1.54/1.72 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 1.54/1.72 inference(monotonicity,[status(thm)],[2690])).
% 1.54/1.72 tff(2914,plain,
% 1.54/1.72 ((~(s(s(s(z))) = z)) <=> (~(s(s(s(z))) = elem!1))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[2913])).
% 1.54/1.72 tff(2915,plain,
% 1.54/1.72 (~(s(s(s(z))) = elem!1)),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[169, 2914])).
% 1.54/1.72 tff(2916,plain,
% 1.54/1.72 ((s(elem!1) = elem!1) <=> (s(z) = elem!1)),
% 1.54/1.72 inference(monotonicity,[status(thm)],[2679])).
% 1.54/1.72 tff(2917,plain,
% 1.54/1.72 ((s(elem!1) = elem!1) <=> (elem!1 = s(z))),
% 1.54/1.72 inference(transitivity,[status(thm)],[2916, 84])).
% 1.54/1.72 tff(2918,plain,
% 1.54/1.72 ((~(s(elem!1) = elem!1)) <=> (~(elem!1 = s(z)))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[2917])).
% 1.54/1.72 tff(2919,plain,
% 1.54/1.72 (~(elem!1 = s(z))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[2699, 2918])).
% 1.54/1.72 tff(2920,plain,
% 1.54/1.72 (r(elem!1, s(z))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[97, 2919])).
% 1.54/1.72 tff(2921,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(z), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(2922,plain,
% 1.54/1.72 (((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(2923,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z)))))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[2922])).
% 1.54/1.72 tff(2924,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.54/1.72 inference(transitivity,[status(thm)],[2923, 2921])).
% 1.54/1.72 tff(2925,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(2926,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z)))))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[2925, 2924])).
% 1.54/1.72 tff(2927,plain,
% 1.54/1.72 ($false),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2926, 306, 2284, 8, 2831, 1470])).
% 1.54/1.72 tff(2928,plain,((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.72 tff(2929,plain,
% 1.54/1.72 (~b(s(s(s(z))), s(z))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2928, 2910, 2912, 8])).
% 1.54/1.72 tff(2930,plain,
% 1.54/1.72 (r(s(s(s(z))), s(z))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[113, 2929])).
% 1.54/1.72 tff(2931,plain,
% 1.54/1.72 (~r(s(s(s(z))), elem!1)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[1481, 2930, 2920])).
% 1.54/1.72 tff(2932,plain,
% 1.54/1.72 (b(s(s(s(z))), elem!1)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[1489, 2931, 2915])).
% 1.54/1.72 tff(2933,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(2934,plain,
% 1.54/1.72 (((~b(s(s(s(z))), z)) | (~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), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(2935,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[2934])).
% 1.54/1.72 tff(2936,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 1.54/1.73 inference(transitivity,[status(thm)],[2935, 2933])).
% 1.54/1.73 tff(2937,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~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))))))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(2938,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[2937, 2936])).
% 1.54/1.73 tff(2939,plain,
% 1.54/1.73 ((~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2938, 306])).
% 1.54/1.73 tff(2940,plain,
% 1.54/1.73 (~b(s(s(s(z))), z)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2939, 2932, 8, 2912, 2910])).
% 1.54/1.73 tff(2941,plain,
% 1.54/1.73 (b(s(s(s(elem!1))), z) <=> b(s(s(s(z))), z)),
% 1.54/1.73 inference(monotonicity,[status(thm)],[1623])).
% 1.54/1.73 tff(2942,plain,
% 1.54/1.73 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), z)),
% 1.54/1.73 inference(monotonicity,[status(thm)],[1620])).
% 1.54/1.73 tff(2943,plain,
% 1.54/1.73 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(z))), z)),
% 1.54/1.73 inference(transitivity,[status(thm)],[2942, 2941])).
% 1.54/1.73 tff(2944,plain,
% 1.54/1.73 (b(s(s(s(z))), z)),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[1664, 2943])).
% 1.54/1.73 tff(2945,plain,
% 1.54/1.73 ($false),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2195, 2944])).
% 1.54/1.73 tff(2946,plain,((~b(s(s(s(elem!1))), elem!1)) | b(s(s(s(z))), z) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.73 tff(2947,plain,
% 1.54/1.73 (~b(s(s(s(elem!1))), elem!1)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2946, 2940, 2694])).
% 1.54/1.73 tff(2948,plain,
% 1.54/1.73 (r(s(s(s(elem!1))), elem!1)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[1636, 2947, 2693])).
% 1.54/1.73 tff(2949,plain,
% 1.54/1.73 (r(s(s(s(z))), elem!1)),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[2948, 2682])).
% 1.54/1.73 tff(2950,plain,
% 1.54/1.73 ($false),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2931, 2949])).
% 1.54/1.73 tff(2951,plain,(r(s(elem!1), elem!1) | (~b(s(z), s(s(s(z))))) | b(elem!1, s(z)) | r(s(s(elem!1)), elem!1) | b(elem!1, z) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.73 tff(2952,plain,
% 1.54/1.73 (r(s(elem!1), elem!1)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2951, 5, 8, 6, 2, 7])).
% 1.54/1.73 tff(2953,plain,
% 1.54/1.73 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(2954,plain,
% 1.54/1.73 (((~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1))) <=> ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(2955,plain,
% 1.54/1.73 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z)))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[2954])).
% 1.54/1.73 tff(2956,plain,
% 1.54/1.73 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))))),
% 1.54/1.73 inference(transitivity,[status(thm)],[2955, 2953])).
% 1.54/1.73 tff(2957,plain,
% 1.54/1.73 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(2958,plain,
% 1.54/1.73 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z)))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[2957, 2956])).
% 1.54/1.73 tff(2959,plain,
% 1.54/1.73 ($false),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2958, 124, 802, 359, 2626])).
% 1.54/1.73 tff(2960,plain,((~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.73 tff(2961,plain,
% 1.54/1.73 (~r(s(elem!1), s(z))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2960, 1474, 2952])).
% 1.54/1.73 tff(2962,plain,
% 1.54/1.73 (~(s(elem!1) = s(z))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2689, 2190])).
% 1.54/1.73 tff(2963,plain,
% 1.54/1.73 ($false),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2612, 43, 2609, 2637, 2249])).
% 1.54/1.73 tff(2964,plain,(r(s(elem!1), s(z)) | b(s(elem!1), s(z)) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.73 tff(2965,plain,
% 1.54/1.73 (b(s(elem!1), s(z))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2964, 2962, 2961])).
% 1.54/1.73 tff(2966,plain,
% 1.54/1.73 (~(elem!1 = s(elem!1))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2639, 2961, 1474])).
% 1.54/1.73 tff(2967,assumption,(s(s(s(z))) = s(s(elem!1))), introduced(assumption)).
% 1.54/1.73 tff(2968,plain,
% 1.54/1.73 (inj_0(s(s(s(z)))) = inj_0(s(s(elem!1)))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[2967])).
% 1.54/1.73 tff(2969,plain,
% 1.54/1.73 (s(s(z)) = s(elem!1)),
% 1.54/1.73 inference(transitivity,[status(thm)],[103, 2968, 66])).
% 1.54/1.73 tff(2970,plain,
% 1.54/1.73 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[2969])).
% 1.54/1.73 tff(2971,plain,
% 1.54/1.73 (inj_0(s(elem!1)) = inj_0(s(s(z)))),
% 1.54/1.73 inference(symmetry,[status(thm)],[2970])).
% 1.54/1.73 tff(2972,plain,
% 1.54/1.73 (elem!1 = s(z)),
% 1.54/1.73 inference(transitivity,[status(thm)],[1651, 2971, 546])).
% 1.54/1.73 tff(2973,plain,
% 1.54/1.73 ($false),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[87, 2972])).
% 1.54/1.73 tff(2974,plain,((~(s(s(s(z))) = s(s(elem!1)))) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.73 tff(2975,plain,
% 1.54/1.73 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2974, 83])).
% 1.54/1.73 tff(2976,assumption,(~(s(s(s(z))) = s(s(elem!1)))), introduced(assumption)).
% 1.54/1.73 tff(2977,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(2978,plain,
% 1.54/1.73 (((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(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))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(2979,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[2978])).
% 1.54/1.73 tff(2980,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.54/1.73 inference(transitivity,[status(thm)],[2979, 2977])).
% 1.54/1.73 tff(2981,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(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)))))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(2982,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1))))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[2981, 2980])).
% 1.54/1.73 tff(2983,plain,
% 1.54/1.73 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2982, 306, 30, 1967, 1470])).
% 1.54/1.73 tff(2984,plain,
% 1.54/1.73 (((~![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))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(2985,plain,
% 1.54/1.73 ((~![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))))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(2986,plain,
% 1.54/1.73 ((~![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)))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[2985, 2984])).
% 1.54/1.73 tff(2987,plain,
% 1.54/1.73 (r(s(s(s(z))), s(s(elem!1)))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2986, 43, 2983, 2976])).
% 1.54/1.73 tff(2988,plain,
% 1.54/1.73 (~b(s(s(s(z))), z)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2228, 838, 1967, 1470])).
% 1.54/1.73 tff(2989,plain,
% 1.54/1.73 (r(s(s(s(z))), z)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2197, 2988])).
% 1.54/1.73 tff(2990,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(2991,plain,
% 1.54/1.73 (((~b(s(s(s(z))), elem!1)) | (~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)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(2992,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[2991])).
% 1.54/1.73 tff(2993,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.54/1.73 inference(transitivity,[status(thm)],[2992, 2990])).
% 1.54/1.73 tff(2994,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(2995,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[2994, 2993])).
% 1.54/1.73 tff(2996,plain,
% 1.54/1.73 (~b(s(s(elem!1)), z)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2995, 306, 838, 30, 1967, 1470])).
% 1.54/1.73 tff(2997,plain,
% 1.54/1.73 (r(s(s(elem!1)), z)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[476, 2996])).
% 1.54/1.73 tff(2998,plain,
% 1.54/1.73 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(2999,plain,
% 1.54/1.73 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(3000,plain,
% 1.54/1.73 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(elem!1))))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[2999, 2998])).
% 1.54/1.73 tff(3001,plain,
% 1.54/1.73 ($false),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3000, 124, 2997, 2989, 2987])).
% 1.54/1.73 tff(3002,plain,((~b(s(s(elem!1)), elem!1)) | (s(s(s(z))) = s(s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.73 tff(3003,plain,
% 1.54/1.73 (~b(s(s(elem!1)), elem!1)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3002, 2975, 1490, 1456, 2191])).
% 1.54/1.73 tff(3004,plain,
% 1.54/1.73 (s(s(elem!1)) = elem!1),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[47, 3003, 6])).
% 1.54/1.73 tff(3005,plain,
% 1.54/1.73 (elem!1 = s(s(elem!1))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[1174, 3004])).
% 1.54/1.73 tff(3006,plain,
% 1.54/1.73 (s(s(s(elem!1))) = s(elem!1)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[1168, 3005])).
% 1.54/1.73 tff(3007,plain,
% 1.54/1.73 (r(z, s(s(s(elem!1)))) <=> r(z, s(elem!1))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[3006])).
% 1.54/1.73 tff(3008,plain,
% 1.54/1.73 (r(s(s(s(elem!1))), elem!1) <=> r(s(elem!1), elem!1)),
% 1.54/1.73 inference(monotonicity,[status(thm)],[3006])).
% 1.54/1.73 tff(3009,plain,
% 1.54/1.73 (r(s(elem!1), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 1.54/1.73 inference(symmetry,[status(thm)],[3008])).
% 1.54/1.73 tff(3010,plain,
% 1.54/1.73 (r(s(s(s(elem!1))), elem!1)),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[2952, 3009])).
% 1.54/1.73 tff(3011,plain,
% 1.54/1.73 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(3012,plain,
% 1.54/1.73 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(3013,plain,
% 1.54/1.73 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1)))))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[3012, 3011])).
% 1.54/1.73 tff(3014,plain,
% 1.54/1.73 (~r(s(z), s(s(s(elem!1))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3013, 124, 1627, 4])).
% 1.54/1.73 tff(3015,plain,
% 1.54/1.73 (((~![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)))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(3016,plain,
% 1.54/1.73 ((~![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)))))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(3017,plain,
% 1.54/1.73 ((~![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))))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[3016, 3015])).
% 1.54/1.73 tff(3018,plain,
% 1.54/1.73 (b(s(z), s(s(s(elem!1))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3017, 43, 645, 3014])).
% 1.54/1.73 tff(3019,plain,
% 1.54/1.73 (~r(s(z), z)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[1049, 4, 246])).
% 1.54/1.73 tff(3020,plain,
% 1.54/1.73 (b(s(z), z)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[221, 3019])).
% 1.54/1.73 tff(3021,assumption,(r(s(s(s(elem!1))), z)), introduced(assumption)).
% 1.54/1.73 tff(3022,plain,
% 1.54/1.73 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(3023,plain,
% 1.54/1.73 (((~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(3024,plain,
% 1.54/1.73 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[3023])).
% 1.54/1.73 tff(3025,plain,
% 1.54/1.73 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.54/1.73 inference(transitivity,[status(thm)],[3024, 3022])).
% 1.54/1.73 tff(3026,plain,
% 1.54/1.73 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(3027,plain,
% 1.54/1.73 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[3026, 3025])).
% 1.54/1.73 tff(3028,plain,
% 1.54/1.73 ($false),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3027, 124, 246, 3021, 1627])).
% 1.54/1.73 tff(3029,plain,((~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.73 tff(3030,plain,
% 1.54/1.73 (~r(s(s(s(elem!1))), z)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3029, 1627, 246])).
% 1.54/1.73 tff(3031,plain,
% 1.54/1.73 (((~![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))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(3032,plain,
% 1.54/1.73 ((~![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))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(3033,plain,
% 1.54/1.73 ((~![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)),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[3032, 3031])).
% 1.54/1.73 tff(3034,plain,
% 1.54/1.73 (b(s(s(s(elem!1))), z)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3033, 43, 579, 3030])).
% 1.54/1.74 tff(3035,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(3036,plain,
% 1.54/1.74 (((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(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))))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(3037,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[3036])).
% 1.54/1.74 tff(3038,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.54/1.74 inference(transitivity,[status(thm)],[3037, 3035])).
% 1.54/1.74 tff(3039,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(3040,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1)))))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[3039, 3038])).
% 1.54/1.74 tff(3041,plain,
% 1.54/1.74 ($false),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3040, 306, 818, 3034, 3020, 3018])).
% 1.54/1.74 tff(3042,plain,((~r(s(z), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.74 tff(3043,plain,
% 1.54/1.74 (~b(z, s(s(s(elem!1))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3042, 3010, 2193, 1501])).
% 1.54/1.74 tff(3044,plain,
% 1.54/1.74 (r(z, s(s(s(elem!1))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[585, 3043])).
% 1.54/1.74 tff(3045,plain,
% 1.54/1.74 (r(z, s(elem!1))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[3044, 3007])).
% 1.54/1.74 tff(3046,plain,
% 1.54/1.74 (~r(elem!1, s(elem!1))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[265, 3045, 2193])).
% 1.54/1.74 tff(3047,plain,
% 1.54/1.74 (b(elem!1, s(elem!1))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[372, 3046, 2966])).
% 1.54/1.74 tff(3048,plain,
% 1.54/1.74 (r(s(s(s(elem!1))), z) <=> r(s(elem!1), z)),
% 1.54/1.74 inference(monotonicity,[status(thm)],[3006])).
% 1.54/1.74 tff(3049,plain,
% 1.54/1.74 ((~r(s(s(s(elem!1))), z)) <=> (~r(s(elem!1), z))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[3048])).
% 1.54/1.74 tff(3050,plain,
% 1.54/1.74 (~r(s(s(s(elem!1))), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3029, 3010, 2193])).
% 1.54/1.74 tff(3051,plain,
% 1.54/1.74 (~r(s(elem!1), z)),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[3050, 3049])).
% 1.54/1.74 tff(3052,plain,
% 1.54/1.74 (b(s(elem!1), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[1185, 43, 77, 3051])).
% 1.54/1.74 tff(3053,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(3054,plain,
% 1.54/1.74 (((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z)))) <=> ((~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(3055,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), s(z)))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[3054])).
% 1.54/1.74 tff(3056,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))),
% 1.54/1.74 inference(transitivity,[status(thm)],[3055, 3053])).
% 1.54/1.74 tff(3057,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(3058,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), s(z)))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[3057, 3056])).
% 1.54/1.74 tff(3059,plain,
% 1.54/1.74 ($false),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3058, 306, 2191, 3052, 3047, 2965, 2248])).
% 1.54/1.74 tff(3060,plain,(b(s(s(s(z))), s(z)) | r(s(s(elem!1)), elem!1) | b(elem!1, z) | r(z, elem!1) | (~b(s(z), s(s(s(z))))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.74 tff(3061,plain,
% 1.54/1.74 (b(s(s(s(z))), s(z))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3060, 5, 2, 7, 8, 6])).
% 1.54/1.74 tff(3062,assumption,(~r(elem!1, z)), introduced(assumption)).
% 1.54/1.74 tff(3063,plain,
% 1.54/1.74 (elem!1 = z),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[174, 3062, 2])).
% 1.54/1.74 tff(3064,plain,
% 1.54/1.74 (z = elem!1),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2172, 3063])).
% 1.54/1.74 tff(3065,plain,
% 1.54/1.74 (s(elem!1) = s(z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2251, 3064])).
% 1.54/1.74 tff(3066,plain,
% 1.54/1.74 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2724, 3065])).
% 1.54/1.74 tff(3067,plain,
% 1.54/1.74 (~(elem!1 = s(s(elem!1)))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[1168, 3066])).
% 1.54/1.74 tff(3068,plain,
% 1.54/1.74 (~(s(s(elem!1)) = elem!1)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[1174, 3067])).
% 1.54/1.74 tff(3069,plain,
% 1.54/1.74 (s(elem!1) = s(z)),
% 1.54/1.74 inference(monotonicity,[status(thm)],[3063])).
% 1.54/1.74 tff(3070,plain,
% 1.54/1.74 (r(s(elem!1), z) <=> r(s(z), z)),
% 1.54/1.74 inference(monotonicity,[status(thm)],[3069])).
% 1.54/1.74 tff(3071,plain,
% 1.54/1.74 (r(s(elem!1), elem!1) <=> r(s(elem!1), z)),
% 1.54/1.74 inference(monotonicity,[status(thm)],[3063])).
% 1.54/1.74 tff(3072,plain,
% 1.54/1.74 (r(s(elem!1), z)),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[2952, 3071])).
% 1.54/1.74 tff(3073,plain,
% 1.54/1.74 (r(s(z), z)),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[3072, 3070])).
% 1.54/1.74 tff(3074,plain,
% 1.54/1.74 (b(s(z), elem!1) <=> b(s(z), z)),
% 1.54/1.74 inference(monotonicity,[status(thm)],[3063])).
% 1.54/1.74 tff(3075,plain,
% 1.54/1.74 (b(s(z), z) <=> b(s(z), elem!1)),
% 1.54/1.74 inference(symmetry,[status(thm)],[3074])).
% 1.54/1.74 tff(3076,plain,
% 1.54/1.74 (b(s(elem!1), z) <=> b(s(z), z)),
% 1.54/1.74 inference(monotonicity,[status(thm)],[3069])).
% 1.54/1.74 tff(3077,plain,
% 1.54/1.74 (b(s(elem!1), z) <=> b(s(z), elem!1)),
% 1.54/1.74 inference(transitivity,[status(thm)],[3076, 3075])).
% 1.54/1.74 tff(3078,plain,
% 1.54/1.74 ((~b(s(elem!1), z)) <=> (~b(s(z), elem!1))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[3077])).
% 1.54/1.74 tff(3079,plain,
% 1.54/1.74 (b(s(elem!1), elem!1) <=> b(s(elem!1), z)),
% 1.54/1.74 inference(monotonicity,[status(thm)],[3063])).
% 1.54/1.74 tff(3080,plain,
% 1.54/1.74 ((~b(s(elem!1), elem!1)) <=> (~b(s(elem!1), z))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[3079])).
% 1.54/1.74 tff(3081,plain,
% 1.54/1.74 (~b(s(elem!1), elem!1)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2909, 3065, 8, 3, 5, 6, 2])).
% 1.54/1.74 tff(3082,plain,
% 1.54/1.74 (~b(s(elem!1), z)),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[3081, 3080])).
% 1.54/1.74 tff(3083,plain,
% 1.54/1.74 (~b(s(z), elem!1)),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[3082, 3078])).
% 1.54/1.74 tff(3084,plain,
% 1.54/1.74 (r(s(z), z) <=> r(elem!1, z)),
% 1.54/1.74 inference(monotonicity,[status(thm)],[85])).
% 1.54/1.74 tff(3085,plain,
% 1.54/1.74 (r(elem!1, z) <=> r(s(z), z)),
% 1.54/1.74 inference(symmetry,[status(thm)],[3084])).
% 1.54/1.74 tff(3086,plain,
% 1.54/1.74 ((~r(elem!1, z)) <=> (~r(s(z), z))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[3085])).
% 1.54/1.74 tff(3087,plain,
% 1.54/1.74 (~r(s(z), z)),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[3062, 3086])).
% 1.54/1.74 tff(3088,plain,
% 1.54/1.74 ($false),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[204, 3087])).
% 1.54/1.74 tff(3089,plain,((~(s(z) = elem!1)) | (~r(s(z), z)) | r(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.74 tff(3090,plain,
% 1.54/1.74 (~(s(z) = elem!1)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3089, 3062, 204])).
% 1.54/1.74 tff(3091,plain,
% 1.54/1.74 (r(s(z), elem!1)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[1500, 43, 2715, 3090])).
% 1.54/1.74 tff(3092,plain,
% 1.54/1.74 ((elem!1 = s(z)) <=> (s(z) = elem!1)),
% 1.54/1.74 inference(symmetry,[status(thm)],[84])).
% 1.54/1.74 tff(3093,plain,
% 1.54/1.74 (s(z) = elem!1),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[10, 3092])).
% 1.54/1.74 tff(3094,assumption,(~(s(z) = elem!1)), introduced(assumption)).
% 1.54/1.74 tff(3095,plain,
% 1.54/1.74 ($false),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3094, 3093])).
% 1.54/1.74 tff(3096,plain,((~(elem!1 = s(z))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.74 tff(3097,plain,
% 1.54/1.74 (~(elem!1 = s(z))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3096, 3090])).
% 1.54/1.74 tff(3098,plain,
% 1.54/1.74 (r(elem!1, s(z))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[96, 43, 5, 3097])).
% 1.54/1.74 tff(3099,plain,
% 1.54/1.74 (~(s(elem!1) = s(z))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2689, 2170])).
% 1.54/1.74 tff(3100,plain,
% 1.54/1.74 (r(s(elem!1), s(z))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2964, 3099, 2609])).
% 1.54/1.74 tff(3101,plain,
% 1.54/1.74 (~r(s(elem!1), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2634, 3100, 204])).
% 1.54/1.74 tff(3102,plain,
% 1.54/1.74 (b(s(elem!1), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2380, 3101])).
% 1.54/1.74 tff(3103,plain,
% 1.54/1.74 (~(elem!1 = z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2172, 2170])).
% 1.54/1.74 tff(3104,plain,
% 1.54/1.74 (b(elem!1, z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[174, 3103, 3062])).
% 1.54/1.74 tff(3105,plain,
% 1.54/1.74 (b(z, elem!1)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[835, 2170, 7])).
% 1.54/1.74 tff(3106,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(3107,plain,
% 1.54/1.74 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z))) <=> ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(3108,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[3107])).
% 1.54/1.74 tff(3109,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)))),
% 1.54/1.74 inference(transitivity,[status(thm)],[3108, 3106])).
% 1.54/1.74 tff(3110,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(3111,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[3110, 3109])).
% 1.54/1.74 tff(3112,plain,
% 1.54/1.74 ($false),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3111, 306, 3105, 3104, 3102, 816])).
% 1.54/1.74 tff(3113,plain,((z = elem!1) | (~b(s(elem!1), elem!1)) | (~r(s(z), z)) | b(s(elem!1), s(z)) | r(elem!1, z) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.74 tff(3114,plain,
% 1.54/1.74 (z = elem!1),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3113, 816, 204, 2609, 3062, 7])).
% 1.54/1.74 tff(3115,plain,
% 1.54/1.74 (~b(s(elem!1), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2718, 3114, 2715])).
% 1.54/1.74 tff(3116,plain,
% 1.54/1.74 ($false),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2709, 3115, 3114, 816])).
% 1.54/1.74 tff(3117,plain,((~b(s(elem!1), elem!1)) | b(s(z), elem!1) | (~r(s(z), z)) | b(s(elem!1), s(z)) | r(elem!1, z) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.74 tff(3118,plain,
% 1.54/1.74 (~b(s(elem!1), elem!1)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3117, 2609, 204, 2715, 3062, 7])).
% 1.54/1.74 tff(3119,plain,
% 1.54/1.74 (r(s(elem!1), elem!1)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[813, 3118, 193])).
% 1.54/1.74 tff(3120,plain,
% 1.54/1.74 (~r(s(elem!1), s(z))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2960, 3119, 3098])).
% 1.54/1.74 tff(3121,plain,
% 1.54/1.74 (s(elem!1) = s(z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2964, 3120, 2609])).
% 1.54/1.74 tff(3122,plain,
% 1.54/1.74 (z = elem!1),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2689, 3121])).
% 1.54/1.74 tff(3123,plain,
% 1.54/1.74 (s(z) = s(elem!1)),
% 1.54/1.74 inference(monotonicity,[status(thm)],[3122])).
% 1.54/1.74 tff(3124,plain,
% 1.54/1.74 (s(s(z)) = s(s(elem!1))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[3123])).
% 1.54/1.74 tff(3125,plain,
% 1.54/1.74 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[3124])).
% 1.54/1.74 tff(3126,plain,
% 1.54/1.74 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.54/1.74 inference(symmetry,[status(thm)],[3125])).
% 1.54/1.74 tff(3127,plain,
% 1.54/1.74 (r(s(s(s(elem!1))), s(s(s(s(s(s(z))))))) <=> r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[3126])).
% 1.54/1.74 tff(3128,plain,
% 1.54/1.74 (r(s(s(s(z))), s(s(s(s(s(s(z))))))) <=> r(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))),
% 1.54/1.74 inference(symmetry,[status(thm)],[3127])).
% 1.54/1.74 tff(3129,plain,
% 1.54/1.74 (b(s(s(s(elem!1))), s(s(s(s(s(s(z))))))) <=> b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[3126])).
% 1.54/1.74 tff(3130,plain,
% 1.54/1.74 ((~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))) <=> (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[3129])).
% 1.54/1.74 tff(3131,plain,
% 1.54/1.74 ((s(s(s(s(s(s(z)))))) = z) <=> (s(s(s(s(s(s(z)))))) = elem!1)),
% 1.54/1.74 inference(monotonicity,[status(thm)],[3122])).
% 1.54/1.74 tff(3132,plain,
% 1.54/1.74 ((~(s(s(s(s(s(s(z)))))) = z)) <=> (~(s(s(s(s(s(s(z)))))) = elem!1))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[3131])).
% 1.54/1.74 tff(3133,plain,
% 1.54/1.74 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[554, 3132])).
% 1.54/1.74 tff(3134,plain,
% 1.54/1.74 (b(s(s(s(z))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 1.54/1.74 inference(monotonicity,[status(thm)],[3125])).
% 1.54/1.74 tff(3135,plain,
% 1.54/1.74 (~r(s(elem!1), s(z))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2960, 802, 359])).
% 1.54/1.74 tff(3136,plain,
% 1.54/1.74 (s(elem!1) = s(z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2964, 3135, 2609])).
% 1.54/1.74 tff(3137,plain,
% 1.54/1.74 (z = elem!1),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2689, 3136])).
% 1.54/1.74 tff(3138,plain,
% 1.54/1.74 (s(z) = s(elem!1)),
% 1.54/1.74 inference(monotonicity,[status(thm)],[3137])).
% 1.54/1.74 tff(3139,plain,
% 1.54/1.74 (s(s(z)) = s(s(elem!1))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[3138])).
% 1.54/1.74 tff(3140,plain,
% 1.54/1.74 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[3139])).
% 1.54/1.74 tff(3141,plain,
% 1.54/1.74 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[3140])).
% 1.54/1.74 tff(3142,plain,
% 1.54/1.74 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 1.54/1.74 inference(monotonicity,[status(thm)],[3141])).
% 1.54/1.74 tff(3143,plain,
% 1.54/1.74 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(z)))), elem!1)),
% 1.54/1.74 inference(monotonicity,[status(thm)],[3137])).
% 1.54/1.74 tff(3144,plain,
% 1.54/1.74 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 1.54/1.74 inference(transitivity,[status(thm)],[3143, 3142])).
% 1.54/1.74 tff(3145,plain,
% 1.54/1.74 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(s(s(elem!1))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[3140])).
% 1.54/1.74 tff(3146,plain,
% 1.54/1.74 (r(elem!1, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(z))))),
% 1.54/1.74 inference(symmetry,[status(thm)],[3145])).
% 1.54/1.74 tff(3147,plain,
% 1.54/1.74 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[1511, 3137])).
% 1.54/1.74 tff(3148,plain,
% 1.54/1.74 (~(elem!1 = s(s(s(elem!1))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[1518, 3147])).
% 1.54/1.74 tff(3149,assumption,(~r(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 1.54/1.74 tff(3150,plain,
% 1.54/1.74 (b(s(s(elem!1)), s(elem!1))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[994, 3149, 403])).
% 1.54/1.74 tff(3151,plain,
% 1.54/1.74 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.54/1.74 inference(symmetry,[status(thm)],[3140])).
% 1.54/1.74 tff(3152,plain,
% 1.54/1.74 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(z))), s(elem!1))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[3151])).
% 1.54/1.74 tff(3153,plain,
% 1.54/1.74 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.54/1.74 inference(symmetry,[status(thm)],[3152])).
% 1.54/1.74 tff(3154,plain,
% 1.54/1.74 (b(s(s(s(z))), s(z)) <=> b(s(s(s(z))), s(elem!1))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[3138])).
% 1.54/1.74 tff(3155,plain,
% 1.54/1.74 (b(s(s(s(z))), s(z)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.54/1.74 inference(transitivity,[status(thm)],[3154, 3153])).
% 1.54/1.74 tff(3156,plain,
% 1.54/1.74 (~(s(s(s(elem!1))) = elem!1)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2187, 3148])).
% 1.54/1.74 tff(3157,plain,
% 1.54/1.74 (b(elem!1, z) <=> b(elem!1, elem!1)),
% 1.54/1.74 inference(monotonicity,[status(thm)],[3137])).
% 1.54/1.74 tff(3158,plain,
% 1.54/1.74 (b(elem!1, elem!1) <=> b(elem!1, z)),
% 1.54/1.74 inference(symmetry,[status(thm)],[3157])).
% 1.54/1.74 tff(3159,plain,
% 1.54/1.74 ((~b(elem!1, elem!1)) <=> (~b(elem!1, z))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[3158])).
% 1.54/1.74 tff(3160,plain,
% 1.54/1.74 (~b(elem!1, z)),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[1468, 3159])).
% 1.54/1.74 tff(3161,plain,
% 1.54/1.74 (~r(s(s(s(z))), s(z))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2182, 3160, 359, 204, 3156])).
% 1.54/1.74 tff(3162,plain,
% 1.54/1.74 (b(s(s(s(z))), s(z))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[113, 3161])).
% 1.54/1.74 tff(3163,plain,
% 1.54/1.74 (b(s(s(s(elem!1))), s(elem!1))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[3162, 3155])).
% 1.54/1.74 tff(3164,plain,
% 1.54/1.74 (b(s(s(s(elem!1))), s(s(s(s(s(s(z))))))) <=> b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[1726])).
% 1.54/1.74 tff(3165,plain,
% 1.54/1.74 (b(s(s(s(z))), s(s(s(s(s(s(z))))))) <=> b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))),
% 1.54/1.74 inference(symmetry,[status(thm)],[3164])).
% 1.54/1.74 tff(3166,plain,
% 1.54/1.74 (r(s(s(s(elem!1))), s(s(s(s(s(s(z))))))) <=> r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[1726])).
% 1.54/1.74 tff(3167,plain,
% 1.54/1.74 ((~r(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))) <=> (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[3166])).
% 1.54/1.74 tff(3168,plain,
% 1.54/1.74 ((s(s(s(s(s(s(z)))))) = z) <=> (s(s(s(s(s(s(z)))))) = elem!1)),
% 1.54/1.74 inference(monotonicity,[status(thm)],[1502])).
% 1.54/1.74 tff(3169,plain,
% 1.54/1.74 ((~(s(s(s(s(s(s(z)))))) = z)) <=> (~(s(s(s(s(s(s(z)))))) = elem!1))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[3168])).
% 1.54/1.74 tff(3170,plain,
% 1.54/1.74 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[554, 3169])).
% 1.54/1.74 tff(3171,plain,
% 1.54/1.74 (~(s(s(s(elem!1))) = elem!1)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2187, 1519])).
% 1.54/1.74 tff(3172,plain,
% 1.54/1.74 (~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[1655, 1519])).
% 1.54/1.74 tff(3173,plain,
% 1.54/1.74 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[1672, 1664, 1663, 30])).
% 1.54/1.74 tff(3174,plain,
% 1.54/1.74 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[610, 3173, 739])).
% 1.54/1.74 tff(3175,plain,
% 1.54/1.74 (~b(s(s(s(z))), elem!1)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2149, 3174, 30, 1502, 3172, 802, 403, 1663, 1664, 1005])).
% 1.54/1.74 tff(3176,plain,
% 1.54/1.74 ($false),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3175, 2213])).
% 1.54/1.74 tff(3177,plain,((~b(s(s(s(elem!1))), elem!1)) | (~(z = elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (s(s(elem!1)) = s(elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (s(s(s(elem!1))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.74 tff(3178,plain,
% 1.54/1.74 (~b(s(s(s(elem!1))), elem!1)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3177, 1663, 30, 802, 403, 1502, 1005, 233])).
% 1.54/1.74 tff(3179,plain,
% 1.54/1.74 (r(s(s(s(elem!1))), elem!1)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[1636, 3178, 3171])).
% 1.54/1.74 tff(3180,plain,
% 1.54/1.74 (r(s(s(s(z))), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[1631, 3179, 1619])).
% 1.54/1.74 tff(3181,plain,
% 1.54/1.74 (~(s(elem!1) = s(s(s(elem!1))))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[150, 1870])).
% 1.54/1.74 tff(3182,plain,
% 1.54/1.74 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(3183,plain,
% 1.54/1.74 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1)))))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(3184,plain,
% 1.54/1.74 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[3183])).
% 1.54/1.74 tff(3185,plain,
% 1.54/1.74 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.54/1.74 inference(transitivity,[status(thm)],[3184, 3182])).
% 1.54/1.74 tff(3186,plain,
% 1.54/1.74 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(3187,plain,
% 1.54/1.74 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[3186, 3185])).
% 1.54/1.74 tff(3188,plain,
% 1.54/1.74 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3187, 124, 802, 3179])).
% 1.54/1.74 tff(3189,plain,
% 1.54/1.74 ((s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[1881, 43, 3188])).
% 1.54/1.74 tff(3190,plain,
% 1.54/1.74 (b(s(elem!1), s(s(s(elem!1))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3189, 3181])).
% 1.54/1.74 tff(3191,plain,
% 1.54/1.74 (r(s(s(s(s(s(s(z)))))), z) <=> r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.54/1.74 inference(monotonicity,[status(thm)],[1502])).
% 1.54/1.74 tff(3192,plain,
% 1.54/1.74 (r(s(s(s(s(s(s(z)))))), elem!1) <=> r(s(s(s(s(s(s(z)))))), z)),
% 1.54/1.74 inference(symmetry,[status(thm)],[3191])).
% 1.54/1.74 tff(3193,plain,
% 1.54/1.74 (r(s(s(s(s(s(s(z)))))), z)),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[2858, 3192])).
% 1.54/1.74 tff(3194,assumption,(r(s(s(s(s(s(s(z)))))), z)), introduced(assumption)).
% 1.54/1.74 tff(3195,assumption,(r(s(s(s(z))), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.54/1.74 tff(3196,plain,
% 1.54/1.74 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), z)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(3197,plain,
% 1.54/1.74 (((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), z)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(3198,plain,
% 1.54/1.74 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), z))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[3197])).
% 1.54/1.74 tff(3199,plain,
% 1.54/1.74 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), z)))),
% 1.54/1.74 inference(transitivity,[status(thm)],[3198, 3196])).
% 1.54/1.74 tff(3200,plain,
% 1.54/1.74 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(3201,plain,
% 1.54/1.74 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), z))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[3200, 3199])).
% 1.54/1.74 tff(3202,plain,
% 1.54/1.74 ($false),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3201, 124, 205, 3195, 3194])).
% 1.54/1.74 tff(3203,plain,((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.74 tff(3204,plain,
% 1.54/1.74 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3203, 3193, 205])).
% 1.54/1.74 tff(3205,assumption,(~r(s(s(s(z))), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.54/1.74 tff(3206,plain,
% 1.54/1.74 ($false),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[559, 43, 556, 538, 3205])).
% 1.54/1.74 tff(3207,plain,(r(s(s(s(z))), s(s(s(s(s(s(z))))))) | b(s(s(s(z))), s(s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.74 tff(3208,plain,
% 1.54/1.74 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3207, 3204])).
% 1.54/1.74 tff(3209,plain,
% 1.54/1.74 (b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[3208, 3165])).
% 1.54/1.74 tff(3210,plain,
% 1.54/1.74 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(3211,plain,
% 1.54/1.74 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(3212,plain,
% 1.54/1.75 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(elem!1)))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[3211, 3210])).
% 1.54/1.75 tff(3213,plain,
% 1.54/1.75 (~r(s(s(s(s(s(s(z)))))), s(elem!1))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3212, 124, 802, 2858])).
% 1.54/1.75 tff(3214,plain,
% 1.54/1.75 ((s(s(s(s(s(s(z)))))) = s(elem!1)) <=> (s(s(s(s(s(s(z)))))) = s(z))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[1504])).
% 1.54/1.75 tff(3215,plain,
% 1.54/1.75 ((s(s(s(s(s(s(z)))))) = s(z)) <=> (s(s(s(s(s(s(z)))))) = s(elem!1))),
% 1.54/1.75 inference(symmetry,[status(thm)],[3214])).
% 1.54/1.75 tff(3216,plain,
% 1.54/1.75 ((~(s(s(s(s(s(s(z)))))) = s(z))) <=> (~(s(s(s(s(s(s(z)))))) = s(elem!1)))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[3215])).
% 1.54/1.75 tff(3217,plain,
% 1.54/1.75 (~(s(s(s(s(s(s(z)))))) = s(elem!1))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[2844, 3216])).
% 1.54/1.75 tff(3218,plain,
% 1.54/1.75 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(elem!1)) | b(s(s(s(s(s(s(z)))))), s(elem!1)) | r(s(s(s(s(s(s(z)))))), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(elem!1)) | b(s(s(s(s(s(s(z)))))), s(elem!1)) | r(s(s(s(s(s(s(z)))))), s(elem!1)))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(3219,plain,
% 1.54/1.75 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(elem!1)) | b(s(s(s(s(s(s(z)))))), s(elem!1)) | r(s(s(s(s(s(s(z)))))), s(elem!1)))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(3220,plain,
% 1.54/1.75 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(elem!1)) | b(s(s(s(s(s(s(z)))))), s(elem!1)) | r(s(s(s(s(s(s(z)))))), s(elem!1))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[3219, 3218])).
% 1.54/1.75 tff(3221,plain,
% 1.54/1.75 (b(s(s(s(s(s(s(z)))))), s(elem!1))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3220, 43, 3217, 3213])).
% 1.54/1.75 tff(3222,assumption,(b(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 1.54/1.75 tff(3223,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(3224,plain,
% 1.54/1.75 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(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(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(3225,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z))))))))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[3224])).
% 1.54/1.75 tff(3226,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))),
% 1.54/1.75 inference(transitivity,[status(thm)],[3225, 3223])).
% 1.54/1.75 tff(3227,plain,
% 1.54/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(3228,plain,
% 1.54/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z))))))))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[3227, 3226])).
% 1.54/1.75 tff(3229,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3228, 306, 759, 3222, 3221, 3209])).
% 1.54/1.75 tff(3230,plain,((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~(z = elem!1)) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(3231,plain,
% 1.54/1.75 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3230, 3190, 759, 1502, 3180, 802])).
% 1.54/1.75 tff(3232,plain,
% 1.54/1.75 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1144, 3231, 3170])).
% 1.54/1.75 tff(3233,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(3234,plain,
% 1.54/1.75 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(3235,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), elem!1))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[3234])).
% 1.54/1.75 tff(3236,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.54/1.75 inference(transitivity,[status(thm)],[3235, 3233])).
% 1.54/1.75 tff(3237,plain,
% 1.54/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(3238,plain,
% 1.54/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), elem!1))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[3237, 3236])).
% 1.54/1.75 tff(3239,plain,
% 1.54/1.75 (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3238, 306, 759, 30, 1663, 3232])).
% 1.54/1.75 tff(3240,plain,
% 1.54/1.75 ((s(s(elem!1)) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = s(s(elem!1)))),
% 1.54/1.75 inference(commutativity,[status(thm)],[])).
% 1.54/1.75 tff(3241,plain,
% 1.54/1.75 ((s(s(z)) = s(s(s(s(s(s(z))))))) <=> (s(s(elem!1)) = s(s(s(s(s(s(z)))))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[1506])).
% 1.54/1.75 tff(3242,plain,
% 1.54/1.75 ((s(s(z)) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = s(s(elem!1)))),
% 1.54/1.75 inference(transitivity,[status(thm)],[3241, 3240])).
% 1.54/1.75 tff(3243,plain,
% 1.54/1.75 ((~(s(s(z)) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(s(s(s(s(z)))))) = s(s(elem!1))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[3242])).
% 1.54/1.75 tff(3244,plain,
% 1.54/1.75 (~(s(s(s(s(s(s(z)))))) = s(s(elem!1)))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[2826, 3243])).
% 1.54/1.75 tff(3245,plain,
% 1.54/1.75 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(elem!1))) | b(s(s(s(s(s(s(z)))))), s(s(elem!1))) | r(s(s(s(s(s(s(z)))))), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(elem!1))) | b(s(s(s(s(s(s(z)))))), s(s(elem!1))) | r(s(s(s(s(s(s(z)))))), s(s(elem!1))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(3246,plain,
% 1.54/1.75 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(elem!1))) | b(s(s(s(s(s(s(z)))))), s(s(elem!1))) | r(s(s(s(s(s(s(z)))))), s(s(elem!1))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(3247,plain,
% 1.54/1.75 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(elem!1))) | b(s(s(s(s(s(s(z)))))), s(s(elem!1))) | r(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[3246, 3245])).
% 1.54/1.75 tff(3248,plain,
% 1.54/1.75 (r(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3247, 43, 3244, 3239])).
% 1.54/1.75 tff(3249,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(3250,plain,
% 1.54/1.75 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(3251,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1)))))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[3250])).
% 1.54/1.75 tff(3252,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.54/1.75 inference(transitivity,[status(thm)],[3251, 3249])).
% 1.54/1.75 tff(3253,plain,
% 1.54/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(3254,plain,
% 1.54/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1)))))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[3253, 3252])).
% 1.54/1.75 tff(3255,plain,
% 1.54/1.75 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3254, 306, 759, 1005, 3190])).
% 1.54/1.75 tff(3256,plain,
% 1.54/1.75 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[610, 3255, 233])).
% 1.54/1.75 tff(3257,plain,
% 1.54/1.75 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(3258,plain,
% 1.54/1.75 (((~r(s(s(s(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(s(s(s(z))))))))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(3259,plain,
% 1.54/1.75 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(z))))))))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[3258])).
% 1.54/1.75 tff(3260,plain,
% 1.54/1.75 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))),
% 1.54/1.75 inference(transitivity,[status(thm)],[3259, 3257])).
% 1.54/1.75 tff(3261,plain,
% 1.54/1.75 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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(s(s(s(z)))))))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(3262,plain,
% 1.54/1.75 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(z))))))))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[3261, 3260])).
% 1.54/1.75 tff(3263,plain,
% 1.54/1.75 (~r(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3262, 124, 3256, 3248])).
% 1.54/1.75 tff(3264,plain,
% 1.54/1.75 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[3263, 3167])).
% 1.54/1.75 tff(3265,plain,
% 1.54/1.75 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3207, 3264])).
% 1.54/1.75 tff(3266,plain,
% 1.54/1.75 (b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[3265, 3165])).
% 1.54/1.75 tff(3267,plain,
% 1.54/1.75 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(3268,plain,
% 1.54/1.75 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(3269,plain,
% 1.54/1.75 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[3268, 3267])).
% 1.54/1.75 tff(3270,plain,
% 1.54/1.75 (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3269, 124, 3256, 3248])).
% 1.54/1.75 tff(3271,plain,
% 1.54/1.75 ((s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2877, 43, 3270])).
% 1.54/1.75 tff(3272,plain,
% 1.54/1.75 (b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3271, 2868])).
% 1.54/1.75 tff(3273,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(3274,plain,
% 1.54/1.75 (((~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), elem!1))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(3275,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z))))))))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[3274])).
% 1.54/1.75 tff(3276,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[3275, 3273])).
% 1.54/1.76 tff(3277,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(3278,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z))))))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[3277, 3276])).
% 1.54/1.76 tff(3279,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3278, 306, 1663, 3232, 3272, 3266])).
% 1.54/1.76 tff(3280,plain,((~b(elem!1, s(s(s(elem!1))))) | (~(z = elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (s(s(elem!1)) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.76 tff(3281,plain,
% 1.54/1.76 (~b(elem!1, s(s(s(elem!1))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3280, 3137, 3163, 30, 3150, 802, 150, 403])).
% 1.54/1.76 tff(3282,assumption,(~b(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 1.54/1.76 tff(3283,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1260, 43, 536, 3282, 1653])).
% 1.54/1.76 tff(3284,plain,(r(elem!1, s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | (elem!1 = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.76 tff(3285,plain,
% 1.54/1.76 (r(elem!1, s(s(s(elem!1))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3284, 3281, 3148])).
% 1.54/1.76 tff(3286,plain,
% 1.54/1.76 (r(elem!1, s(s(s(z))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[3285, 3146])).
% 1.54/1.76 tff(3287,plain,
% 1.54/1.76 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(3288,plain,
% 1.54/1.76 (((~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(z)))) <=> ((~r(s(z), s(s(s(z))))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(3289,plain,
% 1.54/1.76 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z)))))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3288])).
% 1.54/1.76 tff(3290,plain,
% 1.54/1.76 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[3289, 3287])).
% 1.54/1.76 tff(3291,plain,
% 1.54/1.76 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(z))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(3292,plain,
% 1.54/1.76 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z)))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[3291, 3290])).
% 1.54/1.76 tff(3293,plain,
% 1.54/1.76 ((~r(s(z), s(s(s(z))))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z)))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3292, 124])).
% 1.54/1.76 tff(3294,plain,
% 1.54/1.76 (~r(s(z), s(s(s(z))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3293, 3286, 359])).
% 1.54/1.76 tff(3295,assumption,(s(z) = s(s(s(z)))), introduced(assumption)).
% 1.54/1.76 tff(3296,plain,
% 1.54/1.76 (s(s(s(z))) = s(z)),
% 1.54/1.76 inference(symmetry,[status(thm)],[3295])).
% 1.54/1.76 tff(3297,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[108, 3296])).
% 1.54/1.76 tff(3298,plain,(~(s(z) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.76 tff(3299,assumption,(~r(s(z), s(s(s(z))))), introduced(assumption)).
% 1.54/1.76 tff(3300,assumption,(~b(s(z), s(s(s(z))))), introduced(assumption)).
% 1.54/1.76 tff(3301,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1063, 43, 3300, 3299, 3298])).
% 1.54/1.76 tff(3302,plain,(b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.76 tff(3303,plain,
% 1.54/1.76 (b(s(z), s(s(s(z))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3302, 3294])).
% 1.54/1.76 tff(3304,plain,
% 1.54/1.76 (b(s(s(z)), s(z)) <=> b(s(s(elem!1)), s(elem!1))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3139, 3138])).
% 1.54/1.76 tff(3305,plain,
% 1.54/1.76 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(z)), s(z))),
% 1.54/1.76 inference(symmetry,[status(thm)],[3304])).
% 1.54/1.76 tff(3306,plain,
% 1.54/1.76 (b(s(s(z)), s(z))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[3150, 3305])).
% 1.54/1.76 tff(3307,plain,
% 1.54/1.76 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3137])).
% 1.54/1.76 tff(3308,plain,
% 1.54/1.76 ((s(s(s(s(elem!1)))) = z) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[3307, 1542])).
% 1.54/1.76 tff(3309,plain,
% 1.54/1.76 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.54/1.76 inference(transitivity,[status(thm)],[3308, 1543])).
% 1.54/1.76 tff(3310,plain,
% 1.54/1.76 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3309])).
% 1.54/1.76 tff(3311,plain,
% 1.54/1.76 (~(s(s(s(s(elem!1)))) = elem!1)),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[1549, 3310])).
% 1.54/1.76 tff(3312,plain,
% 1.54/1.76 (elem!1 = z),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1618, 3137])).
% 1.54/1.76 tff(3313,assumption,(r(elem!1, s(s(s(z))))), introduced(assumption)).
% 1.54/1.76 tff(3314,assumption,(~r(s(s(s(elem!1))), s(s(elem!1)))), introduced(assumption)).
% 1.54/1.76 tff(3315,plain,
% 1.54/1.76 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[1780])).
% 1.54/1.76 tff(3316,plain,
% 1.54/1.76 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(z)))),
% 1.54/1.76 inference(symmetry,[status(thm)],[3315])).
% 1.54/1.76 tff(3317,plain,
% 1.54/1.76 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[1623])).
% 1.54/1.76 tff(3318,plain,
% 1.54/1.76 ((s(s(s(elem!1))) = s(z)) <=> (s(z) = s(s(s(elem!1))))),
% 1.54/1.76 inference(commutativity,[status(thm)],[])).
% 1.54/1.76 tff(3319,plain,
% 1.54/1.76 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(elem!1))) = s(z))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[1621])).
% 1.54/1.76 tff(3320,plain,
% 1.54/1.76 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(z) = s(s(s(elem!1))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[3319, 3318])).
% 1.54/1.76 tff(3321,plain,
% 1.54/1.76 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.54/1.76 inference(symmetry,[status(thm)],[3320])).
% 1.54/1.76 tff(3322,plain,
% 1.54/1.76 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3321])).
% 1.54/1.76 tff(3323,plain,
% 1.54/1.76 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[645, 3322])).
% 1.54/1.76 tff(3324,plain,
% 1.54/1.76 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[152, 3323])).
% 1.54/1.76 tff(3325,plain,
% 1.54/1.76 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[159, 3324])).
% 1.54/1.76 tff(3326,plain,
% 1.54/1.76 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[610, 3325, 3314])).
% 1.54/1.76 tff(3327,plain,
% 1.54/1.76 (b(s(s(s(z))), s(s(elem!1)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[3326, 3317])).
% 1.54/1.76 tff(3328,plain,
% 1.54/1.76 (b(s(s(s(z))), s(s(z)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[3327, 3316])).
% 1.54/1.76 tff(3329,plain,
% 1.54/1.76 (b(s(s(z)), s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[1780])).
% 1.54/1.76 tff(3330,plain,
% 1.54/1.76 (b(s(s(elem!1)), s(z)) <=> b(s(s(z)), s(z))),
% 1.54/1.76 inference(symmetry,[status(thm)],[3329])).
% 1.54/1.76 tff(3331,plain,
% 1.54/1.76 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(elem!1)), s(z))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[1621])).
% 1.54/1.76 tff(3332,plain,
% 1.54/1.76 (z = elem!1),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2172, 1620])).
% 1.54/1.76 tff(3333,plain,
% 1.54/1.76 (~(s(elem!1) = elem!1)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2698, 3332])).
% 1.54/1.76 tff(3334,plain,
% 1.54/1.76 (~(s(s(elem!1)) = s(elem!1))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[195, 3333])).
% 1.54/1.76 tff(3335,plain,
% 1.54/1.76 (b(s(s(elem!1)), s(elem!1))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[994, 3334, 3149])).
% 1.54/1.76 tff(3336,plain,
% 1.54/1.76 (b(s(s(elem!1)), s(z))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[3335, 3331])).
% 1.54/1.76 tff(3337,plain,
% 1.54/1.76 (b(s(s(z)), s(z))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[3336, 3330])).
% 1.54/1.76 tff(3338,plain,
% 1.54/1.76 (r(s(z), elem!1) <=> r(s(z), z)),
% 1.54/1.76 inference(monotonicity,[status(thm)],[1620])).
% 1.54/1.76 tff(3339,plain,
% 1.54/1.76 (r(s(z), z) <=> r(s(z), elem!1)),
% 1.54/1.76 inference(symmetry,[status(thm)],[3338])).
% 1.54/1.76 tff(3340,plain,
% 1.54/1.76 (r(s(z), elem!1)),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[204, 3339])).
% 1.54/1.76 tff(3341,plain,
% 1.54/1.76 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(3342,plain,
% 1.54/1.76 (((~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(3343,plain,
% 1.54/1.76 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z)))))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3342])).
% 1.54/1.76 tff(3344,plain,
% 1.54/1.76 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[3343, 3341])).
% 1.54/1.76 tff(3345,plain,
% 1.54/1.76 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1)))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(3346,plain,
% 1.54/1.76 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z)))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[3345, 3344])).
% 1.54/1.76 tff(3347,plain,
% 1.54/1.76 ((~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z)))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3346, 124])).
% 1.54/1.76 tff(3348,plain,
% 1.54/1.76 (~r(s(z), s(s(s(z))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3347, 3340, 3313])).
% 1.54/1.76 tff(3349,plain,
% 1.54/1.76 ((s(z) = s(s(s(z)))) | b(s(z), s(s(s(z))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1063, 43, 3348])).
% 1.54/1.76 tff(3350,plain,
% 1.54/1.76 (b(s(z), s(s(s(z))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3349, 1031])).
% 1.54/1.76 tff(3351,plain,
% 1.54/1.76 (~b(s(s(s(z))), s(s(z)))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2774, 306, 2284, 3350, 3337])).
% 1.54/1.76 tff(3352,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3351, 3328])).
% 1.54/1.76 tff(3353,plain,((~(elem!1 = z)) | (~b(s(s(s(z))), s(z))) | r(s(s(s(elem!1))), s(s(elem!1))) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), z)) | r(s(s(elem!1)), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.76 tff(3354,plain,
% 1.54/1.76 (~(elem!1 = z)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3353, 3314, 2284, 3313, 204, 3149])).
% 1.54/1.76 tff(3355,plain,
% 1.54/1.76 (r(elem!1, z)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[174, 3354, 2])).
% 1.54/1.76 tff(3356,plain,
% 1.54/1.76 (~r(elem!1, s(z))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2180, 124, 3355, 204])).
% 1.54/1.76 tff(3357,plain,
% 1.54/1.76 (elem!1 = s(z)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[97, 3356])).
% 1.54/1.76 tff(3358,plain,
% 1.54/1.76 (s(z) = elem!1),
% 1.54/1.76 inference(symmetry,[status(thm)],[3357])).
% 1.54/1.76 tff(3359,plain,
% 1.54/1.76 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(z)))), elem!1)),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3358])).
% 1.54/1.76 tff(3360,plain,
% 1.54/1.76 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(z))),
% 1.54/1.76 inference(symmetry,[status(thm)],[3359])).
% 1.54/1.76 tff(3361,plain,
% 1.54/1.76 (s(elem!1) = s(s(z))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3357])).
% 1.54/1.76 tff(3362,plain,
% 1.54/1.76 (s(s(elem!1)) = s(s(s(z)))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3361])).
% 1.54/1.76 tff(3363,plain,
% 1.54/1.76 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3362])).
% 1.54/1.76 tff(3364,plain,
% 1.54/1.76 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3363])).
% 1.54/1.76 tff(3365,plain,
% 1.54/1.76 ((s(z) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3358])).
% 1.54/1.76 tff(3366,plain,
% 1.54/1.76 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 1.54/1.76 inference(transitivity,[status(thm)],[3365, 1555])).
% 1.54/1.76 tff(3367,plain,
% 1.54/1.76 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3366])).
% 1.54/1.76 tff(3368,plain,
% 1.54/1.76 (~(s(s(s(elem!1))) = elem!1)),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[645, 3367])).
% 1.54/1.76 tff(3369,plain,
% 1.54/1.76 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.54/1.76 inference(symmetry,[status(thm)],[3363])).
% 1.54/1.76 tff(3370,plain,
% 1.54/1.76 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(elem!1))), elem!1)),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3369, 3358])).
% 1.54/1.76 tff(3371,plain,
% 1.54/1.76 ((~r(s(s(s(s(z)))), s(z))) <=> (~r(s(s(s(elem!1))), elem!1))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3370])).
% 1.54/1.76 tff(3372,plain,
% 1.54/1.76 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3363, 3362])).
% 1.54/1.76 tff(3373,plain,
% 1.54/1.76 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(z)))) = s(s(z)))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3363, 3361])).
% 1.54/1.76 tff(3374,plain,
% 1.54/1.76 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(z)) = s(s(s(s(z)))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[3373, 1707])).
% 1.54/1.76 tff(3375,plain,
% 1.54/1.76 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.54/1.76 inference(symmetry,[status(thm)],[3374])).
% 1.54/1.76 tff(3376,plain,
% 1.54/1.76 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3375])).
% 1.54/1.76 tff(3377,plain,
% 1.54/1.76 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[1612, 3376])).
% 1.54/1.76 tff(3378,plain,
% 1.54/1.76 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[152, 3377])).
% 1.54/1.76 tff(3379,plain,
% 1.54/1.76 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[159, 3378])).
% 1.54/1.76 tff(3380,plain,
% 1.54/1.76 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[610, 3379, 3314])).
% 1.54/1.76 tff(3381,plain,
% 1.54/1.76 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[3380, 3372])).
% 1.54/1.76 tff(3382,plain,
% 1.54/1.76 ((z = s(s(s(z)))) <=> (s(s(s(z))) = z)),
% 1.54/1.76 inference(commutativity,[status(thm)],[])).
% 1.54/1.76 tff(3383,plain,
% 1.54/1.76 ((s(s(s(z))) = z) <=> (z = s(s(s(z))))),
% 1.54/1.76 inference(symmetry,[status(thm)],[3382])).
% 1.54/1.76 tff(3384,plain,
% 1.54/1.76 ((~(s(s(s(z))) = z)) <=> (~(z = s(s(s(z)))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3383])).
% 1.54/1.76 tff(3385,plain,
% 1.54/1.76 (~(z = s(s(s(z))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[169, 3384])).
% 1.54/1.76 tff(3386,plain,
% 1.54/1.76 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(3387,plain,
% 1.54/1.76 (((~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(elem!1, s(s(s(z))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(3388,plain,
% 1.54/1.76 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3387])).
% 1.54/1.76 tff(3389,plain,
% 1.54/1.76 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[3388, 3386])).
% 1.54/1.76 tff(3390,plain,
% 1.54/1.76 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, z)))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(3391,plain,
% 1.54/1.76 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[3390, 3389])).
% 1.54/1.76 tff(3392,plain,
% 1.54/1.76 ((~r(elem!1, z)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3391, 124])).
% 1.54/1.76 tff(3393,plain,
% 1.54/1.76 (~r(z, s(s(s(z))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3392, 3355, 3313])).
% 1.54/1.76 tff(3394,plain,
% 1.54/1.76 ((z = s(s(s(z)))) | b(z, s(s(s(z))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2415, 43, 3393])).
% 1.54/1.76 tff(3395,plain,
% 1.54/1.76 (b(z, s(s(s(z))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3394, 3385])).
% 1.54/1.76 tff(3396,plain,
% 1.54/1.76 (~r(s(s(s(z))), z)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2312, 3355, 3313])).
% 1.54/1.76 tff(3397,plain,
% 1.54/1.76 (b(s(s(s(z))), z)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[202, 43, 169, 3396])).
% 1.54/1.76 tff(3398,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(3399,plain,
% 1.54/1.76 (((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(3400,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z)))))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3399])).
% 1.54/1.76 tff(3401,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[3400, 3398])).
% 1.54/1.76 tff(3402,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(3403,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z)))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[3402, 3401])).
% 1.54/1.76 tff(3404,plain,
% 1.54/1.76 (~b(s(s(s(s(z)))), z)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3403, 306, 3397, 3395, 3381])).
% 1.54/1.76 tff(3405,plain,
% 1.54/1.76 (r(s(s(s(s(z)))), z)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[695, 3404])).
% 1.54/1.76 tff(3406,plain,
% 1.54/1.76 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(3407,plain,
% 1.54/1.76 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(3408,plain,
% 1.54/1.76 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[3407, 3406])).
% 1.54/1.76 tff(3409,plain,
% 1.54/1.76 (~r(s(s(s(s(z)))), s(z))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3408, 124, 204, 3405])).
% 1.54/1.76 tff(3410,plain,
% 1.54/1.76 (~r(s(s(s(elem!1))), elem!1)),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[3409, 3371])).
% 1.54/1.76 tff(3411,plain,
% 1.54/1.76 (b(s(s(s(elem!1))), elem!1)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1636, 3410, 3368])).
% 1.54/1.76 tff(3412,plain,
% 1.54/1.76 (b(s(s(s(s(z)))), elem!1)),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[3411, 3364])).
% 1.54/1.76 tff(3413,plain,
% 1.54/1.76 (b(s(s(s(s(z)))), s(z))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[3412, 3360])).
% 1.54/1.76 tff(3414,plain,
% 1.54/1.76 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(3415,plain,
% 1.54/1.76 (((~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(3416,plain,
% 1.54/1.76 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3415])).
% 1.54/1.76 tff(3417,plain,
% 1.54/1.76 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 1.54/1.76 inference(transitivity,[status(thm)],[3416, 3414])).
% 1.54/1.76 tff(3418,plain,
% 1.54/1.76 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(3419,plain,
% 1.54/1.76 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[3418, 3417])).
% 1.54/1.76 tff(3420,plain,
% 1.54/1.76 (~r(s(z), s(s(s(s(z)))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3419, 124, 204, 3405])).
% 1.54/1.76 tff(3421,plain,
% 1.54/1.76 ((s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z)))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[680, 43, 3420])).
% 1.54/1.76 tff(3422,plain,
% 1.54/1.76 (b(s(z), s(s(s(s(z)))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3421, 670])).
% 1.54/1.76 tff(3423,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(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)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(3424,plain,
% 1.54/1.77 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(3425,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[3424])).
% 1.54/1.77 tff(3426,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.54/1.77 inference(transitivity,[status(thm)],[3425, 3423])).
% 1.54/1.77 tff(3427,plain,
% 1.54/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(3428,plain,
% 1.54/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[3427, 3426])).
% 1.54/1.77 tff(3429,plain,
% 1.54/1.77 (~b(s(s(s(s(z)))), s(z))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3428, 306, 2284, 3422, 3381])).
% 1.54/1.77 tff(3430,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3429, 3413])).
% 1.54/1.77 tff(3431,plain,(r(s(s(s(elem!1))), s(s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~r(s(z), z)) | b(elem!1, s(z)) | (~r(elem!1, s(s(s(z))))) | b(elem!1, z) | r(s(s(elem!1)), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(3432,plain,
% 1.54/1.77 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3431, 3286, 204, 3149, 3162, 3160, 5])).
% 1.54/1.77 tff(3433,plain,
% 1.54/1.77 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 1.54/1.77 inference(symmetry,[status(thm)],[1951])).
% 1.54/1.77 tff(3434,plain,
% 1.54/1.77 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(elem!1)))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[3433])).
% 1.54/1.77 tff(3435,plain,
% 1.54/1.77 (s(s(elem!1)) = s(s(s(elem!1)))),
% 1.54/1.77 inference(transitivity,[status(thm)],[140, 3434, 1280])).
% 1.54/1.77 tff(3436,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[157, 3435])).
% 1.54/1.77 tff(3437,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,[]))).
% 1.54/1.77 tff(3438,plain,
% 1.54/1.77 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3437, 232])).
% 1.54/1.77 tff(3439,assumption,(r(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 1.54/1.77 tff(3440,plain,
% 1.54/1.77 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(3441,plain,
% 1.54/1.77 (((~r(elem!1, s(s(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))))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(3442,plain,
% 1.54/1.77 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1)))))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[3441])).
% 1.54/1.77 tff(3443,plain,
% 1.54/1.77 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.54/1.77 inference(transitivity,[status(thm)],[3442, 3440])).
% 1.54/1.77 tff(3444,plain,
% 1.54/1.77 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(3445,plain,
% 1.54/1.77 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1)))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[3444, 3443])).
% 1.54/1.77 tff(3446,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3445, 124, 802, 565, 3439])).
% 1.54/1.77 tff(3447,plain,((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(3448,plain,
% 1.54/1.77 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3447, 3285, 802])).
% 1.54/1.77 tff(3449,plain,
% 1.54/1.77 ((s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1881, 43, 3448])).
% 1.54/1.77 tff(3450,plain,
% 1.54/1.77 (b(s(elem!1), s(s(s(elem!1))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3449, 3181])).
% 1.54/1.77 tff(3451,assumption,(b(s(s(z)), s(z))), introduced(assumption)).
% 1.54/1.77 tff(3452,plain,
% 1.54/1.77 (r(s(s(s(s(z)))), z)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[695, 693])).
% 1.54/1.77 tff(3453,plain,
% 1.54/1.77 (~r(s(s(s(s(z)))), s(z))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3408, 124, 204, 397])).
% 1.54/1.77 tff(3454,plain,
% 1.54/1.77 (b(s(s(s(s(z)))), s(z))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[327, 43, 324, 3453])).
% 1.54/1.77 tff(3455,assumption,(b(s(s(s(s(z)))), s(s(z)))), introduced(assumption)).
% 1.54/1.77 tff(3456,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(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(z)))) | (~b(s(s(z)), s(z))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(3457,plain,
% 1.54/1.77 (((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(3458,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(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(z)))) | (~b(s(s(z)), s(z)))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[3457])).
% 1.54/1.77 tff(3459,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(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(z)))) | (~b(s(s(z)), s(z))))),
% 1.54/1.77 inference(transitivity,[status(thm)],[3458, 3456])).
% 1.54/1.77 tff(3460,plain,
% 1.54/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(3461,plain,
% 1.54/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z)))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[3460, 3459])).
% 1.54/1.77 tff(3462,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3461, 306, 2284, 8, 3455, 3451, 3454])).
% 1.54/1.77 tff(3463,plain,((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(3464,plain,
% 1.54/1.77 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3463, 3452, 3451, 2284, 204, 8])).
% 1.54/1.77 tff(3465,plain,
% 1.54/1.77 (b(s(s(s(s(elem!1)))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(z)))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[1704, 1622])).
% 1.54/1.77 tff(3466,plain,
% 1.54/1.77 (b(s(s(s(s(z)))), s(s(z)))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[1973, 3465])).
% 1.54/1.77 tff(3467,assumption,(~b(s(s(s(s(z)))), s(s(z)))), introduced(assumption)).
% 1.54/1.77 tff(3468,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3467, 3466])).
% 1.54/1.77 tff(3469,plain,((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | b(s(s(s(s(z)))), s(s(z))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(3470,plain,
% 1.54/1.77 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3469, 3464, 1620])).
% 1.54/1.77 tff(3471,plain,
% 1.54/1.77 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1302, 3470, 1717])).
% 1.54/1.77 tff(3472,plain,
% 1.54/1.77 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(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))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(3473,plain,
% 1.54/1.77 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(3474,plain,
% 1.54/1.77 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[3473, 3472])).
% 1.54/1.77 tff(3475,plain,
% 1.54/1.77 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3474, 124, 653, 3471])).
% 1.54/1.77 tff(3476,assumption,(~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))), introduced(assumption)).
% 1.54/1.77 tff(3477,plain,
% 1.54/1.77 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1958, 43, 3476, 3475])).
% 1.54/1.77 tff(3478,plain,
% 1.54/1.77 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[2079, 693, 1620])).
% 1.54/1.77 tff(3479,plain,
% 1.54/1.77 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1736, 3478, 1731])).
% 1.54/1.77 tff(3480,plain,
% 1.54/1.77 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1740, 124, 802, 3479])).
% 1.54/1.77 tff(3481,plain,
% 1.54/1.77 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1767, 43, 1516, 3480])).
% 1.54/1.77 tff(3482,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(3483,plain,
% 1.54/1.77 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(3484,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1)))))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[3483])).
% 1.54/1.77 tff(3485,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.54/1.77 inference(transitivity,[status(thm)],[3484, 3482])).
% 1.54/1.77 tff(3486,plain,
% 1.54/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), 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))))))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(3487,plain,
% 1.54/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1)))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[3486, 3485])).
% 1.54/1.77 tff(3488,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3487, 306, 759, 3222, 3481, 3477])).
% 1.54/1.77 tff(3489,plain,(b(s(s(s(s(z)))), z) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (s(s(s(s(elem!1)))) = s(elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~(elem!1 = z)) | (s(s(s(s(elem!1)))) = elem!1) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~r(s(z), z)) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(3490,plain,
% 1.54/1.77 (b(s(s(s(s(z)))), z)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3489, 3163, 3450, 3438, 3147, 3432, 802, 1285, 3312, 3311, 3306, 3162, 204, 3303])).
% 1.54/1.77 tff(3491,plain,
% 1.54/1.77 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[3490, 3144])).
% 1.54/1.77 tff(3492,plain,
% 1.54/1.77 ((s(s(s(s(s(s(z)))))) = z) <=> (s(s(s(s(s(s(z)))))) = elem!1)),
% 1.54/1.77 inference(monotonicity,[status(thm)],[3137])).
% 1.54/1.77 tff(3493,plain,
% 1.54/1.77 ((~(s(s(s(s(s(s(z)))))) = z)) <=> (~(s(s(s(s(s(s(z)))))) = elem!1))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[3492])).
% 1.54/1.77 tff(3494,plain,
% 1.54/1.77 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[554, 3493])).
% 1.54/1.77 tff(3495,plain,
% 1.54/1.77 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3431, 3149, 204, 5, 3313, 2, 2284])).
% 1.54/1.77 tff(3496,plain,
% 1.54/1.77 (~(s(s(s(s(z)))) = s(s(s(z))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1722, 1620])).
% 1.54/1.77 tff(3497,plain,
% 1.54/1.77 (~(s(s(s(z))) = s(s(s(s(z)))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1971, 3496])).
% 1.54/1.77 tff(3498,plain,
% 1.54/1.77 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[2027, 3497, 347])).
% 1.54/1.77 tff(3499,plain,
% 1.54/1.77 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[2022, 3498, 1620, 653])).
% 1.54/1.77 tff(3500,plain,
% 1.54/1.77 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1302, 3499, 1712])).
% 1.54/1.77 tff(3501,plain,
% 1.54/1.77 (b(s(s(s(s(z)))), s(s(z)))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3469, 3500, 1620])).
% 1.54/1.77 tff(3502,plain,
% 1.54/1.77 (b(s(s(elem!1)), z) <=> b(s(s(z)), z)),
% 1.54/1.77 inference(monotonicity,[status(thm)],[1622])).
% 1.54/1.77 tff(3503,plain,
% 1.54/1.77 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), z)),
% 1.54/1.77 inference(monotonicity,[status(thm)],[1620])).
% 1.54/1.77 tff(3504,plain,
% 1.54/1.77 (b(s(s(elem!1)), elem!1) <=> b(s(s(z)), z)),
% 1.54/1.77 inference(transitivity,[status(thm)],[3503, 3502])).
% 1.54/1.77 tff(3505,plain,
% 1.54/1.77 ((s(s(elem!1)) = elem!1) <=> (s(s(elem!1)) = z)),
% 1.54/1.77 inference(monotonicity,[status(thm)],[1620])).
% 1.54/1.77 tff(3506,plain,
% 1.54/1.77 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 1.54/1.77 inference(symmetry,[status(thm)],[3505])).
% 1.54/1.77 tff(3507,plain,
% 1.54/1.77 ((~(s(s(elem!1)) = z)) <=> (~(s(s(elem!1)) = elem!1))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[3506])).
% 1.54/1.77 tff(3508,plain,
% 1.54/1.77 (~(s(s(elem!1)) = elem!1)),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[454, 3507])).
% 1.54/1.77 tff(3509,plain,
% 1.54/1.77 (b(s(s(elem!1)), elem!1)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[47, 3508, 6])).
% 1.54/1.77 tff(3510,plain,
% 1.54/1.77 (b(s(s(z)), z)),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[3509, 3504])).
% 1.54/1.77 tff(3511,plain,
% 1.54/1.77 (b(z, s(s(elem!1))) <=> b(z, s(s(z)))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[1622])).
% 1.54/1.77 tff(3512,plain,
% 1.54/1.77 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(z))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[1623])).
% 1.54/1.77 tff(3513,plain,
% 1.54/1.77 (r(z, s(s(s(z)))) <=> r(z, s(s(s(elem!1))))),
% 1.54/1.77 inference(symmetry,[status(thm)],[3512])).
% 1.54/1.77 tff(3514,plain,
% 1.54/1.77 (r(elem!1, s(s(s(z)))) <=> r(z, s(s(s(z))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[1620])).
% 1.54/1.77 tff(3515,plain,
% 1.54/1.77 (r(z, s(s(s(z))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[3313, 3514])).
% 1.54/1.77 tff(3516,plain,
% 1.54/1.77 (r(z, s(s(s(elem!1))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[3515, 3513])).
% 1.54/1.77 tff(3517,plain,
% 1.54/1.77 (~r(z, s(s(elem!1)))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[950, 3516, 653])).
% 1.54/1.77 tff(3518,plain,
% 1.54/1.77 (b(z, s(s(elem!1)))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[460, 3517])).
% 1.54/1.77 tff(3519,plain,
% 1.54/1.77 (b(z, s(s(z)))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[3518, 3511])).
% 1.54/1.77 tff(3520,plain,
% 1.54/1.77 (~r(s(s(s(s(z)))), z)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3463, 3501, 3350, 3337, 204, 2284])).
% 1.54/1.77 tff(3521,plain,
% 1.54/1.77 (b(s(s(s(s(z)))), z)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[695, 3520])).
% 1.54/1.77 tff(3522,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(3523,plain,
% 1.54/1.77 (((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(3524,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[3523])).
% 1.54/1.77 tff(3525,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.54/1.77 inference(transitivity,[status(thm)],[3524, 3522])).
% 1.54/1.77 tff(3526,plain,
% 1.54/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(3527,plain,
% 1.54/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[3526, 3525])).
% 1.54/1.77 tff(3528,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3527, 306, 3521, 3519, 3510, 3501])).
% 1.54/1.77 tff(3529,plain,((~(elem!1 = z)) | (~r(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | b(s(s(s(z))), s(s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | r(s(s(elem!1)), elem!1) | r(s(s(elem!1)), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(3530,plain,
% 1.54/1.77 (~(elem!1 = z)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3529, 3495, 2284, 204, 347, 3313, 6, 3149])).
% 1.54/1.77 tff(3531,plain,
% 1.54/1.77 (r(elem!1, z)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[174, 3530, 2])).
% 1.54/1.77 tff(3532,plain,
% 1.54/1.77 (~r(elem!1, s(z))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[2180, 124, 3531, 204])).
% 1.54/1.77 tff(3533,plain,
% 1.54/1.77 (elem!1 = s(z)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[97, 3532])).
% 1.54/1.77 tff(3534,plain,
% 1.54/1.77 (s(elem!1) = s(s(z))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[3533])).
% 1.54/1.77 tff(3535,plain,
% 1.54/1.77 (s(s(elem!1)) = s(s(s(z)))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[3534])).
% 1.54/1.77 tff(3536,plain,
% 1.54/1.77 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[3535])).
% 1.54/1.77 tff(3537,plain,
% 1.54/1.77 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.54/1.77 inference(symmetry,[status(thm)],[3536])).
% 1.54/1.77 tff(3538,plain,
% 1.54/1.77 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[3536])).
% 1.54/1.77 tff(3539,plain,
% 1.54/1.77 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 1.54/1.77 inference(symmetry,[status(thm)],[3538])).
% 1.54/1.77 tff(3540,plain,
% 1.54/1.77 (b(s(z), s(s(s(s(s(z)))))) <=> b(s(z), s(s(s(s(elem!1)))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[3539])).
% 1.54/1.77 tff(3541,plain,
% 1.54/1.77 (b(s(z), s(s(s(s(elem!1))))) <=> b(s(z), s(s(s(s(s(z))))))),
% 1.54/1.77 inference(symmetry,[status(thm)],[3540])).
% 1.54/1.77 tff(3542,plain,
% 1.54/1.77 (b(elem!1, s(s(s(s(elem!1))))) <=> b(s(z), s(s(s(s(elem!1)))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[3533])).
% 1.54/1.78 tff(3543,plain,
% 1.54/1.78 (s(z) = elem!1),
% 1.54/1.78 inference(symmetry,[status(thm)],[3533])).
% 1.54/1.78 tff(3544,plain,
% 1.54/1.78 ((s(s(s(s(s(z))))) = s(z)) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.54/1.78 inference(monotonicity,[status(thm)],[3539, 3543])).
% 1.54/1.78 tff(3545,plain,
% 1.54/1.78 ((s(s(s(s(s(z))))) = s(z)) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[3544, 1542])).
% 1.54/1.78 tff(3546,plain,
% 1.54/1.78 ((~(s(s(s(s(s(z))))) = s(z))) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[3545])).
% 1.54/1.78 tff(3547,plain,
% 1.54/1.78 (~(elem!1 = s(s(s(s(elem!1)))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[500, 3546])).
% 1.54/1.78 tff(3548,plain,
% 1.54/1.78 (r(elem!1, s(s(elem!1))) <=> r(s(z), s(s(s(z))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[3533, 3535])).
% 1.54/1.78 tff(3549,plain,
% 1.54/1.78 (r(s(z), s(s(s(z)))) <=> r(elem!1, s(s(elem!1)))),
% 1.54/1.78 inference(symmetry,[status(thm)],[3548])).
% 1.54/1.78 tff(3550,plain,
% 1.54/1.78 (r(elem!1, s(s(s(z)))) <=> r(s(z), s(s(s(z))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[3533])).
% 1.54/1.78 tff(3551,plain,
% 1.54/1.78 (r(s(z), s(s(s(z))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[3313, 3550])).
% 1.54/1.78 tff(3552,plain,
% 1.54/1.78 (r(elem!1, s(s(elem!1)))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[3551, 3549])).
% 1.54/1.78 tff(3553,plain,
% 1.54/1.78 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(z)))) = s(s(z)))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[3536, 3534])).
% 1.54/1.78 tff(3554,plain,
% 1.54/1.78 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(z)) = s(s(s(s(z)))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[3553, 1707])).
% 1.54/1.78 tff(3555,plain,
% 1.54/1.78 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.54/1.78 inference(symmetry,[status(thm)],[3554])).
% 1.54/1.78 tff(3556,plain,
% 1.54/1.78 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[3555])).
% 1.54/1.78 tff(3557,plain,
% 1.54/1.78 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[1612, 3556])).
% 1.54/1.78 tff(3558,plain,
% 1.54/1.78 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[1284, 3557])).
% 1.54/1.78 tff(3559,plain,
% 1.54/1.78 (b(s(s(s(s(elem!1)))), s(s(elem!1))) <=> b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[3535])).
% 1.54/1.78 tff(3560,plain,
% 1.54/1.78 (b(s(s(s(s(elem!1)))), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.54/1.78 inference(symmetry,[status(thm)],[3559])).
% 1.54/1.78 tff(3561,plain,
% 1.54/1.78 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[3539])).
% 1.54/1.78 tff(3562,plain,
% 1.54/1.78 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.54/1.78 inference(transitivity,[status(thm)],[3561, 3560])).
% 1.54/1.78 tff(3563,plain,
% 1.54/1.78 ((~b(s(s(s(s(s(z))))), s(s(s(z))))) <=> (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[3562])).
% 1.54/1.78 tff(3564,plain,
% 1.54/1.78 (~r(z, s(s(s(z))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[3392, 3531, 3313])).
% 1.54/1.78 tff(3565,plain,
% 1.54/1.78 ((z = s(s(s(z)))) | b(z, s(s(s(z))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[2415, 43, 3564])).
% 1.54/1.78 tff(3566,plain,
% 1.54/1.78 (b(z, s(s(s(z))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[3565, 3385])).
% 1.54/1.78 tff(3567,plain,
% 1.54/1.78 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(z)))), elem!1)),
% 1.54/1.78 inference(monotonicity,[status(thm)],[3543])).
% 1.54/1.78 tff(3568,plain,
% 1.54/1.78 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(z))),
% 1.54/1.78 inference(symmetry,[status(thm)],[3567])).
% 1.54/1.78 tff(3569,plain,
% 1.54/1.78 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 1.54/1.78 inference(monotonicity,[status(thm)],[3536])).
% 1.54/1.78 tff(3570,plain,
% 1.54/1.78 ((s(z) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[3543])).
% 1.54/1.78 tff(3571,plain,
% 1.54/1.78 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 1.54/1.78 inference(transitivity,[status(thm)],[3570, 1555])).
% 1.54/1.78 tff(3572,plain,
% 1.54/1.78 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[3571])).
% 1.54/1.78 tff(3573,plain,
% 1.54/1.78 (~(s(s(s(elem!1))) = elem!1)),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[645, 3572])).
% 1.54/1.78 tff(3574,plain,
% 1.54/1.78 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(elem!1))), elem!1)),
% 1.54/1.78 inference(monotonicity,[status(thm)],[3537, 3543])).
% 1.54/1.78 tff(3575,plain,
% 1.54/1.78 ((~r(s(s(s(s(z)))), s(z))) <=> (~r(s(s(s(elem!1))), elem!1))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[3574])).
% 1.54/1.78 tff(3576,plain,
% 1.54/1.78 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[3536, 3535])).
% 1.54/1.78 tff(3577,plain,
% 1.54/1.78 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[3495, 3576])).
% 1.54/1.78 tff(3578,plain,
% 1.54/1.78 (~r(s(s(s(s(z)))), s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[1040, 124, 3551, 3577])).
% 1.54/1.78 tff(3579,plain,
% 1.54/1.78 (~r(s(s(s(elem!1))), elem!1)),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[3578, 3575])).
% 1.54/1.78 tff(3580,plain,
% 1.54/1.78 (b(s(s(s(elem!1))), elem!1)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[1636, 3579, 3573])).
% 1.54/1.78 tff(3581,plain,
% 1.54/1.78 (b(s(s(s(s(z)))), elem!1)),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[3580, 3569])).
% 1.54/1.78 tff(3582,plain,
% 1.54/1.78 (b(s(s(s(s(z)))), s(z))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[3581, 3568])).
% 1.54/1.78 tff(3583,plain,
% 1.54/1.78 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(3584,plain,
% 1.54/1.78 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(3585,plain,
% 1.54/1.78 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[3584, 3583])).
% 1.54/1.78 tff(3586,plain,
% 1.54/1.78 (~r(s(z), s(s(s(s(z)))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[3585, 124, 3551, 3577])).
% 1.54/1.78 tff(3587,plain,
% 1.54/1.78 ((s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z)))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[680, 43, 3586])).
% 1.54/1.78 tff(3588,plain,
% 1.54/1.78 (b(s(z), s(s(s(s(z)))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[3587, 670])).
% 1.54/1.78 tff(3589,plain,
% 1.54/1.78 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[15])).
% 1.54/1.78 tff(3590,plain,
% 1.54/1.78 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[3589])).
% 1.54/1.78 tff(3591,plain,
% 1.54/1.78 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 1.54/1.78 inference(symmetry,[status(thm)],[3590])).
% 1.54/1.78 tff(3592,plain,
% 1.54/1.78 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(s(s(elem!1)))), s(z))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[3591])).
% 1.54/1.78 tff(3593,plain,
% 1.54/1.78 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(s(s(s(s(z))))), s(z))),
% 1.54/1.78 inference(symmetry,[status(thm)],[3592])).
% 1.54/1.78 tff(3594,plain,
% 1.54/1.78 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(elem!1)))), s(z))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[10])).
% 1.54/1.78 tff(3595,plain,
% 1.54/1.78 (s(z) = elem!1),
% 1.54/1.78 inference(symmetry,[status(thm)],[10])).
% 1.54/1.78 tff(3596,plain,
% 1.54/1.78 ((s(s(s(s(s(z))))) = s(z)) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.54/1.78 inference(monotonicity,[status(thm)],[3591, 3595])).
% 1.54/1.78 tff(3597,plain,
% 1.54/1.78 ((s(s(s(s(s(z))))) = s(z)) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[3596, 1542])).
% 1.54/1.78 tff(3598,plain,
% 1.54/1.78 ((s(s(s(s(s(z))))) = s(z)) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.54/1.78 inference(transitivity,[status(thm)],[3597, 1543])).
% 1.54/1.78 tff(3599,plain,
% 1.54/1.78 ((~(s(s(s(s(s(z))))) = s(z))) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[3598])).
% 1.54/1.78 tff(3600,plain,
% 1.54/1.78 (~(s(s(s(s(elem!1)))) = elem!1)),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[500, 3599])).
% 1.54/1.78 tff(3601,plain,
% 1.54/1.78 (r(s(s(s(s(s(z))))), s(z)) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 1.54/1.78 inference(monotonicity,[status(thm)],[3591, 3595])).
% 1.54/1.78 tff(3602,plain,
% 1.54/1.78 ((~r(s(s(s(s(s(z))))), s(z))) <=> (~r(s(s(s(s(elem!1)))), elem!1))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[3601])).
% 1.54/1.78 tff(3603,assumption,(b(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 1.54/1.78 tff(3604,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), 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(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), 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(s(s(z))))), z)))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(3605,plain,
% 1.54/1.78 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), 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(s(s(z))))), z)))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(3606,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), 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(s(s(z))))), z))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[3605])).
% 1.54/1.78 tff(3607,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), 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(s(s(z))))), z)))),
% 1.54/1.78 inference(transitivity,[status(thm)],[3606, 3604])).
% 1.54/1.78 tff(3608,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(3609,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), 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(s(s(z))))), z))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[3608, 3607])).
% 1.54/1.78 tff(3610,plain,
% 1.54/1.78 (~b(s(s(s(s(s(z))))), z)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[3609, 306, 2284, 859, 3603, 245])).
% 1.54/1.78 tff(3611,plain,
% 1.54/1.78 (((~![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))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(3612,plain,
% 1.54/1.78 ((~![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))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(3613,plain,
% 1.54/1.78 ((~![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)),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[3612, 3611])).
% 1.54/1.78 tff(3614,plain,
% 1.54/1.78 (r(s(s(s(s(s(z))))), z)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[3613, 43, 2842, 3610])).
% 1.54/1.78 tff(3615,plain,
% 1.54/1.78 (~r(s(s(s(s(s(z))))), s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[1110, 124, 204, 3614])).
% 1.54/1.78 tff(3616,plain,
% 1.54/1.78 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[3615, 3602])).
% 1.54/1.78 tff(3617,plain,
% 1.54/1.78 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[1736, 3616, 3600])).
% 1.54/1.78 tff(3618,plain,
% 1.54/1.78 (b(s(s(s(s(elem!1)))), s(z))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[3617, 3594])).
% 1.54/1.78 tff(3619,plain,
% 1.54/1.78 (b(s(s(s(s(s(z))))), s(z))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[3618, 3593])).
% 1.54/1.78 tff(3620,assumption,(b(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 1.54/1.78 tff(3621,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(3622,plain,
% 1.54/1.78 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(3623,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(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(z)))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[3622])).
% 1.54/1.78 tff(3624,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(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(z))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[3623, 3621])).
% 1.54/1.78 tff(3625,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(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))))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(3626,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[3625, 3624])).
% 1.54/1.78 tff(3627,plain,
% 1.54/1.78 (~b(s(s(s(s(s(z))))), s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[3626, 306, 2284, 3603, 245, 3620])).
% 1.54/1.78 tff(3628,plain,
% 1.54/1.78 ($false),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[3627, 3619])).
% 1.54/1.78 tff(3629,plain,((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~(elem!1 = s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(z), z)) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.78 tff(3630,plain,
% 1.54/1.78 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[3629, 3533, 2284, 3588, 3582, 204, 3566])).
% 1.54/1.78 tff(3631,plain,
% 1.54/1.78 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[3630, 3563])).
% 1.54/1.78 tff(3632,plain,
% 1.54/1.78 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[1302, 3631, 3558])).
% 1.54/1.78 tff(3633,plain,
% 1.54/1.78 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[1918, 3632, 3552])).
% 1.54/1.78 tff(3634,plain,
% 1.54/1.78 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[1923, 3633, 3547])).
% 1.54/1.78 tff(3635,plain,
% 1.54/1.78 (b(s(z), s(s(s(s(elem!1)))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[3634, 3542])).
% 1.54/1.78 tff(3636,plain,
% 1.54/1.78 (b(s(z), s(s(s(s(s(z))))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[3635, 3541])).
% 1.54/1.78 tff(3637,plain,
% 1.54/1.78 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(s(s(elem!1)))), s(z))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[3539])).
% 1.54/1.78 tff(3638,plain,
% 1.54/1.78 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(s(s(s(s(z))))), s(z))),
% 1.54/1.78 inference(symmetry,[status(thm)],[3637])).
% 1.54/1.78 tff(3639,plain,
% 1.54/1.78 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(elem!1)))), s(z))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[3533])).
% 1.54/1.78 tff(3640,plain,
% 1.54/1.78 ((s(s(s(s(s(z))))) = s(z)) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.54/1.78 inference(transitivity,[status(thm)],[3545, 1543])).
% 1.54/1.78 tff(3641,plain,
% 1.54/1.78 ((~(s(s(s(s(s(z))))) = s(z))) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[3640])).
% 1.54/1.78 tff(3642,plain,
% 1.54/1.78 (~(s(s(s(s(elem!1)))) = elem!1)),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[500, 3641])).
% 1.54/1.78 tff(3643,plain,
% 1.54/1.78 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[1297, 3632, 3552])).
% 1.54/1.78 tff(3644,plain,
% 1.54/1.78 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[1736, 3643, 3642])).
% 1.54/1.78 tff(3645,plain,
% 1.54/1.78 (b(s(s(s(s(elem!1)))), s(z))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[3644, 3639])).
% 1.54/1.78 tff(3646,plain,
% 1.54/1.78 (b(s(s(s(s(s(z))))), s(z))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[3645, 3638])).
% 1.54/1.78 tff(3647,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(3648,plain,
% 1.54/1.78 (((~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(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(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(3649,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z)))))))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[3648])).
% 1.54/1.78 tff(3650,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[3649, 3647])).
% 1.54/1.78 tff(3651,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(3652,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z)))))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[3651, 3650])).
% 1.54/1.78 tff(3653,plain,
% 1.54/1.78 ((~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(s(z)))))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[3652, 306, 3582])).
% 1.54/1.78 tff(3654,plain,
% 1.54/1.78 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[3653, 3646, 3636])).
% 1.54/1.78 tff(3655,plain,
% 1.54/1.78 (s(s(s(z))) = s(s(elem!1))),
% 1.54/1.78 inference(symmetry,[status(thm)],[3535])).
% 1.54/1.78 tff(3656,plain,
% 1.54/1.78 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[3539, 3655])).
% 1.54/1.78 tff(3657,plain,
% 1.54/1.78 (r(s(s(s(s(elem!1)))), s(s(elem!1))) <=> r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.54/1.78 inference(symmetry,[status(thm)],[3656])).
% 1.54/1.78 tff(3658,plain,
% 1.54/1.78 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[3632, 3657])).
% 1.54/1.78 tff(3659,plain,
% 1.54/1.78 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(3660,plain,
% 1.54/1.78 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(3661,plain,
% 1.54/1.78 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[3660, 3659])).
% 1.54/1.78 tff(3662,plain,
% 1.54/1.78 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[3661, 124, 3577, 3658])).
% 1.54/1.78 tff(3663,plain,
% 1.54/1.78 (((~![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))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(3664,plain,
% 1.54/1.78 ((~![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))))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(3665,plain,
% 1.54/1.78 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(s(z))))) | b(s(s(s(s(s(z))))), s(s(s(s(z))))) | r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[3664, 3663])).
% 1.54/1.78 tff(3666,plain,
% 1.54/1.78 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) | b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[3665, 43, 3662])).
% 1.54/1.78 tff(3667,plain,
% 1.54/1.78 (s(s(s(s(s(z))))) = s(s(s(s(z))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[3666, 3654])).
% 1.54/1.78 tff(3668,plain,
% 1.54/1.78 (s(s(s(s(s(s(z)))))) = s(s(s(s(s(z)))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[3667])).
% 1.54/1.78 tff(3669,plain,
% 1.54/1.78 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(s(z))))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[3538])).
% 1.54/1.78 tff(3670,plain,
% 1.54/1.78 (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))),
% 1.54/1.78 inference(transitivity,[status(thm)],[3669, 3668, 3667, 3537])).
% 1.54/1.78 tff(3671,plain,
% 1.54/1.78 (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[1719, 3558])).
% 1.54/1.78 tff(3672,plain,
% 1.54/1.78 ($false),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[3671, 3670])).
% 1.54/1.78 tff(3673,plain,(r(s(s(elem!1)), s(elem!1)) | (~b(s(s(s(z))), s(z))) | (~r(s(z), z)) | (~r(elem!1, s(s(s(z))))) | b(elem!1, s(z)) | b(elem!1, z) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(3674,plain,
% 1.54/1.79 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[3673, 3286, 204, 3149, 5, 3160, 3162, 6])).
% 1.54/1.79 tff(3675,plain,
% 1.54/1.79 (b(z, s(s(z))) <=> b(elem!1, s(s(z)))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[3137])).
% 1.54/1.79 tff(3676,plain,
% 1.54/1.79 (b(elem!1, s(s(z))) <=> b(z, s(s(z)))),
% 1.54/1.79 inference(symmetry,[status(thm)],[3675])).
% 1.54/1.79 tff(3677,plain,
% 1.54/1.79 (b(elem!1, s(s(z))) <=> b(elem!1, s(s(elem!1)))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[3139])).
% 1.54/1.79 tff(3678,plain,
% 1.54/1.79 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(z)))),
% 1.54/1.79 inference(symmetry,[status(thm)],[3677])).
% 1.54/1.79 tff(3679,plain,
% 1.54/1.79 (b(elem!1, s(s(elem!1))) <=> b(z, s(s(z)))),
% 1.54/1.79 inference(transitivity,[status(thm)],[3678, 3676])).
% 1.54/1.79 tff(3680,plain,
% 1.54/1.79 (b(z, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[3137])).
% 1.54/1.79 tff(3681,plain,
% 1.54/1.79 (b(elem!1, s(s(s(elem!1)))) <=> b(z, s(s(s(elem!1))))),
% 1.54/1.79 inference(symmetry,[status(thm)],[3680])).
% 1.54/1.79 tff(3682,plain,
% 1.54/1.79 ((~b(elem!1, s(s(s(elem!1))))) <=> (~b(z, s(s(s(elem!1)))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[3681])).
% 1.54/1.79 tff(3683,plain,
% 1.54/1.79 (~b(z, s(s(s(elem!1))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[3281, 3682])).
% 1.54/1.79 tff(3684,plain,
% 1.54/1.79 (r(z, s(s(s(elem!1))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[585, 3683])).
% 1.54/1.79 tff(3685,plain,
% 1.54/1.79 (~r(z, s(s(elem!1)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[950, 3432, 3684])).
% 1.54/1.79 tff(3686,plain,
% 1.54/1.79 (b(z, s(s(elem!1)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[460, 3685])).
% 1.54/1.79 tff(3687,plain,
% 1.54/1.79 (b(elem!1, s(s(elem!1)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[2757, 3686, 3137])).
% 1.54/1.79 tff(3688,plain,
% 1.54/1.79 (b(z, s(s(z)))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[3687, 3679])).
% 1.54/1.79 tff(3689,plain,
% 1.54/1.79 (b(s(s(z)), z) <=> b(s(s(z)), elem!1)),
% 1.54/1.79 inference(monotonicity,[status(thm)],[3137])).
% 1.54/1.79 tff(3690,plain,
% 1.54/1.79 (b(s(s(z)), elem!1) <=> b(s(s(z)), z)),
% 1.54/1.79 inference(symmetry,[status(thm)],[3689])).
% 1.54/1.79 tff(3691,plain,
% 1.54/1.79 (b(s(s(z)), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 1.54/1.79 inference(monotonicity,[status(thm)],[3139])).
% 1.54/1.79 tff(3692,plain,
% 1.54/1.79 (b(s(s(elem!1)), elem!1) <=> b(s(s(z)), elem!1)),
% 1.54/1.79 inference(symmetry,[status(thm)],[3691])).
% 1.54/1.79 tff(3693,plain,
% 1.54/1.79 (b(s(s(elem!1)), elem!1) <=> b(s(s(z)), z)),
% 1.54/1.79 inference(transitivity,[status(thm)],[3692, 3690])).
% 1.54/1.79 tff(3694,plain,
% 1.54/1.79 (b(s(s(z)), z)),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[30, 3693])).
% 1.54/1.79 tff(3695,plain,
% 1.54/1.79 (~b(s(s(s(z))), elem!1)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[2071, 3490, 3694, 3688, 3674, 3312])).
% 1.54/1.79 tff(3696,plain,
% 1.54/1.79 (~b(s(s(s(elem!1))), elem!1)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[2215, 3695, 3137])).
% 1.54/1.79 tff(3697,plain,
% 1.54/1.79 (r(s(s(s(elem!1))), elem!1)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1636, 3696, 3156])).
% 1.54/1.79 tff(3698,plain,
% 1.54/1.79 (r(s(s(s(z))), z)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1631, 3697, 3312])).
% 1.54/1.79 tff(3699,plain,
% 1.54/1.79 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[3230, 3698, 3163, 3137, 3450, 802])).
% 1.54/1.79 tff(3700,plain,
% 1.54/1.79 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1144, 3699, 3494])).
% 1.54/1.79 tff(3701,plain,
% 1.54/1.79 (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1719, 1285])).
% 1.54/1.79 tff(3702,assumption,(s(s(s(s(elem!1)))) = s(s(s(s(s(s(z))))))), introduced(assumption)).
% 1.54/1.79 tff(3703,plain,
% 1.54/1.79 (s(s(s(s(s(s(z)))))) = s(s(s(s(elem!1))))),
% 1.54/1.79 inference(symmetry,[status(thm)],[3702])).
% 1.54/1.79 tff(3704,plain,
% 1.54/1.79 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(s(s(elem!1)))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[3703])).
% 1.54/1.79 tff(3705,plain,
% 1.54/1.79 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[1898])).
% 1.54/1.79 tff(3706,plain,
% 1.54/1.79 (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))),
% 1.54/1.79 inference(transitivity,[status(thm)],[3705, 2823, 3704, 1280])).
% 1.54/1.79 tff(3707,assumption,(~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))), introduced(assumption)).
% 1.54/1.79 tff(3708,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[3707, 3706])).
% 1.54/1.79 tff(3709,plain,((~(s(s(s(s(elem!1)))) = s(s(s(s(s(s(z)))))))) | (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(3710,plain,
% 1.54/1.79 (~(s(s(s(s(elem!1)))) = s(s(s(s(s(s(z)))))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[3709, 3137, 3701])).
% 1.54/1.79 tff(3711,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(3712,plain,
% 1.54/1.79 (((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(3713,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), elem!1))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[3712])).
% 1.54/1.79 tff(3714,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.54/1.79 inference(transitivity,[status(thm)],[3713, 3711])).
% 1.54/1.79 tff(3715,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(3716,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), elem!1))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[3715, 3714])).
% 1.54/1.79 tff(3717,plain,
% 1.54/1.79 (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[3716, 306, 30, 3687, 3700])).
% 1.54/1.79 tff(3718,plain,
% 1.54/1.79 ((s(s(z)) = s(s(s(s(s(s(z))))))) <=> (s(s(elem!1)) = s(s(s(s(s(s(z)))))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[3139])).
% 1.54/1.79 tff(3719,plain,
% 1.54/1.79 ((s(s(z)) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = s(s(elem!1)))),
% 1.54/1.79 inference(transitivity,[status(thm)],[3718, 3240])).
% 1.54/1.79 tff(3720,plain,
% 1.54/1.79 ((~(s(s(z)) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(s(s(s(s(z)))))) = s(s(elem!1))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[3719])).
% 1.54/1.79 tff(3721,plain,
% 1.54/1.79 (~(s(s(s(s(s(s(z)))))) = s(s(elem!1)))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[2826, 3720])).
% 1.54/1.79 tff(3722,plain,
% 1.54/1.79 (r(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[3247, 43, 3721, 3717])).
% 1.54/1.79 tff(3723,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(3724,plain,
% 1.54/1.79 (((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(3725,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z))))))))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[3724])).
% 1.54/1.79 tff(3726,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[3725, 3723])).
% 1.54/1.79 tff(3727,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(3728,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z))))))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[3727, 3726])).
% 1.54/1.79 tff(3729,plain,
% 1.54/1.79 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[3728, 306, 30, 1003, 2076, 2812])).
% 1.54/1.79 tff(3730,assumption,(~(s(s(s(s(elem!1)))) = s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.54/1.79 tff(3731,plain,
% 1.54/1.79 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z))))))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(3732,plain,
% 1.54/1.79 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z))))))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(3733,plain,
% 1.54/1.79 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[3732, 3731])).
% 1.54/1.79 tff(3734,plain,
% 1.54/1.79 (r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[3733, 43, 3730, 3729])).
% 1.54/1.79 tff(3735,assumption,(r(s(s(s(s(s(s(z)))))), s(s(elem!1)))), introduced(assumption)).
% 1.54/1.79 tff(3736,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(3737,plain,
% 1.54/1.79 (((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(3738,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[3737])).
% 1.54/1.79 tff(3739,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[3738, 3736])).
% 1.54/1.79 tff(3740,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(3741,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[3740, 3739])).
% 1.54/1.79 tff(3742,plain,
% 1.54/1.79 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[3741, 306, 30, 1003, 2076])).
% 1.54/1.79 tff(3743,plain,
% 1.54/1.79 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1302, 3742, 1717])).
% 1.54/1.79 tff(3744,plain,
% 1.54/1.79 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(3745,plain,
% 1.54/1.79 (((~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(3746,plain,
% 1.54/1.79 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z))))))))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[3745])).
% 1.54/1.79 tff(3747,plain,
% 1.54/1.79 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[3746, 3744])).
% 1.54/1.79 tff(3748,plain,
% 1.54/1.79 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(3749,plain,
% 1.54/1.79 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z))))))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[3748, 3747])).
% 1.54/1.79 tff(3750,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[3749, 124, 3743, 3735, 3734])).
% 1.54/1.79 tff(3751,plain,((~b(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(s(z))))))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(3752,plain,
% 1.54/1.79 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[3751, 3722, 3710, 1285, 30, 3687, 3700])).
% 1.54/1.79 tff(3753,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[3752, 3491])).
% 1.54/1.79 tff(3754,plain,((~r(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~r(s(z), z)) | (s(s(s(elem!1))) = s(elem!1)) | (~r(elem!1, s(z))) | r(s(s(elem!1)), s(elem!1)) | b(elem!1, s(z)) | r(s(s(elem!1)), elem!1) | (s(s(elem!1)) = s(elem!1)) | b(s(elem!1), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(3755,plain,
% 1.54/1.79 (r(s(s(elem!1)), s(elem!1))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[3754, 3119, 204, 150, 3098, 30, 5, 6, 392, 2609])).
% 1.54/1.79 tff(3756,plain,
% 1.54/1.79 (r(elem!1, s(z)) <=> r(elem!1, s(elem!1))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[3123])).
% 1.54/1.79 tff(3757,plain,
% 1.54/1.79 (r(elem!1, s(elem!1))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[3098, 3756])).
% 1.54/1.79 tff(3758,plain,
% 1.54/1.79 (~r(elem!1, s(s(elem!1)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1236, 124, 3757, 3755])).
% 1.54/1.79 tff(3759,plain,
% 1.54/1.79 (b(elem!1, s(s(elem!1)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[516, 3758, 360])).
% 1.54/1.79 tff(3760,plain,
% 1.54/1.79 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(z))), s(elem!1))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[3126])).
% 1.54/1.79 tff(3761,plain,
% 1.54/1.79 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.54/1.79 inference(symmetry,[status(thm)],[3760])).
% 1.54/1.79 tff(3762,plain,
% 1.54/1.79 (b(s(s(s(z))), s(z)) <=> b(s(s(s(z))), s(elem!1))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[3123])).
% 1.54/1.79 tff(3763,plain,
% 1.54/1.79 (b(s(s(s(z))), s(z)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.54/1.79 inference(transitivity,[status(thm)],[3762, 3761])).
% 1.54/1.79 tff(3764,plain,
% 1.54/1.79 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1511, 3122])).
% 1.54/1.79 tff(3765,plain,
% 1.54/1.79 (~(elem!1 = s(s(s(elem!1))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1518, 3764])).
% 1.54/1.79 tff(3766,plain,
% 1.54/1.79 (~(s(s(s(elem!1))) = elem!1)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[2187, 3765])).
% 1.54/1.79 tff(3767,plain,
% 1.54/1.79 (b(elem!1, z) <=> b(elem!1, elem!1)),
% 1.54/1.79 inference(monotonicity,[status(thm)],[3122])).
% 1.54/1.79 tff(3768,plain,
% 1.54/1.79 (b(elem!1, elem!1) <=> b(elem!1, z)),
% 1.54/1.79 inference(symmetry,[status(thm)],[3767])).
% 1.54/1.79 tff(3769,plain,
% 1.54/1.79 ((~b(elem!1, elem!1)) <=> (~b(elem!1, z))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[3768])).
% 1.54/1.79 tff(3770,plain,
% 1.54/1.79 (~b(elem!1, z)),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[1468, 3769])).
% 1.54/1.79 tff(3771,plain,
% 1.54/1.79 (~r(s(s(s(z))), s(z))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[2182, 3770, 3098, 204, 3766])).
% 1.54/1.79 tff(3772,plain,
% 1.54/1.79 (b(s(s(s(z))), s(z))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[113, 3771])).
% 1.54/1.79 tff(3773,plain,
% 1.54/1.79 (b(s(s(s(elem!1))), s(elem!1))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[3772, 3763])).
% 1.54/1.79 tff(3774,plain,
% 1.54/1.79 (~b(s(s(s(elem!1))), elem!1)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[2215, 1, 1502])).
% 1.54/1.79 tff(3775,plain,
% 1.54/1.79 (r(s(s(s(elem!1))), elem!1)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1636, 3774, 3171])).
% 1.54/1.79 tff(3776,plain,
% 1.54/1.79 (r(s(s(s(z))), z)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1631, 3775, 1619])).
% 1.54/1.79 tff(3777,plain,
% 1.54/1.79 (r(s(z), s(s(s(z)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[1503, 1507])).
% 1.54/1.79 tff(3778,plain,
% 1.54/1.79 ((~r(s(z), s(s(s(z))))) <=> (~r(s(elem!1), s(s(s(elem!1)))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[3777])).
% 1.54/1.79 tff(3779,plain,
% 1.54/1.79 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 1.54/1.79 inference(monotonicity,[status(thm)],[1502])).
% 1.54/1.79 tff(3780,plain,
% 1.54/1.79 ((~(s(s(s(z))) = z)) <=> (~(s(s(s(z))) = elem!1))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[3779])).
% 1.54/1.79 tff(3781,plain,
% 1.54/1.79 (~(s(s(s(z))) = elem!1)),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[169, 3780])).
% 1.54/1.79 tff(3782,plain,
% 1.54/1.80 (r(s(s(s(z))), elem!1)),
% 1.54/1.80 inference(unit_resolution,[status(thm)],[1489, 1, 3781])).
% 1.54/1.80 tff(3783,plain,
% 1.54/1.80 (((~![X0: $i, X2: $i, X1: $i] : ((~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(z), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(z), elem!1)))),
% 1.54/1.80 inference(rewrite,[status(thm)],[])).
% 1.54/1.80 tff(3784,plain,
% 1.54/1.80 (((~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1)))),
% 1.54/1.80 inference(rewrite,[status(thm)],[])).
% 1.54/1.80 tff(3785,plain,
% 1.54/1.80 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1))))),
% 1.54/1.80 inference(monotonicity,[status(thm)],[3784])).
% 1.54/1.80 tff(3786,plain,
% 1.54/1.80 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1)))),
% 1.54/1.80 inference(transitivity,[status(thm)],[3785, 3783])).
% 1.54/1.80 tff(3787,plain,
% 1.54/1.80 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))))),
% 1.54/1.80 inference(quant_inst,[status(thm)],[])).
% 1.54/1.80 tff(3788,plain,
% 1.54/1.80 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1))),
% 1.54/1.80 inference(modus_ponens,[status(thm)],[3787, 3786])).
% 1.54/1.80 tff(3789,plain,
% 1.54/1.80 ($false),
% 1.54/1.80 inference(unit_resolution,[status(thm)],[3788, 124, 4, 2859, 1034])).
% 1.54/1.80 tff(3790,plain,((~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.80 tff(3791,plain,
% 1.64/1.80 (~r(s(z), s(s(s(z))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3790, 3782, 4])).
% 1.64/1.80 tff(3792,plain,
% 1.64/1.80 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[3791, 3778])).
% 1.64/1.80 tff(3793,plain,
% 1.64/1.80 ((s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[1881, 43, 3792])).
% 1.64/1.80 tff(3794,plain,
% 1.64/1.80 (b(s(elem!1), s(s(s(elem!1))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3793, 3181])).
% 1.64/1.80 tff(3795,plain,
% 1.64/1.80 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3230, 3794, 759, 1502, 3776, 802])).
% 1.64/1.80 tff(3796,plain,
% 1.64/1.80 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[1144, 3795, 3170])).
% 1.64/1.80 tff(3797,plain,
% 1.64/1.80 (~(s(s(s(s(elem!1)))) = s(s(s(s(s(s(z)))))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3709, 1502, 3701])).
% 1.64/1.80 tff(3798,plain,
% 1.64/1.80 (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3716, 306, 30, 1003, 3796])).
% 1.64/1.80 tff(3799,plain,
% 1.64/1.80 (r(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3247, 43, 3244, 3798])).
% 1.64/1.80 tff(3800,plain,
% 1.64/1.80 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3751, 3799, 3797, 1285, 30, 1003, 3796])).
% 1.64/1.80 tff(3801,plain,
% 1.64/1.80 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[1736, 3800, 1550])).
% 1.64/1.80 tff(3802,plain,
% 1.64/1.80 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(3803,plain,
% 1.64/1.80 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(3804,plain,
% 1.64/1.80 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[3803, 3802])).
% 1.64/1.80 tff(3805,plain,
% 1.64/1.80 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3804, 124, 3775, 3801])).
% 1.64/1.80 tff(3806,plain,
% 1.64/1.80 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[1958, 43, 3438, 3805])).
% 1.64/1.80 tff(3807,plain,
% 1.64/1.80 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[1740, 124, 802, 3801])).
% 1.64/1.80 tff(3808,plain,
% 1.64/1.80 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[1767, 43, 1512, 3807])).
% 1.64/1.80 tff(3809,plain,
% 1.64/1.80 ($false),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3487, 306, 759, 3794, 3808, 3806])).
% 1.64/1.80 tff(3810,plain,(b(s(s(s(z))), elem!1) | (~b(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~(z = elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.80 tff(3811,plain,
% 1.64/1.80 (b(s(s(s(z))), elem!1)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3810, 3773, 3119, 30, 3759, 3122, 150, 3091])).
% 1.64/1.80 tff(3812,plain,
% 1.64/1.80 (b(s(s(s(elem!1))), elem!1)),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[3811, 3134])).
% 1.64/1.80 tff(3813,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(3814,plain,
% 1.64/1.80 (((~b(s(s(elem!1)), elem!1)) | (~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(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(3815,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[3814])).
% 1.64/1.80 tff(3816,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.64/1.80 inference(transitivity,[status(thm)],[3815, 3813])).
% 1.64/1.80 tff(3817,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(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))))))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(3818,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[3817, 3816])).
% 1.64/1.80 tff(3819,plain,
% 1.64/1.80 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3818, 306, 30, 3759, 3812])).
% 1.64/1.80 tff(3820,plain,
% 1.64/1.80 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[891, 3819, 232])).
% 1.64/1.80 tff(3821,plain,
% 1.64/1.80 (r(s(z), s(s(s(z)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[3123, 3125])).
% 1.64/1.80 tff(3822,plain,
% 1.64/1.80 ((~r(s(z), s(s(s(z))))) <=> (~r(s(elem!1), s(s(s(elem!1)))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[3821])).
% 1.64/1.80 tff(3823,plain,
% 1.64/1.80 (r(s(s(z)), s(z)) <=> r(s(s(elem!1)), s(elem!1))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[3124, 3123])).
% 1.64/1.80 tff(3824,plain,
% 1.64/1.80 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(z)), s(z))),
% 1.64/1.80 inference(symmetry,[status(thm)],[3823])).
% 1.64/1.80 tff(3825,plain,
% 1.64/1.80 (r(s(s(z)), s(z))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[3755, 3824])).
% 1.64/1.80 tff(3826,plain,
% 1.64/1.80 (r(s(s(z)), s(s(s(z)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[3124, 3125])).
% 1.64/1.80 tff(3827,plain,
% 1.64/1.80 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(z))))),
% 1.64/1.80 inference(symmetry,[status(thm)],[3826])).
% 1.64/1.80 tff(3828,plain,
% 1.64/1.80 (r(s(s(z)), s(s(s(z))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[3820, 3827])).
% 1.64/1.80 tff(3829,plain,
% 1.64/1.80 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(3830,plain,
% 1.64/1.80 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(3831,plain,
% 1.64/1.80 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z)))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[3830, 3829])).
% 1.64/1.80 tff(3832,plain,
% 1.64/1.80 ($false),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3831, 124, 1034, 2479, 2516])).
% 1.64/1.80 tff(3833,plain,((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.80 tff(3834,plain,
% 1.64/1.80 (~r(s(z), s(s(s(z))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3833, 3828, 3825])).
% 1.64/1.80 tff(3835,plain,
% 1.64/1.80 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[3834, 3822])).
% 1.64/1.80 tff(3836,plain,
% 1.64/1.80 ((s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[1881, 43, 3835])).
% 1.64/1.80 tff(3837,plain,
% 1.64/1.80 (b(s(elem!1), s(s(s(elem!1))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3836, 3181])).
% 1.64/1.80 tff(3838,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(3839,plain,
% 1.64/1.80 (((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(3840,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[3839])).
% 1.64/1.80 tff(3841,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.64/1.80 inference(transitivity,[status(thm)],[3840, 3838])).
% 1.64/1.80 tff(3842,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(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)))))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(3843,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[3842, 3841])).
% 1.64/1.80 tff(3844,plain,
% 1.64/1.80 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3843, 306, 30, 3759, 3812])).
% 1.64/1.80 tff(3845,plain,
% 1.64/1.80 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[610, 3844, 233])).
% 1.64/1.80 tff(3846,plain,
% 1.64/1.80 (b(z, s(s(z)))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[1003, 2039])).
% 1.64/1.80 tff(3847,plain,
% 1.64/1.80 (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[1719, 1717])).
% 1.64/1.80 tff(3848,plain,
% 1.64/1.80 (~(s(s(s(s(elem!1)))) = s(s(s(s(s(s(z)))))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3709, 1502, 3847])).
% 1.64/1.80 tff(3849,plain,
% 1.64/1.80 ((s(elem!1) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = s(elem!1))),
% 1.64/1.80 inference(commutativity,[status(thm)],[])).
% 1.64/1.80 tff(3850,plain,
% 1.64/1.80 ((s(s(s(s(s(s(z)))))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(s(s(z)))))))),
% 1.64/1.80 inference(symmetry,[status(thm)],[3849])).
% 1.64/1.80 tff(3851,plain,
% 1.64/1.80 ((~(s(s(s(s(s(s(z)))))) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(s(s(s(z))))))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[3850])).
% 1.64/1.80 tff(3852,plain,
% 1.64/1.80 (~(s(elem!1) = s(s(s(s(s(s(z)))))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[3217, 3851])).
% 1.64/1.80 tff(3853,plain,
% 1.64/1.80 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(z)))))))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(3854,plain,
% 1.64/1.80 (((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(z))))))))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(z)))))))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(3855,plain,
% 1.64/1.80 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(z))))))))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[3854])).
% 1.64/1.80 tff(3856,plain,
% 1.64/1.80 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(z)))))))))),
% 1.64/1.80 inference(transitivity,[status(thm)],[3855, 3853])).
% 1.64/1.80 tff(3857,plain,
% 1.64/1.80 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(z)))))))))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(3858,plain,
% 1.64/1.80 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(z))))))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[3857, 3856])).
% 1.64/1.80 tff(3859,plain,
% 1.64/1.80 (~r(s(elem!1), s(s(s(s(s(s(z)))))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3858, 124, 802, 2858])).
% 1.64/1.80 tff(3860,plain,
% 1.64/1.80 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(s(s(s(z))))))) | b(s(elem!1), s(s(s(s(s(s(z))))))) | r(s(elem!1), s(s(s(s(s(s(z))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(s(s(s(z))))))) | b(s(elem!1), s(s(s(s(s(s(z))))))) | r(s(elem!1), s(s(s(s(s(s(z))))))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(3861,plain,
% 1.64/1.80 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(s(s(s(z))))))) | b(s(elem!1), s(s(s(s(s(s(z))))))) | r(s(elem!1), s(s(s(s(s(s(z))))))))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(3862,plain,
% 1.64/1.80 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(s(s(s(z))))))) | b(s(elem!1), s(s(s(s(s(s(z))))))) | r(s(elem!1), s(s(s(s(s(s(z)))))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[3861, 3860])).
% 1.64/1.80 tff(3863,plain,
% 1.64/1.80 ((s(elem!1) = s(s(s(s(s(s(z))))))) | b(s(elem!1), s(s(s(s(s(s(z)))))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3862, 43, 3859])).
% 1.64/1.80 tff(3864,plain,
% 1.64/1.80 (b(s(elem!1), s(s(s(s(s(s(z)))))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3863, 3852])).
% 1.64/1.80 tff(3865,plain,
% 1.64/1.80 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[1767, 43, 1516, 1991])).
% 1.64/1.80 tff(3866,plain,
% 1.64/1.80 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(3867,plain,
% 1.64/1.80 (((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(3868,plain,
% 1.64/1.80 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z))))))))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[3867])).
% 1.64/1.80 tff(3869,plain,
% 1.64/1.80 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.80 inference(transitivity,[status(thm)],[3868, 3866])).
% 1.64/1.80 tff(3870,plain,
% 1.64/1.80 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(3871,plain,
% 1.64/1.80 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z))))))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[3870, 3869])).
% 1.64/1.80 tff(3872,plain,
% 1.64/1.80 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3871, 124, 1289, 2858])).
% 1.64/1.80 tff(3873,plain,
% 1.64/1.80 (b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3733, 43, 3730, 3872])).
% 1.64/1.80 tff(3874,assumption,(b(s(elem!1), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.64/1.80 tff(3875,assumption,(b(s(s(s(s(s(s(z)))))), s(elem!1))), introduced(assumption)).
% 1.64/1.80 tff(3876,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(3877,plain,
% 1.64/1.80 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(3878,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z))))))))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[3877])).
% 1.64/1.81 tff(3879,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[3878, 3876])).
% 1.64/1.81 tff(3880,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(3881,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z))))))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[3880, 3879])).
% 1.64/1.81 tff(3882,plain,
% 1.64/1.81 ($false),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[3881, 306, 3222, 3875, 3874, 3873, 3865])).
% 1.64/1.81 tff(3883,plain,((~r(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (s(s(s(s(elem!1)))) = s(elem!1)) | (s(s(s(s(elem!1)))) = s(s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.81 tff(3884,plain,
% 1.64/1.81 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[3883, 3221, 3222, 3864, 1512, 3848, 2858, 802])).
% 1.64/1.81 tff(3885,plain,
% 1.64/1.81 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1736, 3884, 1550])).
% 1.64/1.81 tff(3886,plain,
% 1.64/1.81 (b(s(s(s(s(z)))), z)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[2079, 3885, 1619])).
% 1.64/1.81 tff(3887,plain,
% 1.64/1.81 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[2071, 3886, 2034, 3846, 1967, 1619])).
% 1.64/1.81 tff(3888,plain,
% 1.64/1.81 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[2027, 3887, 1972])).
% 1.64/1.81 tff(3889,plain,
% 1.64/1.81 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[2022, 3888, 1619, 653])).
% 1.64/1.81 tff(3890,plain,
% 1.64/1.81 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1302, 3889, 1717])).
% 1.64/1.81 tff(3891,plain,
% 1.64/1.81 ((elem!1 = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = elem!1)),
% 1.64/1.81 inference(commutativity,[status(thm)],[])).
% 1.64/1.81 tff(3892,plain,
% 1.64/1.81 ((s(s(s(s(s(s(z)))))) = elem!1) <=> (elem!1 = s(s(s(s(s(s(z)))))))),
% 1.64/1.81 inference(symmetry,[status(thm)],[3891])).
% 1.64/1.81 tff(3893,plain,
% 1.64/1.81 ((~(s(s(s(s(s(s(z)))))) = elem!1)) <=> (~(elem!1 = s(s(s(s(s(s(z))))))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[3892])).
% 1.64/1.81 tff(3894,plain,
% 1.64/1.81 (~(elem!1 = s(s(s(s(s(s(z)))))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[3170, 3893])).
% 1.64/1.81 tff(3895,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(3896,plain,
% 1.64/1.81 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(3897,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), 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(s(z)))))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[3896])).
% 1.64/1.81 tff(3898,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), 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(s(z)))))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[3897, 3895])).
% 1.64/1.81 tff(3899,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), 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(s(z)))))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(3900,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[3899, 3898])).
% 1.64/1.81 tff(3901,plain,
% 1.64/1.81 (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[3900, 306, 759, 3222, 3221])).
% 1.64/1.81 tff(3902,plain,
% 1.64/1.81 ((s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))) | r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[2877, 43, 3901])).
% 1.64/1.81 tff(3903,plain,
% 1.64/1.81 (r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[3902, 2868])).
% 1.64/1.81 tff(3904,plain,
% 1.64/1.81 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(3905,plain,
% 1.64/1.81 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(3906,plain,
% 1.64/1.81 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[3905])).
% 1.64/1.81 tff(3907,plain,
% 1.64/1.81 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[3906, 3904])).
% 1.64/1.81 tff(3908,plain,
% 1.64/1.81 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(3909,plain,
% 1.64/1.81 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[3908, 3907])).
% 1.64/1.81 tff(3910,plain,
% 1.64/1.81 (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[3909, 124, 878, 3903])).
% 1.64/1.81 tff(3911,plain,
% 1.64/1.81 (b(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[3247, 43, 3244, 3910])).
% 1.64/1.81 tff(3912,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(3913,plain,
% 1.64/1.81 (((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(3914,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(s(z))))))))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[3913])).
% 1.64/1.81 tff(3915,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[3914, 3912])).
% 1.64/1.81 tff(3916,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(3917,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(s(z))))))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[3916, 3915])).
% 1.64/1.81 tff(3918,plain,
% 1.64/1.81 (~b(elem!1, s(s(s(s(s(s(z)))))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[3917, 306, 30, 1003, 3911])).
% 1.64/1.81 tff(3919,plain,
% 1.64/1.81 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(s(s(z))))))) | b(elem!1, s(s(s(s(s(s(z))))))) | r(elem!1, s(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(s(z))))))) | b(elem!1, s(s(s(s(s(s(z))))))) | r(elem!1, s(s(s(s(s(s(z))))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(3920,plain,
% 1.64/1.81 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(s(s(z))))))) | b(elem!1, s(s(s(s(s(s(z))))))) | r(elem!1, s(s(s(s(s(s(z))))))))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(3921,plain,
% 1.64/1.81 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(s(s(z))))))) | b(elem!1, s(s(s(s(s(s(z))))))) | r(elem!1, s(s(s(s(s(s(z)))))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[3920, 3919])).
% 1.64/1.81 tff(3922,plain,
% 1.64/1.81 ((elem!1 = s(s(s(s(s(s(z))))))) | r(elem!1, s(s(s(s(s(s(z)))))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[3921, 43, 3918])).
% 1.64/1.81 tff(3923,plain,
% 1.64/1.81 (r(elem!1, s(s(s(s(s(s(z)))))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[3922, 3894])).
% 1.64/1.81 tff(3924,plain,
% 1.64/1.81 (r(s(s(s(z))), s(s(s(s(s(s(z))))))) <=> r(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))),
% 1.64/1.81 inference(symmetry,[status(thm)],[3166])).
% 1.64/1.81 tff(3925,plain,
% 1.64/1.81 ((~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))) <=> (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[3164])).
% 1.64/1.81 tff(3926,plain,
% 1.64/1.81 (~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[3228, 306, 759, 3222, 3221])).
% 1.64/1.81 tff(3927,plain,
% 1.64/1.81 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[3926, 3925])).
% 1.64/1.81 tff(3928,plain,
% 1.64/1.81 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[3207, 3927])).
% 1.64/1.81 tff(3929,plain,
% 1.64/1.81 (r(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[3928, 3924])).
% 1.64/1.81 tff(3930,plain,
% 1.64/1.81 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(3931,plain,
% 1.64/1.81 (((~r(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(elem!1)))))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(3932,plain,
% 1.64/1.81 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(z))))))))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[3931])).
% 1.64/1.81 tff(3933,plain,
% 1.64/1.81 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[3932, 3930])).
% 1.64/1.81 tff(3934,plain,
% 1.64/1.81 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(3935,plain,
% 1.64/1.81 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(z))))))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[3934, 3933])).
% 1.64/1.81 tff(3936,plain,
% 1.64/1.81 (~r(elem!1, s(s(s(elem!1))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[3935, 124, 3929, 3923])).
% 1.64/1.81 tff(3937,plain,
% 1.64/1.81 (b(elem!1, s(s(s(elem!1))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[3284, 3936, 1519])).
% 1.64/1.81 tff(3938,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(3939,plain,
% 1.64/1.81 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(3940,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[3939])).
% 1.64/1.81 tff(3941,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[3940, 3938])).
% 1.64/1.81 tff(3942,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(3943,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[3942, 3941])).
% 1.64/1.82 tff(3944,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[3943, 306, 759, 30, 3937, 3885, 3890])).
% 1.64/1.82 tff(3945,plain,((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(3946,plain,
% 1.64/1.82 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[3945, 3773, 30, 1285, 3845, 3811, 3837, 3119, 3759, 3820, 3122])).
% 1.64/1.82 tff(3947,plain,
% 1.64/1.82 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[1144, 3946, 3133])).
% 1.64/1.82 tff(3948,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(3949,plain,
% 1.64/1.82 (((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(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(s(z))))))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(3950,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(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(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z))))))))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[3949])).
% 1.64/1.82 tff(3951,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(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(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.82 inference(transitivity,[status(thm)],[3950, 3948])).
% 1.64/1.82 tff(3952,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(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(s(z)))))))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(3953,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z))))))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[3952, 3951])).
% 1.64/1.82 tff(3954,plain,
% 1.64/1.82 (~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[3953, 306, 30, 3759, 3812, 3947])).
% 1.64/1.82 tff(3955,plain,
% 1.64/1.82 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[3954, 3130])).
% 1.64/1.82 tff(3956,plain,
% 1.64/1.82 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[3207, 3955])).
% 1.64/1.82 tff(3957,plain,
% 1.64/1.82 (r(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[3956, 3128])).
% 1.64/1.82 tff(3958,plain,
% 1.64/1.82 (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[3716, 306, 30, 3759, 3947])).
% 1.64/1.82 tff(3959,plain,
% 1.64/1.82 ((s(s(z)) = s(s(s(s(s(s(z))))))) <=> (s(s(elem!1)) = s(s(s(s(s(s(z)))))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[3124])).
% 1.64/1.82 tff(3960,plain,
% 1.64/1.82 ((s(s(z)) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = s(s(elem!1)))),
% 1.64/1.82 inference(transitivity,[status(thm)],[3959, 3240])).
% 1.64/1.82 tff(3961,plain,
% 1.64/1.82 ((~(s(s(z)) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(s(s(s(s(z)))))) = s(s(elem!1))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[3960])).
% 1.64/1.82 tff(3962,plain,
% 1.64/1.82 (~(s(s(s(s(s(s(z)))))) = s(s(elem!1)))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[2826, 3961])).
% 1.64/1.82 tff(3963,plain,
% 1.64/1.82 (r(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[3247, 43, 3962, 3958])).
% 1.64/1.82 tff(3964,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[3262, 124, 3845, 3963, 3957])).
% 1.64/1.82 tff(3965,plain,(b(s(elem!1), s(z)) | (~b(s(s(elem!1)), elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (elem!1 = s(s(elem!1))) | (~r(s(z), z)) | b(elem!1, s(z)) | r(s(s(elem!1)), elem!1) | (s(elem!1) = elem!1) | b(s(z), elem!1) | r(elem!1, z) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(3966,plain,
% 1.64/1.82 (b(s(elem!1), s(z))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[3965, 92, 144, 187, 204, 5, 6, 181, 2715, 3062, 7])).
% 1.64/1.82 tff(3967,plain,
% 1.64/1.82 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[2974, 3097])).
% 1.64/1.82 tff(3968,assumption,(b(s(s(elem!1)), z)), introduced(assumption)).
% 1.64/1.82 tff(3969,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(3970,plain,
% 1.64/1.82 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(3971,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[3970])).
% 1.64/1.82 tff(3972,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))),
% 1.64/1.82 inference(transitivity,[status(thm)],[3971, 3969])).
% 1.64/1.82 tff(3973,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(3974,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[3973, 3972])).
% 1.64/1.82 tff(3975,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[3974, 306, 3105, 3104, 30, 3968])).
% 1.64/1.82 tff(3976,plain,((z = elem!1) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | r(elem!1, z) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(3977,plain,
% 1.64/1.82 (~b(s(s(elem!1)), z)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[3976, 2170, 3062, 7, 30])).
% 1.64/1.82 tff(3978,plain,
% 1.64/1.82 (r(s(s(elem!1)), z)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[476, 3977])).
% 1.64/1.82 tff(3979,plain,
% 1.64/1.82 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(3980,plain,
% 1.64/1.82 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(3981,plain,
% 1.64/1.82 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z)))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[3980, 3979])).
% 1.64/1.82 tff(3982,plain,
% 1.64/1.82 (~r(s(s(elem!1)), s(z))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[3981, 124, 3978, 204])).
% 1.64/1.82 tff(3983,assumption,(~r(s(s(elem!1)), s(z))), introduced(assumption)).
% 1.64/1.82 tff(3984,plain,
% 1.64/1.82 (((~![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)))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(3985,plain,
% 1.64/1.82 ((~![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)))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(3986,plain,
% 1.64/1.82 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[3985, 3984])).
% 1.64/1.82 tff(3987,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[3986, 43, 2649, 1417, 3983])).
% 1.64/1.82 tff(3988,plain,(r(s(s(elem!1)), s(z)) | b(s(s(elem!1)), s(z)) | (s(s(elem!1)) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(3989,plain,
% 1.64/1.82 (r(s(s(elem!1)), s(z)) | b(s(s(elem!1)), s(z))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[3988, 80])).
% 1.64/1.82 tff(3990,plain,
% 1.64/1.82 (b(s(s(elem!1)), s(z))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[3989, 3982])).
% 1.64/1.82 tff(3991,plain,
% 1.64/1.82 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(3992,plain,
% 1.64/1.82 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(3993,plain,
% 1.64/1.82 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[3992, 3991])).
% 1.64/1.82 tff(3994,plain,
% 1.64/1.82 (~r(s(z), s(s(elem!1)))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[3993, 124, 3978, 204])).
% 1.64/1.82 tff(3995,plain,
% 1.64/1.82 (((~![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))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(3996,plain,
% 1.64/1.82 ((~![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))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(3997,plain,
% 1.64/1.82 ((~![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)))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[3996, 3995])).
% 1.64/1.82 tff(3998,plain,
% 1.64/1.82 (b(s(z), s(s(elem!1)))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[3997, 43, 79, 3994])).
% 1.64/1.82 tff(3999,assumption,(b(s(z), s(s(elem!1)))), introduced(assumption)).
% 1.64/1.82 tff(4000,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(4001,plain,
% 1.64/1.82 (((~b(s(s(elem!1)), s(elem!1))) | (~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(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(4002,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z)))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[4001])).
% 1.64/1.82 tff(4003,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))))),
% 1.64/1.82 inference(transitivity,[status(thm)],[4002, 4000])).
% 1.64/1.82 tff(4004,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~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))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(4005,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z)))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[4004, 4003])).
% 1.64/1.82 tff(4006,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4005, 306, 1005, 3999, 24, 2647])).
% 1.64/1.82 tff(4007,plain,((~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(4008,plain,
% 1.64/1.82 (~b(s(s(elem!1)), s(elem!1))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4007, 3998, 2647, 3990])).
% 1.64/1.82 tff(4009,plain,
% 1.64/1.82 (r(s(s(elem!1)), s(elem!1))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[994, 4008, 392])).
% 1.64/1.82 tff(4010,plain,
% 1.64/1.82 (~r(s(elem!1), z)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[471, 4009, 3978])).
% 1.64/1.82 tff(4011,plain,
% 1.64/1.82 (b(s(elem!1), z)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[2380, 4010])).
% 1.64/1.82 tff(4012,assumption,(b(elem!1, z)), introduced(assumption)).
% 1.64/1.82 tff(4013,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(4014,plain,
% 1.64/1.82 (((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(4015,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1)))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[4014])).
% 1.64/1.82 tff(4016,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))))),
% 1.64/1.82 inference(transitivity,[status(thm)],[4015, 4013])).
% 1.64/1.82 tff(4017,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(4018,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1)))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[4017, 4016])).
% 1.64/1.82 tff(4019,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4018, 306, 838, 4012, 1199, 815])).
% 1.64/1.82 tff(4020,plain,((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(4021,plain,
% 1.64/1.82 (~b(elem!1, s(elem!1))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4020, 4011, 3104, 3105])).
% 1.64/1.82 tff(4022,plain,
% 1.64/1.82 (r(elem!1, s(elem!1))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[372, 4021, 365])).
% 1.64/1.82 tff(4023,plain,
% 1.64/1.82 (~r(elem!1, s(s(elem!1)))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[1238, 4022, 4009])).
% 1.64/1.82 tff(4024,plain,
% 1.64/1.82 (b(elem!1, s(s(elem!1)))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[516, 4023, 360])).
% 1.64/1.82 tff(4025,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(4026,plain,
% 1.64/1.82 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1))))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(4027,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1))))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[4026])).
% 1.64/1.82 tff(4028,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))))),
% 1.64/1.82 inference(transitivity,[status(thm)],[4027, 4025])).
% 1.64/1.82 tff(4029,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(4030,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[4029, 4028])).
% 1.64/1.82 tff(4031,plain,
% 1.64/1.82 (~b(z, s(s(elem!1)))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4030, 306, 3105, 3104, 30])).
% 1.64/1.82 tff(4032,plain,
% 1.64/1.82 (r(z, s(s(elem!1)))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[460, 4031])).
% 1.64/1.82 tff(4033,plain,
% 1.64/1.82 (~r(z, s(elem!1))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[799, 4009, 4032])).
% 1.64/1.82 tff(4034,plain,
% 1.64/1.82 (b(z, s(elem!1))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[275, 4033])).
% 1.64/1.82 tff(4035,plain,
% 1.64/1.82 (~b(s(elem!1), elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[2341, 4024, 3105, 30, 4034])).
% 1.64/1.82 tff(4036,plain,
% 1.64/1.82 (r(s(elem!1), elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[813, 4035, 193])).
% 1.64/1.82 tff(4037,plain,
% 1.64/1.82 ((s(z) = s(elem!1)) <=> (s(elem!1) = s(z))),
% 1.64/1.82 inference(commutativity,[status(thm)],[])).
% 1.64/1.82 tff(4038,plain,
% 1.64/1.82 ((s(elem!1) = s(z)) <=> (s(z) = s(elem!1))),
% 1.64/1.82 inference(symmetry,[status(thm)],[4037])).
% 1.64/1.82 tff(4039,plain,
% 1.64/1.82 ((~(s(elem!1) = s(z))) <=> (~(s(z) = s(elem!1)))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[4038])).
% 1.64/1.82 tff(4040,plain,
% 1.64/1.82 (~(s(z) = s(elem!1))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[3099, 4039])).
% 1.64/1.82 tff(4041,plain,
% 1.64/1.82 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(4042,plain,
% 1.64/1.83 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(4043,plain,
% 1.64/1.83 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1)))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[4042, 4041])).
% 1.64/1.83 tff(4044,plain,
% 1.64/1.83 (~r(s(z), s(elem!1))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4043, 124, 4036, 4])).
% 1.64/1.83 tff(4045,plain,
% 1.64/1.83 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(elem!1)) | b(s(z), s(elem!1)) | r(s(z), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(elem!1)) | b(s(z), s(elem!1)) | r(s(z), s(elem!1)))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(4046,plain,
% 1.64/1.83 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(elem!1)) | b(s(z), s(elem!1)) | r(s(z), s(elem!1)))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(4047,plain,
% 1.64/1.83 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(elem!1)) | b(s(z), s(elem!1)) | r(s(z), s(elem!1))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[4046, 4045])).
% 1.64/1.83 tff(4048,plain,
% 1.64/1.83 ((s(z) = s(elem!1)) | b(s(z), s(elem!1))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4047, 43, 4044])).
% 1.64/1.83 tff(4049,plain,
% 1.64/1.83 (b(s(z), s(elem!1))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4048, 4040])).
% 1.64/1.83 tff(4050,assumption,(b(s(z), s(elem!1))), introduced(assumption)).
% 1.64/1.83 tff(4051,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(4052,plain,
% 1.64/1.83 (((~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(4053,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[4052])).
% 1.64/1.83 tff(4054,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.64/1.83 inference(transitivity,[status(thm)],[4053, 4051])).
% 1.64/1.83 tff(4055,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(4056,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(elem!1)))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[4055, 4054])).
% 1.64/1.83 tff(4057,plain,
% 1.64/1.83 (~b(s(z), s(s(s(elem!1))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4056, 306, 838, 759, 1199, 4050])).
% 1.64/1.83 tff(4058,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(z, elem!1)))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(4059,plain,
% 1.64/1.83 (((~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(z, elem!1)))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(4060,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(z, elem!1))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[4059])).
% 1.64/1.83 tff(4061,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(z, elem!1)))),
% 1.64/1.83 inference(transitivity,[status(thm)],[4060, 4058])).
% 1.64/1.83 tff(4062,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(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))))))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(4063,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(z, elem!1))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[4062, 4061])).
% 1.64/1.83 tff(4064,plain,
% 1.64/1.83 (~b(z, s(s(s(elem!1))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4063, 306, 838, 759, 1199, 817])).
% 1.64/1.83 tff(4065,plain,
% 1.64/1.83 (r(z, s(s(s(elem!1))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[585, 4064])).
% 1.64/1.83 tff(4066,assumption,(r(s(z), s(s(s(elem!1))))), introduced(assumption)).
% 1.64/1.83 tff(4067,plain,
% 1.64/1.83 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(4068,plain,
% 1.64/1.83 (((~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(4069,plain,
% 1.64/1.83 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[4068])).
% 1.64/1.83 tff(4070,plain,
% 1.64/1.83 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 1.64/1.83 inference(transitivity,[status(thm)],[4069, 4067])).
% 1.64/1.83 tff(4071,plain,
% 1.64/1.83 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(4072,plain,
% 1.64/1.83 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[4071, 4070])).
% 1.64/1.83 tff(4073,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4072, 124, 564, 204, 4066])).
% 1.64/1.83 tff(4074,plain,((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(4075,plain,
% 1.64/1.83 (~r(s(z), s(s(s(elem!1))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4074, 4065, 204])).
% 1.64/1.83 tff(4076,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[3017, 43, 645, 4075, 4057])).
% 1.64/1.83 tff(4077,plain,((~b(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), z)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(4078,plain,
% 1.64/1.83 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4077, 3105, 204, 4011, 4049, 4034])).
% 1.64/1.83 tff(4079,plain,
% 1.64/1.83 (r(s(s(s(elem!1))), s(elem!1))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[664, 4078, 150])).
% 1.64/1.83 tff(4080,plain,
% 1.64/1.83 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(4081,plain,
% 1.64/1.83 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(4082,plain,
% 1.64/1.83 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1)))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[4081, 4080])).
% 1.64/1.83 tff(4083,plain,
% 1.64/1.83 ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1)))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4082, 124])).
% 1.64/1.83 tff(4084,plain,
% 1.64/1.83 (~r(elem!1, s(s(s(elem!1))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4083, 654, 255])).
% 1.64/1.83 tff(4085,plain,
% 1.64/1.83 (b(elem!1, s(s(s(elem!1))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[3284, 4084, 1642])).
% 1.64/1.83 tff(4086,plain,
% 1.64/1.83 (~b(s(s(s(elem!1))), elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1672, 4085, 741, 30])).
% 1.64/1.83 tff(4087,plain,
% 1.64/1.83 (r(s(s(s(elem!1))), elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1636, 4086, 1526])).
% 1.64/1.83 tff(4088,plain,
% 1.64/1.83 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(4089,plain,
% 1.64/1.83 (((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(4090,plain,
% 1.64/1.83 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[4089])).
% 1.64/1.83 tff(4091,plain,
% 1.64/1.83 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.64/1.83 inference(transitivity,[status(thm)],[4090, 4088])).
% 1.64/1.83 tff(4092,plain,
% 1.64/1.83 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(4093,plain,
% 1.64/1.83 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[4092, 4091])).
% 1.64/1.83 tff(4094,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4093, 124, 654, 255, 4087])).
% 1.64/1.83 tff(4095,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (s(s(s(elem!1))) = elem!1) | (~b(s(s(elem!1)), elem!1)) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(4096,plain,
% 1.64/1.83 (s(s(s(elem!1))) = elem!1),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4095, 4079, 4022, 30, 233, 4009])).
% 1.64/1.83 tff(4097,plain,
% 1.64/1.83 (elem!1 = s(s(s(elem!1)))),
% 1.64/1.83 inference(symmetry,[status(thm)],[2184])).
% 1.64/1.83 tff(4098,plain,
% 1.64/1.83 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.64/1.83 inference(transitivity,[status(thm)],[1430, 4097])).
% 1.64/1.83 tff(4099,plain,
% 1.64/1.83 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[4098])).
% 1.64/1.83 tff(4100,plain,
% 1.64/1.83 (s(s(z)) = s(s(elem!1))),
% 1.64/1.83 inference(transitivity,[status(thm)],[103, 4099, 139])).
% 1.64/1.83 tff(4101,plain,
% 1.64/1.83 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[4100])).
% 1.64/1.83 tff(4102,plain,
% 1.64/1.83 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 1.64/1.83 inference(symmetry,[status(thm)],[4101])).
% 1.64/1.83 tff(4103,plain,
% 1.64/1.83 (s(elem!1) = s(z)),
% 1.64/1.83 inference(transitivity,[status(thm)],[67, 4102, 546])).
% 1.64/1.83 tff(4104,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[2249, 4103])).
% 1.64/1.83 tff(4105,plain,((~(s(s(s(z))) = elem!1)) | (s(elem!1) = s(z)) | (~(s(s(s(elem!1))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(4106,plain,
% 1.64/1.83 (~(s(s(s(z))) = elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4105, 2184, 2249])).
% 1.64/1.83 tff(4107,plain,
% 1.64/1.83 (r(s(s(s(z))), elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1489, 4106, 1])).
% 1.64/1.83 tff(4108,plain,
% 1.64/1.83 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(4109,plain,
% 1.64/1.83 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1))))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(4110,plain,
% 1.64/1.83 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1)))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[4109, 4108])).
% 1.64/1.83 tff(4111,plain,
% 1.64/1.83 (~r(s(s(s(z))), s(elem!1))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4110, 124, 802, 4107])).
% 1.64/1.83 tff(4112,plain,
% 1.64/1.83 (~r(s(s(s(z))), s(z))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1481, 4107, 359])).
% 1.64/1.83 tff(4113,plain,
% 1.64/1.83 (b(s(s(s(z))), s(z))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[113, 4112])).
% 1.64/1.83 tff(4114,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(4115,plain,
% 1.64/1.83 (((~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(elem!1)))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(4116,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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)), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1)))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[4115])).
% 1.64/1.83 tff(4117,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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)), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))))),
% 1.64/1.83 inference(transitivity,[status(thm)],[4116, 4114])).
% 1.64/1.83 tff(4118,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(elem!1))))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(4119,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1)))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[4118, 4117])).
% 1.64/1.83 tff(4120,plain,
% 1.64/1.83 (~b(s(s(s(z))), s(elem!1))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4119, 306, 30, 4113, 3999, 2647])).
% 1.64/1.83 tff(4121,assumption,(s(s(s(z))) = s(elem!1)), introduced(assumption)).
% 1.64/1.83 tff(4122,plain,
% 1.64/1.83 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[4121])).
% 1.64/1.83 tff(4123,plain,
% 1.64/1.83 (s(s(z)) = s(s(s(elem!1)))),
% 1.64/1.83 inference(transitivity,[status(thm)],[103, 4122, 135, 4097])).
% 1.64/1.83 tff(4124,plain,
% 1.64/1.83 (inj_0(s(s(z))) = inj_0(s(s(s(elem!1))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[4123])).
% 1.64/1.83 tff(4125,plain,
% 1.64/1.83 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(z)))),
% 1.64/1.83 inference(symmetry,[status(thm)],[4124])).
% 1.64/1.83 tff(4126,plain,
% 1.64/1.83 (s(s(elem!1)) = s(z)),
% 1.64/1.83 inference(transitivity,[status(thm)],[140, 4125, 546])).
% 1.64/1.83 tff(4127,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[80, 4126])).
% 1.64/1.83 tff(4128,plain,((~(s(s(s(z))) = s(elem!1))) | (~(s(s(s(elem!1))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(4129,plain,
% 1.64/1.83 (~(s(s(s(z))) = s(elem!1))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4128, 2184])).
% 1.64/1.83 tff(4130,plain,
% 1.64/1.83 (((~![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)))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(4131,plain,
% 1.64/1.83 ((~![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)))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(4132,plain,
% 1.64/1.83 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(elem!1)) | b(s(s(s(z))), s(elem!1)) | r(s(s(s(z))), s(elem!1))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[4131, 4130])).
% 1.64/1.83 tff(4133,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4132, 43, 4129, 4120, 4111])).
% 1.64/1.83 tff(4134,plain,((~(s(s(s(elem!1))) = elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | b(s(s(s(z))), elem!1) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(4135,plain,
% 1.64/1.84 (b(s(s(s(z))), elem!1)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4134, 4096, 3998, 2647, 4036, 359, 30, 3099])).
% 1.64/1.84 tff(4136,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(4137,plain,
% 1.64/1.84 (((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z))) <=> ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(4138,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[4137])).
% 1.64/1.84 tff(4139,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 1.64/1.84 inference(transitivity,[status(thm)],[4138, 4136])).
% 1.64/1.84 tff(4140,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(4141,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[4140, 4139])).
% 1.64/1.84 tff(4142,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4141, 306, 838, 30, 1003, 1967, 1531])).
% 1.64/1.84 tff(4143,plain,((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(4144,plain,
% 1.64/1.84 (~b(s(s(s(z))), z)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4143, 4135, 30, 3105, 4024])).
% 1.64/1.84 tff(4145,plain,
% 1.64/1.84 (r(s(s(s(z))), z)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[2197, 4144])).
% 1.64/1.84 tff(4146,plain,
% 1.64/1.84 (~r(s(s(s(z))), s(z))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[211, 4145, 204])).
% 1.64/1.84 tff(4147,plain,
% 1.64/1.84 (b(s(s(s(z))), s(z))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[113, 4146])).
% 1.64/1.84 tff(4148,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(4149,plain,
% 1.64/1.84 (((~b(s(s(elem!1)), elem!1)) | (~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))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(4150,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[4149])).
% 1.64/1.84 tff(4151,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.64/1.84 inference(transitivity,[status(thm)],[4150, 4148])).
% 1.64/1.84 tff(4152,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~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)))))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(4153,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[4152, 4151])).
% 1.64/1.84 tff(4154,plain,
% 1.64/1.84 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4153, 306, 30, 4147, 3998, 3990])).
% 1.64/1.84 tff(4155,plain,
% 1.64/1.84 (r(s(s(s(z))), s(s(elem!1)))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[2986, 43, 4154, 3967])).
% 1.64/1.84 tff(4156,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[3000, 124, 3978, 4145, 4155])).
% 1.64/1.84 tff(4157,plain,((z = elem!1) | (~b(s(s(elem!1)), elem!1)) | (~r(s(z), z)) | (~b(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(z), elem!1)) | (s(elem!1) = elem!1) | (elem!1 = s(s(elem!1))) | r(elem!1, z) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(4158,plain,
% 1.64/1.84 (z = elem!1),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4157, 92, 204, 3966, 3098, 144, 3091, 181, 187, 3062, 7])).
% 1.64/1.84 tff(4159,plain,
% 1.64/1.84 (s(z) = s(elem!1)),
% 1.64/1.84 inference(monotonicity,[status(thm)],[4158])).
% 1.64/1.84 tff(4160,plain,
% 1.64/1.84 (b(s(elem!1), s(z)) <=> b(s(elem!1), s(elem!1))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[4159])).
% 1.64/1.84 tff(4161,plain,
% 1.64/1.84 (b(s(elem!1), s(elem!1)) <=> b(s(elem!1), s(z))),
% 1.64/1.84 inference(symmetry,[status(thm)],[4160])).
% 1.64/1.84 tff(4162,plain,
% 1.64/1.84 ((~b(s(elem!1), s(elem!1))) <=> (~b(s(elem!1), s(z)))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[4161])).
% 1.64/1.84 tff(4163,plain,
% 1.64/1.84 ((~![X: $i] : (~b(X, X))) | (~b(s(elem!1), s(elem!1)))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(4164,plain,
% 1.64/1.84 (~b(s(elem!1), s(elem!1))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4163, 1466])).
% 1.64/1.84 tff(4165,plain,
% 1.64/1.84 (~b(s(elem!1), s(z))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[4164, 4162])).
% 1.64/1.84 tff(4166,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[3966, 4165])).
% 1.64/1.84 tff(4167,plain,((s(s(elem!1)) = elem!1) | (~r(s(z), z)) | r(elem!1, z) | r(z, elem!1) | b(elem!1, s(z)) | r(s(s(elem!1)), elem!1) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(4168,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4167, 3083, 3073, 5, 3062, 7, 6, 3068])).
% 1.64/1.84 tff(4169,plain,(r(elem!1, z) | b(elem!1, s(z)) | r(z, elem!1) | r(s(s(elem!1)), elem!1) | (~b(s(z), s(s(s(z))))) | b(elem!1, s(s(s(z)))) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(4170,plain,
% 1.64/1.84 (r(elem!1, z)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4169, 3, 7, 6, 8, 5, 2])).
% 1.64/1.84 tff(4171,plain,
% 1.64/1.84 (~b(z, elem!1)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[2316, 4170, 3, 8, 5, 6, 2])).
% 1.64/1.84 tff(4172,plain,
% 1.64/1.84 (z = elem!1),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[835, 4171, 7])).
% 1.64/1.84 tff(4173,plain,
% 1.64/1.84 (r(elem!1, z) <=> r(elem!1, elem!1)),
% 1.64/1.84 inference(monotonicity,[status(thm)],[4172])).
% 1.64/1.84 tff(4174,plain,
% 1.64/1.84 (r(elem!1, elem!1) <=> r(elem!1, z)),
% 1.64/1.84 inference(symmetry,[status(thm)],[4173])).
% 1.64/1.84 tff(4175,plain,
% 1.64/1.84 ((~r(elem!1, elem!1)) <=> (~r(elem!1, z))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[4174])).
% 1.64/1.84 tff(4176,plain,
% 1.64/1.84 (^[X: $i] : refl((~r(X, X)) <=> (~r(X, X)))),
% 1.64/1.84 inference(bind,[status(th)],[])).
% 1.64/1.84 tff(4177,plain,
% 1.64/1.84 (![X: $i] : (~r(X, X)) <=> ![X: $i] : (~r(X, X))),
% 1.64/1.84 inference(quant_intro,[status(thm)],[4176])).
% 1.64/1.84 tff(4178,plain,
% 1.64/1.84 (![X: $i] : (~r(X, X)) <=> ![X: $i] : (~r(X, X))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(4179,axiom,(![X: $i] : (~r(X, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ri')).
% 1.64/1.84 tff(4180,plain,
% 1.64/1.84 (![X: $i] : (~r(X, X))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[4179, 4178])).
% 1.64/1.84 tff(4181,plain,(
% 1.64/1.84 ![X: $i] : (~r(X, X))),
% 1.64/1.84 inference(skolemize,[status(sab)],[4180])).
% 1.64/1.84 tff(4182,plain,
% 1.64/1.84 (![X: $i] : (~r(X, X))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[4181, 4177])).
% 1.64/1.84 tff(4183,plain,
% 1.64/1.84 ((~![X: $i] : (~r(X, X))) | (~r(elem!1, elem!1))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(4184,plain,
% 1.64/1.84 (~r(elem!1, elem!1)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4183, 4182])).
% 1.64/1.84 tff(4185,plain,
% 1.64/1.84 (~r(elem!1, z)),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[4184, 4175])).
% 1.64/1.84 tff(4186,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4170, 4185])).
% 1.64/1.84 tff(4187,plain,(b(elem!1, s(s(s(z)))) | r(z, elem!1) | (~b(s(z), s(s(s(z))))) | b(elem!1, s(z)) | r(s(s(elem!1)), elem!1) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(4188,plain,
% 1.64/1.84 (b(elem!1, s(s(s(z))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4187, 5, 8, 7, 6, 2])).
% 1.64/1.84 tff(4189,plain,
% 1.64/1.84 (~b(s(z), elem!1)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[2928, 4188, 3061, 8])).
% 1.64/1.84 tff(4190,plain,
% 1.64/1.84 (~r(s(z), z)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4167, 3068, 5, 2715, 7, 6, 3062])).
% 1.64/1.84 tff(4191,plain,
% 1.64/1.84 (~r(s(z), elem!1)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1524, 4190, 3064])).
% 1.64/1.84 tff(4192,plain,
% 1.64/1.84 ((s(z) = elem!1) | r(s(z), elem!1)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1500, 43, 2715])).
% 1.64/1.84 tff(4193,plain,
% 1.64/1.84 (s(z) = elem!1),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4192, 4191])).
% 1.64/1.84 tff(4194,plain,
% 1.64/1.84 (s(z) = z),
% 1.64/1.84 inference(transitivity,[status(thm)],[4193, 3063])).
% 1.64/1.84 tff(4195,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[216, 4194])).
% 1.64/1.84 tff(4196,plain,(r(elem!1, z) | b(s(z), elem!1) | b(elem!1, s(z)) | r(z, elem!1) | r(s(s(elem!1)), elem!1) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(4197,plain,
% 1.64/1.84 (r(elem!1, z)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4196, 4189, 5, 7, 6, 2])).
% 1.64/1.84 tff(4198,plain,
% 1.64/1.84 (~(s(s(s(z))) = elem!1)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1472, 1470])).
% 1.64/1.84 tff(4199,plain,
% 1.64/1.84 (~b(s(z), elem!1)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[2928, 1470, 2284, 8])).
% 1.64/1.84 tff(4200,plain,
% 1.64/1.84 (r(s(s(s(z))), elem!1)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1489, 1, 1483])).
% 1.64/1.84 tff(4201,plain,
% 1.64/1.84 (~r(s(s(s(z))), z)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[2561, 4200, 246])).
% 1.64/1.84 tff(4202,plain,
% 1.64/1.84 (b(s(s(s(z))), z)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[2197, 4201])).
% 1.64/1.84 tff(4203,plain,
% 1.64/1.84 ((~b(s(s(s(z))), elem!1)) <=> (~b(s(s(s(z))), s(z)))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[2232])).
% 1.64/1.84 tff(4204,plain,
% 1.64/1.84 (~b(s(s(s(z))), s(z))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[1, 4203])).
% 1.64/1.84 tff(4205,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[2284, 4204])).
% 1.64/1.84 tff(4206,plain,((~(s(z) = elem!1)) | (~b(s(s(s(z))), s(z))) | b(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(4207,plain,
% 1.64/1.84 (~(s(z) = elem!1)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4206, 1, 2284])).
% 1.64/1.84 tff(4208,plain,
% 1.64/1.84 (r(s(z), elem!1)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4192, 4207])).
% 1.64/1.84 tff(4209,plain,
% 1.64/1.84 (~r(s(z), z)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1049, 4208, 246])).
% 1.64/1.84 tff(4210,plain,
% 1.64/1.84 (b(s(z), z)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[221, 4209])).
% 1.64/1.84 tff(4211,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(z), z)))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(4212,plain,
% 1.64/1.84 (((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(z), z)))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(4213,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(z), z))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[4212])).
% 1.64/1.84 tff(4214,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(z), z)))),
% 1.64/1.84 inference(transitivity,[status(thm)],[4213, 4211])).
% 1.64/1.84 tff(4215,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(4216,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(z), z))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[4215, 4214])).
% 1.64/1.84 tff(4217,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4216, 306, 8, 1531, 247, 485])).
% 1.64/1.84 tff(4218,plain,((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(4219,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4218, 4210, 4202, 8, 485])).
% 1.64/1.84 tff(4220,plain,(b(s(s(s(z))), elem!1) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~r(elem!1, z)) | b(s(z), elem!1) | (s(s(s(z))) = elem!1) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(4221,plain,
% 1.64/1.84 (b(s(s(s(z))), elem!1)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4220, 2282, 8, 246, 4199, 4198, 2284])).
% 1.64/1.84 tff(4222,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(4223,plain,
% 1.64/1.84 (((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), z))) <=> ((~b(z, elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(4224,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), elem!1))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[4223])).
% 1.64/1.84 tff(4225,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.64/1.84 inference(transitivity,[status(thm)],[4224, 4222])).
% 1.64/1.84 tff(4226,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(4227,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), elem!1))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[4226, 4225])).
% 1.64/1.84 tff(4228,plain,
% 1.64/1.84 (~b(s(s(s(s(s(s(z)))))), z)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4227, 306, 838, 2284, 2812, 1470])).
% 1.64/1.84 tff(4229,assumption,(~r(s(s(s(s(s(s(z)))))), z)), introduced(assumption)).
% 1.64/1.84 tff(4230,assumption,(~b(s(s(s(s(s(s(z)))))), z)), introduced(assumption)).
% 1.64/1.84 tff(4231,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[856, 43, 554, 4230, 4229])).
% 1.64/1.84 tff(4232,plain,(r(s(s(s(s(s(s(z)))))), z) | b(s(s(s(s(s(s(z)))))), z)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(4233,plain,
% 1.64/1.84 (r(s(s(s(s(s(s(z)))))), z)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4232, 4228])).
% 1.64/1.84 tff(4234,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(4235,plain,
% 1.64/1.84 (((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(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(s(z))))))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(4236,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(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(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[4235])).
% 1.64/1.84 tff(4237,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(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(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.64/1.84 inference(transitivity,[status(thm)],[4236, 4234])).
% 1.64/1.84 tff(4238,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(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(s(z)))))))))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(4239,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[4238, 4237])).
% 1.64/1.84 tff(4240,plain,
% 1.64/1.84 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4239, 306, 2284, 1967, 2812, 1470])).
% 1.64/1.84 tff(4241,plain,
% 1.64/1.84 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[3207, 4240])).
% 1.64/1.84 tff(4242,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[3203, 4241, 4233, 2370])).
% 1.64/1.84 tff(4243,plain,((~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(4244,plain,
% 1.64/1.84 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4243, 4221, 2284, 1470, 838])).
% 1.64/1.84 tff(4245,plain,
% 1.64/1.84 (~b(s(s(s(z))), z)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[2228, 4221, 838, 1470])).
% 1.64/1.84 tff(4246,plain,
% 1.64/1.84 (r(s(s(s(z))), z)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[2197, 4245])).
% 1.64/1.84 tff(4247,assumption,(b(s(s(s(s(s(s(z)))))), s(z))), introduced(assumption)).
% 1.64/1.84 tff(4248,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(4249,plain,
% 1.64/1.84 (((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(4250,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z)))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[4249])).
% 1.64/1.85 tff(4251,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[4250, 4248])).
% 1.64/1.85 tff(4252,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(4253,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[4252, 4251])).
% 1.64/1.85 tff(4254,plain,
% 1.64/1.85 (~b(s(s(s(s(s(s(z)))))), z)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4253, 306, 2284, 8, 485, 4247])).
% 1.64/1.85 tff(4255,plain,
% 1.64/1.85 (r(s(s(s(s(s(s(z)))))), z)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4232, 4254])).
% 1.64/1.85 tff(4256,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(4257,plain,
% 1.64/1.85 (((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(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(s(z))))))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(4258,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(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(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[4257])).
% 1.64/1.85 tff(4259,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(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(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[4258, 4256])).
% 1.64/1.85 tff(4260,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(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(s(z)))))))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(4261,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[4260, 4259])).
% 1.64/1.85 tff(4262,plain,
% 1.64/1.85 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4261, 306, 2284, 8, 4247])).
% 1.64/1.85 tff(4263,plain,
% 1.64/1.85 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[3207, 4262])).
% 1.64/1.85 tff(4264,plain,
% 1.64/1.85 ($false),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[3203, 4263, 4255, 205])).
% 1.64/1.85 tff(4265,plain,((~b(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.85 tff(4266,plain,
% 1.64/1.85 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4265, 4246, 2284, 8, 2282])).
% 1.64/1.85 tff(4267,plain,
% 1.64/1.85 (r(s(s(s(s(s(s(z)))))), s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[651, 43, 2844, 4266])).
% 1.64/1.85 tff(4268,assumption,(r(s(s(s(s(s(s(z)))))), s(z))), introduced(assumption)).
% 1.64/1.85 tff(4269,assumption,(~b(s(s(s(s(s(s(z)))))), elem!1)), introduced(assumption)).
% 1.64/1.85 tff(4270,plain,
% 1.64/1.85 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[2974, 87])).
% 1.64/1.85 tff(4271,plain,
% 1.64/1.85 (~b(s(s(elem!1)), elem!1)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[3002, 4270, 838, 1470, 1967])).
% 1.64/1.85 tff(4272,plain,
% 1.64/1.85 (s(s(elem!1)) = elem!1),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[47, 4271, 6])).
% 1.64/1.85 tff(4273,assumption,(s(s(s(s(s(s(z)))))) = elem!1), introduced(assumption)).
% 1.64/1.85 tff(4274,plain,
% 1.64/1.85 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 1.64/1.85 inference(transitivity,[status(thm)],[4273, 1427])).
% 1.64/1.85 tff(4275,plain,
% 1.64/1.85 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(elem!1)))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[4274])).
% 1.64/1.85 tff(4276,plain,
% 1.64/1.85 (s(s(s(s(s(z))))) = s(elem!1)),
% 1.64/1.85 inference(transitivity,[status(thm)],[2823, 4275, 66])).
% 1.64/1.85 tff(4277,plain,
% 1.64/1.85 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(elem!1))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[4276])).
% 1.64/1.85 tff(4278,plain,
% 1.64/1.85 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.64/1.85 inference(transitivity,[status(thm)],[497, 4277, 135, 1427])).
% 1.64/1.85 tff(4279,plain,
% 1.64/1.85 (inj_0(s(s(s(s(z))))) = inj_0(s(s(elem!1)))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[4278])).
% 1.64/1.85 tff(4280,plain,
% 1.64/1.85 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(z)))))),
% 1.64/1.85 inference(symmetry,[status(thm)],[4279])).
% 1.64/1.85 tff(4281,plain,
% 1.64/1.85 (s(elem!1) = s(s(s(z)))),
% 1.64/1.85 inference(transitivity,[status(thm)],[67, 4280, 320])).
% 1.64/1.85 tff(4282,plain,
% 1.64/1.85 (~(s(elem!1) = s(s(s(z))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[2356, 1171])).
% 1.64/1.85 tff(4283,plain,
% 1.64/1.85 ($false),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4282, 4281])).
% 1.64/1.85 tff(4284,plain,((~(s(s(s(s(s(s(z)))))) = elem!1)) | (~(s(s(elem!1)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.85 tff(4285,plain,
% 1.64/1.85 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4284, 4272])).
% 1.64/1.85 tff(4286,plain,
% 1.64/1.85 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1144, 4285, 4269])).
% 1.64/1.85 tff(4287,plain,
% 1.64/1.85 (r(elem!1, s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[97, 87])).
% 1.64/1.85 tff(4288,plain,
% 1.64/1.85 ($false),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[2904, 124, 4287, 4286, 4268])).
% 1.64/1.85 tff(4289,plain,((elem!1 = s(z)) | (~r(s(s(s(s(s(s(z)))))), s(z))) | b(s(s(s(s(s(s(z)))))), elem!1) | r(s(s(elem!1)), elem!1) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.85 tff(4290,plain,
% 1.64/1.85 (elem!1 = s(z)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4289, 4267, 4244, 6, 838, 1470, 4221, 5])).
% 1.64/1.85 tff(4291,plain,
% 1.64/1.85 (s(elem!1) = s(s(z))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[4290])).
% 1.64/1.85 tff(4292,plain,
% 1.64/1.85 (r(s(elem!1), z) <=> r(s(s(z)), z)),
% 1.64/1.85 inference(monotonicity,[status(thm)],[4291])).
% 1.64/1.85 tff(4293,plain,
% 1.64/1.85 ((~r(s(elem!1), z)) <=> (~r(s(s(z)), z))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[4292])).
% 1.64/1.85 tff(4294,plain,
% 1.64/1.85 (b(elem!1, z) <=> b(s(z), z)),
% 1.64/1.85 inference(monotonicity,[status(thm)],[10])).
% 1.64/1.85 tff(4295,plain,
% 1.64/1.85 (b(s(z), z) <=> b(elem!1, z)),
% 1.64/1.85 inference(symmetry,[status(thm)],[4294])).
% 1.64/1.85 tff(4296,plain,
% 1.64/1.85 (b(elem!1, z)),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[247, 4295])).
% 1.64/1.85 tff(4297,plain,
% 1.64/1.85 ($false),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[2, 4296])).
% 1.64/1.85 tff(4298,plain,((~(elem!1 = s(z))) | b(elem!1, z) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.85 tff(4299,plain,
% 1.64/1.85 (~b(s(z), z)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4298, 4290, 2])).
% 1.64/1.85 tff(4300,plain,
% 1.64/1.85 (r(s(z), z)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[221, 4299])).
% 1.64/1.85 tff(4301,plain,
% 1.64/1.85 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(z))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[4290])).
% 1.64/1.85 tff(4302,plain,
% 1.64/1.85 (r(s(elem!1), s(z))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[802, 4301])).
% 1.64/1.85 tff(4303,plain,
% 1.64/1.85 (~r(s(elem!1), z)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[2634, 4302, 4300])).
% 1.64/1.85 tff(4304,plain,
% 1.64/1.85 (~r(s(s(z)), z)),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[4303, 4293])).
% 1.64/1.85 tff(4305,plain,
% 1.64/1.85 (r(s(elem!1), s(z)) <=> r(s(s(z)), s(z))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[4291])).
% 1.64/1.85 tff(4306,plain,
% 1.64/1.85 (r(s(s(z)), s(z))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[4302, 4305])).
% 1.64/1.85 tff(4307,plain,
% 1.64/1.85 ((s(s(s(s(s(s(z)))))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(s(s(z)))))))),
% 1.64/1.85 inference(commutativity,[status(thm)],[])).
% 1.64/1.85 tff(4308,plain,
% 1.64/1.85 ((s(s(z)) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = s(s(z)))),
% 1.64/1.85 inference(symmetry,[status(thm)],[4307])).
% 1.64/1.85 tff(4309,plain,
% 1.64/1.85 ((~(s(s(z)) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(s(s(s(s(z)))))) = s(s(z))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[4308])).
% 1.64/1.85 tff(4310,plain,
% 1.64/1.85 (~(s(s(s(s(s(s(z)))))) = s(s(z)))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[2826, 4309])).
% 1.64/1.85 tff(4311,plain,
% 1.64/1.85 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(4312,plain,
% 1.64/1.85 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(4313,plain,
% 1.64/1.85 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(z))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[4312, 4311])).
% 1.64/1.85 tff(4314,plain,
% 1.64/1.85 (~r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4313, 124, 2479, 4268])).
% 1.64/1.85 tff(4315,plain,
% 1.64/1.85 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(z))) | b(s(s(s(s(s(s(z)))))), s(s(z))) | r(s(s(s(s(s(s(z)))))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(z))) | b(s(s(s(s(s(s(z)))))), s(s(z))) | r(s(s(s(s(s(s(z)))))), s(s(z))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(4316,plain,
% 1.64/1.85 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(z))) | b(s(s(s(s(s(s(z)))))), s(s(z))) | r(s(s(s(s(s(s(z)))))), s(s(z))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(4317,plain,
% 1.64/1.85 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(z))) | b(s(s(s(s(s(s(z)))))), s(s(z))) | r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[4316, 4315])).
% 1.64/1.85 tff(4318,plain,
% 1.64/1.85 ((s(s(s(s(s(s(z)))))) = s(s(z))) | b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4317, 43, 4314])).
% 1.64/1.85 tff(4319,plain,
% 1.64/1.85 (b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4318, 4310])).
% 1.64/1.85 tff(4320,plain,
% 1.64/1.85 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(4321,plain,
% 1.64/1.85 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(4322,plain,
% 1.64/1.85 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z)))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[4321, 4320])).
% 1.64/1.85 tff(4323,plain,
% 1.64/1.85 ($false),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4322, 124, 204, 3194, 4268])).
% 1.64/1.85 tff(4324,plain,((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.85 tff(4325,plain,
% 1.64/1.85 (~r(s(s(s(s(s(s(z)))))), z)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4324, 4268, 204])).
% 1.64/1.85 tff(4326,plain,
% 1.64/1.85 (b(s(s(s(s(s(s(z)))))), z)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4232, 4325])).
% 1.64/1.85 tff(4327,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(4328,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(4329,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[4328, 4327])).
% 1.64/1.85 tff(4330,plain,
% 1.64/1.85 ($false),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4329, 306, 8, 2061, 4326, 485, 4319])).
% 1.64/1.85 tff(4331,plain,((~r(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(z, s(z))) | (~r(s(z), z)) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.85 tff(4332,plain,
% 1.64/1.85 (~b(s(s(z)), z)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4331, 4306, 8, 2282, 4267, 4300])).
% 1.64/1.85 tff(4333,plain,
% 1.64/1.85 (r(s(s(z)), z)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[2531, 4332])).
% 1.64/1.85 tff(4334,plain,
% 1.64/1.85 ($false),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4333, 4304])).
% 1.64/1.85 tff(4335,plain,((~b(z, elem!1)) | (~b(s(z), s(s(s(z))))) | (~r(s(elem!1), elem!1)) | b(elem!1, z) | r(s(s(elem!1)), elem!1) | (~b(elem!1, s(s(s(z))))) | b(elem!1, s(z)) | (~b(s(s(s(z))), s(z))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.85 tff(4336,plain,
% 1.64/1.85 (~b(z, elem!1)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4335, 2952, 8, 2, 6, 4188, 5, 3061, 4197])).
% 1.64/1.85 tff(4337,plain,
% 1.64/1.85 (z = elem!1),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[835, 4336, 7])).
% 1.64/1.85 tff(4338,plain,
% 1.64/1.85 (r(elem!1, z) <=> r(elem!1, elem!1)),
% 1.64/1.85 inference(monotonicity,[status(thm)],[4337])).
% 1.64/1.85 tff(4339,plain,
% 1.64/1.85 (r(elem!1, elem!1) <=> r(elem!1, z)),
% 1.64/1.85 inference(symmetry,[status(thm)],[4338])).
% 1.64/1.85 tff(4340,plain,
% 1.64/1.85 ((~r(elem!1, elem!1)) <=> (~r(elem!1, z))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[4339])).
% 1.64/1.85 tff(4341,plain,
% 1.64/1.85 (~r(elem!1, z)),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[4184, 4340])).
% 1.64/1.85 tff(4342,plain,
% 1.64/1.85 ($false),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4197, 4341])).
% 1.64/1.85 tff(4343,plain,(b(elem!1, s(z)) | r(z, elem!1) | (~b(s(z), s(s(s(z))))) | b(elem!1, z) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.85 tff(4344,plain,
% 1.64/1.85 (b(elem!1, s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4343, 8, 7, 2, 6])).
% 1.64/1.85 tff(4345,plain,
% 1.64/1.85 (b(elem!1, s(z)) <=> b(z, s(z))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[1620])).
% 1.64/1.85 tff(4346,assumption,(b(elem!1, s(z))), introduced(assumption)).
% 1.64/1.85 tff(4347,plain,
% 1.64/1.85 (b(z, s(z))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[4346, 4345])).
% 1.64/1.85 tff(4348,plain,
% 1.64/1.85 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(z)), s(z))),
% 1.64/1.85 inference(transitivity,[status(thm)],[3331, 3330])).
% 1.64/1.85 tff(4349,plain,
% 1.64/1.85 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(z))), s(z))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[1623, 1621])).
% 1.64/1.85 tff(4350,plain,
% 1.64/1.85 (r(s(s(s(z))), s(z)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 1.64/1.85 inference(symmetry,[status(thm)],[4349])).
% 1.64/1.85 tff(4351,plain,
% 1.64/1.85 (r(s(s(s(elem!1))), s(elem!1))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[206, 4350])).
% 1.64/1.85 tff(4352,plain,
% 1.64/1.85 (s(elem!1) = s(z)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[2251, 3332])).
% 1.64/1.85 tff(4353,plain,
% 1.64/1.85 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[2724, 4352])).
% 1.64/1.85 tff(4354,plain,
% 1.64/1.85 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[152, 4353])).
% 1.64/1.85 tff(4355,plain,
% 1.64/1.85 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(z))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[1622, 1623])).
% 1.64/1.85 tff(4356,plain,
% 1.64/1.85 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.64/1.85 inference(symmetry,[status(thm)],[4355])).
% 1.64/1.85 tff(4357,plain,
% 1.64/1.85 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(z)), s(s(s(z))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[1622])).
% 1.64/1.85 tff(4358,plain,
% 1.64/1.85 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[4357, 4356])).
% 1.64/1.85 tff(4359,plain,
% 1.64/1.85 ((~b(s(s(elem!1)), s(s(s(z))))) <=> (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[4358])).
% 1.64/1.85 tff(4360,plain,
% 1.64/1.85 (~(elem!1 = s(s(elem!1)))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1168, 4353])).
% 1.64/1.85 tff(4361,plain,
% 1.64/1.85 (~(s(s(elem!1)) = elem!1)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1174, 4360])).
% 1.64/1.85 tff(4362,plain,
% 1.64/1.85 (b(s(s(elem!1)), elem!1)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[47, 4361, 6])).
% 1.64/1.85 tff(4363,plain,
% 1.64/1.85 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1511, 3332])).
% 1.64/1.85 tff(4364,plain,
% 1.64/1.85 (~(elem!1 = s(s(s(elem!1))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1518, 4363])).
% 1.64/1.85 tff(4365,plain,
% 1.64/1.85 (~(s(s(s(elem!1))) = elem!1)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[2187, 4364])).
% 1.64/1.85 tff(4366,plain,
% 1.64/1.85 ((~b(s(s(elem!1)), s(z))) <=> (~b(s(s(z)), s(z)))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[3330])).
% 1.64/1.85 tff(4367,plain,
% 1.64/1.85 (r(s(elem!1), z) <=> r(s(z), z)),
% 1.64/1.85 inference(monotonicity,[status(thm)],[1621])).
% 1.64/1.85 tff(4368,plain,
% 1.64/1.85 (r(s(z), z) <=> r(s(elem!1), z)),
% 1.64/1.85 inference(symmetry,[status(thm)],[4367])).
% 1.64/1.85 tff(4369,plain,
% 1.64/1.85 ((~r(s(z), z)) <=> (~r(s(elem!1), z))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[4368])).
% 1.64/1.85 tff(4370,plain,
% 1.64/1.85 (~r(s(z), z)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[211, 205, 206])).
% 1.64/1.85 tff(4371,plain,
% 1.64/1.85 (~r(s(elem!1), z)),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[4370, 4369])).
% 1.64/1.85 tff(4372,plain,
% 1.64/1.85 (b(s(elem!1), z)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[2380, 4371])).
% 1.64/1.85 tff(4373,plain,
% 1.64/1.85 (b(s(z), elem!1)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[2718, 4372, 3332])).
% 1.64/1.85 tff(4374,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(4375,plain,
% 1.64/1.85 (((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(4376,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z)))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[4375])).
% 1.64/1.85 tff(4377,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[4376, 4374])).
% 1.64/1.85 tff(4378,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(4379,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z)))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[4378, 4377])).
% 1.64/1.85 tff(4380,plain,
% 1.64/1.85 ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z)))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4379, 306])).
% 1.64/1.85 tff(4381,plain,
% 1.64/1.85 (~b(s(s(elem!1)), s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4380, 4373, 4346, 30])).
% 1.64/1.85 tff(4382,plain,
% 1.64/1.85 (~b(s(s(z)), s(z))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[4381, 4366])).
% 1.64/1.85 tff(4383,plain,
% 1.64/1.85 (r(s(s(z)), s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[2474, 43, 4382, 2470])).
% 1.64/1.85 tff(4384,plain,
% 1.64/1.85 (r(s(s(s(s(elem!1)))), z) <=> r(s(s(s(s(z)))), z)),
% 1.64/1.85 inference(monotonicity,[status(thm)],[1704])).
% 1.64/1.85 tff(4385,plain,
% 1.64/1.85 (r(s(s(s(s(elem!1)))), elem!1) <=> r(s(s(s(s(elem!1)))), z)),
% 1.64/1.85 inference(monotonicity,[status(thm)],[1620])).
% 1.64/1.85 tff(4386,plain,
% 1.64/1.85 (r(s(s(s(s(elem!1)))), elem!1) <=> r(s(s(s(s(z)))), z)),
% 1.64/1.85 inference(transitivity,[status(thm)],[4385, 4384])).
% 1.64/1.85 tff(4387,plain,
% 1.64/1.85 ((z = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = z)),
% 1.64/1.85 inference(commutativity,[status(thm)],[])).
% 1.64/1.85 tff(4388,plain,
% 1.64/1.85 ((elem!1 = s(s(s(s(elem!1))))) <=> (z = s(s(s(s(elem!1)))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[1620])).
% 1.64/1.85 tff(4389,plain,
% 1.64/1.85 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = z)),
% 1.64/1.85 inference(transitivity,[status(thm)],[4388, 4387])).
% 1.64/1.85 tff(4390,plain,
% 1.64/1.85 ((s(s(s(s(elem!1)))) = z) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.64/1.85 inference(symmetry,[status(thm)],[4389])).
% 1.64/1.85 tff(4391,plain,
% 1.64/1.85 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.64/1.85 inference(transitivity,[status(thm)],[4390, 1543])).
% 1.64/1.85 tff(4392,plain,
% 1.64/1.85 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[4391])).
% 1.64/1.85 tff(4393,plain,
% 1.64/1.85 (~(s(s(s(s(elem!1)))) = elem!1)),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[1549, 4392])).
% 1.64/1.85 tff(4394,plain,
% 1.64/1.85 (r(s(elem!1), elem!1) <=> r(s(elem!1), z)),
% 1.64/1.85 inference(monotonicity,[status(thm)],[1620])).
% 1.64/1.86 tff(4395,plain,
% 1.64/1.86 (r(s(elem!1), z) <=> r(s(elem!1), elem!1)),
% 1.64/1.86 inference(symmetry,[status(thm)],[4394])).
% 1.64/1.86 tff(4396,plain,
% 1.64/1.86 (r(s(z), z) <=> r(s(elem!1), elem!1)),
% 1.64/1.86 inference(transitivity,[status(thm)],[4368, 4395])).
% 1.64/1.86 tff(4397,plain,
% 1.64/1.86 ((~r(s(z), z)) <=> (~r(s(elem!1), elem!1))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[4396])).
% 1.64/1.86 tff(4398,plain,
% 1.64/1.86 (~r(s(elem!1), elem!1)),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[4370, 4397])).
% 1.64/1.86 tff(4399,plain,
% 1.64/1.86 (b(s(elem!1), elem!1)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[813, 4398, 3333])).
% 1.64/1.86 tff(4400,plain,
% 1.64/1.86 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1284, 4353])).
% 1.64/1.86 tff(4401,plain,
% 1.64/1.86 (b(elem!1, s(elem!1)) <=> b(z, s(elem!1))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[1620])).
% 1.64/1.86 tff(4402,plain,
% 1.64/1.86 (b(z, s(elem!1)) <=> b(elem!1, s(elem!1))),
% 1.64/1.86 inference(symmetry,[status(thm)],[4401])).
% 1.64/1.86 tff(4403,plain,
% 1.64/1.86 (b(elem!1, s(z)) <=> b(elem!1, s(elem!1))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[1503])).
% 1.64/1.86 tff(4404,plain,
% 1.64/1.86 (b(elem!1, s(elem!1)) <=> b(elem!1, s(z))),
% 1.64/1.86 inference(symmetry,[status(thm)],[4403])).
% 1.64/1.86 tff(4405,plain,
% 1.64/1.86 ((~b(elem!1, s(elem!1))) <=> (~b(elem!1, s(z)))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[4404])).
% 1.64/1.86 tff(4406,plain,
% 1.64/1.86 (b(z, s(elem!1)) <=> b(elem!1, s(elem!1))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[1502])).
% 1.64/1.86 tff(4407,plain,
% 1.64/1.86 ((~b(z, s(elem!1))) <=> (~b(elem!1, s(elem!1)))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[4406])).
% 1.64/1.86 tff(4408,assumption,(~b(z, s(elem!1))), introduced(assumption)).
% 1.64/1.86 tff(4409,plain,
% 1.64/1.86 (~b(elem!1, s(elem!1))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[4408, 4407])).
% 1.64/1.86 tff(4410,plain,
% 1.64/1.86 (~b(elem!1, s(z))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[4409, 4405])).
% 1.64/1.86 tff(4411,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4346, 4410])).
% 1.64/1.86 tff(4412,plain,((~(z = elem!1)) | (~b(elem!1, s(z))) | b(z, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(4413,plain,
% 1.64/1.86 (b(z, s(elem!1))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4412, 3332, 4346])).
% 1.64/1.86 tff(4414,plain,
% 1.64/1.86 (b(elem!1, s(elem!1))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[4413, 4402])).
% 1.64/1.86 tff(4415,plain,
% 1.64/1.86 (r(s(elem!1), s(s(elem!1))) <=> r(s(z), s(s(elem!1)))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[1621])).
% 1.64/1.86 tff(4416,plain,
% 1.64/1.86 (r(s(z), s(s(elem!1))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.64/1.86 inference(symmetry,[status(thm)],[4415])).
% 1.64/1.86 tff(4417,plain,
% 1.64/1.86 (r(s(z), s(s(z))) <=> r(s(z), s(s(elem!1)))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[1780])).
% 1.64/1.86 tff(4418,plain,
% 1.64/1.86 (r(s(z), s(s(z))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.64/1.86 inference(transitivity,[status(thm)],[4417, 4416])).
% 1.64/1.86 tff(4419,plain,
% 1.64/1.86 (b(s(z), z)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[221, 4370])).
% 1.64/1.86 tff(4420,plain,
% 1.64/1.86 (b(s(s(elem!1)), z)),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[30, 3503])).
% 1.64/1.86 tff(4421,plain,
% 1.64/1.86 (b(s(s(z)), z)),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[4420, 3502])).
% 1.64/1.86 tff(4422,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(4423,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(4424,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z))))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[4423, 4422])).
% 1.64/1.86 tff(4425,plain,
% 1.64/1.86 (~b(s(z), s(s(z)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4424, 306, 8, 4421, 4419, 4347])).
% 1.64/1.86 tff(4426,plain,
% 1.64/1.86 ((s(z) = s(s(z))) <=> (s(s(z)) = s(z))),
% 1.64/1.86 inference(commutativity,[status(thm)],[])).
% 1.64/1.86 tff(4427,plain,
% 1.64/1.86 ((s(s(z)) = s(z)) <=> (s(z) = s(s(z)))),
% 1.64/1.86 inference(symmetry,[status(thm)],[4426])).
% 1.64/1.86 tff(4428,plain,
% 1.64/1.86 ((~(s(s(z)) = s(z))) <=> (~(s(z) = s(s(z))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[4427])).
% 1.64/1.86 tff(4429,plain,
% 1.64/1.86 (~(s(z) = s(s(z)))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[2470, 4428])).
% 1.64/1.86 tff(4430,plain,
% 1.64/1.86 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(4431,plain,
% 1.64/1.86 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(4432,plain,
% 1.64/1.86 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z)))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[4431, 4430])).
% 1.64/1.86 tff(4433,plain,
% 1.64/1.86 ((s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4432, 43])).
% 1.64/1.86 tff(4434,plain,
% 1.64/1.86 (b(s(z), s(s(z))) | r(s(z), s(s(z)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4433, 4429])).
% 1.64/1.86 tff(4435,plain,
% 1.64/1.86 (r(s(z), s(s(z)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4434, 4425])).
% 1.64/1.86 tff(4436,plain,
% 1.64/1.86 (r(s(elem!1), s(s(elem!1)))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[4435, 4418])).
% 1.64/1.86 tff(4437,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(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))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(4438,plain,
% 1.64/1.86 (((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~b(s(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))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(4439,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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)))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[4438])).
% 1.64/1.86 tff(4440,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[4439, 4437])).
% 1.64/1.86 tff(4441,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(4442,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(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)))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[4441, 4440])).
% 1.64/1.86 tff(4443,plain,
% 1.64/1.86 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4442, 306, 816, 2076, 815])).
% 1.64/1.86 tff(4444,plain,
% 1.64/1.86 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1767, 43, 1516, 4443])).
% 1.64/1.86 tff(4445,assumption,(r(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 1.64/1.86 tff(4446,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(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)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(4447,plain,
% 1.64/1.86 (((~b(s(elem!1), elem!1)) | (~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))))) <=> ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(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)))), s(s(elem!1)))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(4448,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[4447])).
% 1.64/1.86 tff(4449,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[4448, 4446])).
% 1.64/1.86 tff(4450,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~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)))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(4451,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(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)))), s(s(elem!1))))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[4450, 4449])).
% 1.64/1.86 tff(4452,plain,
% 1.64/1.86 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4451, 306, 30, 816, 2076, 815])).
% 1.64/1.86 tff(4453,plain,
% 1.64/1.86 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1302, 4452, 1717])).
% 1.64/1.86 tff(4454,plain,
% 1.64/1.86 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), 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))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(4455,plain,
% 1.64/1.86 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(4456,plain,
% 1.64/1.86 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[4455, 4454])).
% 1.64/1.86 tff(4457,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4456, 124, 4453, 4445, 4444])).
% 1.64/1.86 tff(4458,plain,((~b(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (s(s(s(s(elem!1)))) = s(elem!1)) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(4459,plain,
% 1.64/1.86 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4458, 4436, 4414, 30, 4363, 4400, 4399])).
% 1.64/1.86 tff(4460,plain,
% 1.64/1.86 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1736, 4459, 4393])).
% 1.64/1.86 tff(4461,plain,
% 1.64/1.86 (r(s(s(s(s(z)))), z)),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[4460, 4386])).
% 1.64/1.86 tff(4462,plain,
% 1.64/1.86 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(4463,plain,
% 1.64/1.86 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(4464,plain,
% 1.64/1.86 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[4463, 4462])).
% 1.64/1.86 tff(4465,plain,
% 1.64/1.86 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4464, 124, 205, 4461])).
% 1.64/1.86 tff(4466,plain,
% 1.64/1.86 (s(s(s(z))) = s(s(s(s(z))))),
% 1.64/1.86 inference(symmetry,[status(thm)],[1702])).
% 1.64/1.86 tff(4467,plain,
% 1.64/1.86 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(z)))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[4466])).
% 1.64/1.86 tff(4468,plain,
% 1.64/1.86 (s(s(z)) = s(s(s(z)))),
% 1.64/1.86 inference(transitivity,[status(thm)],[103, 4467, 320])).
% 1.64/1.86 tff(4469,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[2508, 4468])).
% 1.64/1.86 tff(4470,plain,(~(s(s(s(s(z)))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(4471,plain,
% 1.64/1.86 (r(s(s(s(s(z)))), s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[712, 4470])).
% 1.64/1.86 tff(4472,plain,
% 1.64/1.86 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4471, 4465])).
% 1.64/1.86 tff(4473,plain,
% 1.64/1.86 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(4474,plain,
% 1.64/1.86 (((~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(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(4475,plain,
% 1.64/1.86 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[4474])).
% 1.64/1.86 tff(4476,plain,
% 1.64/1.86 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 1.64/1.86 inference(transitivity,[status(thm)],[4475, 4473])).
% 1.64/1.86 tff(4477,plain,
% 1.64/1.86 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(4478,plain,
% 1.64/1.86 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[4477, 4476])).
% 1.64/1.86 tff(4479,plain,
% 1.64/1.86 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4478, 124, 205, 4461])).
% 1.64/1.86 tff(4480,plain,
% 1.64/1.86 (~(s(s(s(z))) = s(s(s(s(z)))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1971, 4470])).
% 1.64/1.86 tff(4481,plain,
% 1.64/1.86 (r(s(s(s(z))), s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z)))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[2027, 4480])).
% 1.64/1.86 tff(4482,plain,
% 1.64/1.86 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4481, 4479])).
% 1.64/1.86 tff(4483,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(4484,plain,
% 1.64/1.86 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(4485,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[4484])).
% 1.64/1.86 tff(4486,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[4485, 4483])).
% 1.64/1.86 tff(4487,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(4488,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[4487, 4486])).
% 1.64/1.87 tff(4489,plain,
% 1.64/1.87 (~b(s(s(s(s(z)))), s(z))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4488, 306, 8, 4482, 4472])).
% 1.64/1.87 tff(4490,plain,
% 1.64/1.87 (b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[327, 43, 324])).
% 1.64/1.87 tff(4491,plain,
% 1.64/1.87 (r(s(s(s(s(z)))), s(z))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4490, 4489])).
% 1.64/1.87 tff(4492,plain,
% 1.64/1.87 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), s(elem!1))),
% 1.64/1.87 inference(symmetry,[status(thm)],[3331])).
% 1.64/1.87 tff(4493,plain,
% 1.64/1.87 ((~b(s(s(elem!1)), s(z))) <=> (~b(s(s(elem!1)), s(elem!1)))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[4492])).
% 1.64/1.87 tff(4494,plain,
% 1.64/1.87 (~b(s(s(elem!1)), s(elem!1))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[4381, 4493])).
% 1.64/1.87 tff(4495,plain,
% 1.64/1.87 (r(s(s(elem!1)), s(elem!1))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[994, 4494, 3334])).
% 1.64/1.87 tff(4496,plain,
% 1.64/1.87 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[886, 4495, 4351])).
% 1.64/1.87 tff(4497,plain,
% 1.64/1.87 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[891, 4496, 4354])).
% 1.64/1.87 tff(4498,plain,
% 1.64/1.87 (b(s(s(z)), s(s(s(z))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[4497, 4355])).
% 1.64/1.87 tff(4499,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(4500,plain,
% 1.64/1.87 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(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(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(4501,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), 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(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[4500])).
% 1.64/1.87 tff(4502,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), 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(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.64/1.87 inference(transitivity,[status(thm)],[4501, 4499])).
% 1.64/1.87 tff(4503,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), 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(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(4504,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[4503, 4502])).
% 1.64/1.87 tff(4505,plain,
% 1.64/1.87 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4504, 306, 4482, 4498, 4472])).
% 1.64/1.87 tff(4506,plain,
% 1.64/1.87 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z))))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(4507,plain,
% 1.64/1.87 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z))))))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(4508,plain,
% 1.64/1.87 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z)))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[4507, 4506])).
% 1.64/1.87 tff(4509,plain,
% 1.64/1.87 ((s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4508, 43])).
% 1.64/1.87 tff(4510,plain,
% 1.64/1.87 (b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4509, 1612])).
% 1.64/1.87 tff(4511,plain,
% 1.64/1.87 (r(s(s(z)), s(s(s(s(z)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4510, 4505])).
% 1.64/1.87 tff(4512,plain,
% 1.64/1.87 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(4513,plain,
% 1.64/1.87 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(4514,plain,
% 1.64/1.87 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[4513, 4512])).
% 1.64/1.87 tff(4515,plain,
% 1.64/1.87 ($false),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4514, 124, 4511, 4491, 4383])).
% 1.64/1.87 tff(4516,plain,((~r(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~(elem!1 = z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.87 tff(4517,plain,
% 1.64/1.87 (~r(s(s(s(z))), z)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4516, 1620, 8, 4362, 4346, 206])).
% 1.64/1.87 tff(4518,plain,
% 1.64/1.87 (~r(s(s(s(elem!1))), elem!1)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1631, 4517, 1620])).
% 1.64/1.87 tff(4519,plain,
% 1.64/1.87 (b(s(s(s(elem!1))), elem!1)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1636, 4518, 4365])).
% 1.64/1.87 tff(4520,plain,
% 1.64/1.87 (b(s(s(s(z))), elem!1)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[2215, 4519, 3332])).
% 1.64/1.87 tff(4521,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(4522,plain,
% 1.64/1.87 (((~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(z)))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(4523,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[4522])).
% 1.64/1.87 tff(4524,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.64/1.87 inference(transitivity,[status(thm)],[4523, 4521])).
% 1.64/1.87 tff(4525,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(4526,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[4525, 4524])).
% 1.64/1.87 tff(4527,plain,
% 1.64/1.87 ((~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4526, 306])).
% 1.64/1.87 tff(4528,plain,
% 1.64/1.87 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4527, 4520, 8, 4346, 4362])).
% 1.64/1.87 tff(4529,plain,
% 1.64/1.87 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[4528, 4359])).
% 1.64/1.87 tff(4530,plain,
% 1.64/1.87 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[891, 4529, 4354])).
% 1.64/1.87 tff(4531,plain,
% 1.64/1.87 (~r(s(s(elem!1)), s(elem!1))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[886, 4530, 4351])).
% 1.64/1.87 tff(4532,plain,
% 1.64/1.87 (b(s(s(elem!1)), s(elem!1))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[994, 4531, 3334])).
% 1.64/1.87 tff(4533,plain,
% 1.64/1.87 (b(s(s(z)), s(z))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[4532, 4348])).
% 1.64/1.87 tff(4534,plain,
% 1.64/1.87 (b(s(s(s(z))), z)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[2197, 4517])).
% 1.64/1.87 tff(4535,plain,
% 1.64/1.87 (b(s(s(elem!1)), z)),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[4362, 3503])).
% 1.64/1.87 tff(4536,plain,
% 1.64/1.87 (b(s(s(z)), z)),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[4535, 3502])).
% 1.64/1.87 tff(4537,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(4538,plain,
% 1.64/1.87 (((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(4539,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[4538])).
% 1.64/1.87 tff(4540,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 1.64/1.87 inference(transitivity,[status(thm)],[4539, 4537])).
% 1.64/1.87 tff(4541,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(4542,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[4541, 4540])).
% 1.64/1.87 tff(4543,plain,
% 1.64/1.87 ($false),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4542, 306, 8, 4536, 4534, 4533, 4347])).
% 1.64/1.87 tff(4544,plain,((~(elem!1 = z)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.87 tff(4545,plain,
% 1.64/1.87 (~(elem!1 = z)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4544, 114, 4344, 8, 6])).
% 1.64/1.87 tff(4546,plain,
% 1.64/1.87 (r(elem!1, z)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[174, 4545, 2])).
% 1.64/1.87 tff(4547,plain,
% 1.64/1.87 (b(s(s(s(z))), s(z)) <=> b(elem!1, s(z))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[1430])).
% 1.64/1.87 tff(4548,plain,
% 1.64/1.87 (b(elem!1, s(z)) <=> b(s(s(s(z))), s(z))),
% 1.64/1.87 inference(symmetry,[status(thm)],[4547])).
% 1.64/1.87 tff(4549,plain,
% 1.64/1.87 (b(s(s(s(z))), s(z))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[4346, 4548])).
% 1.64/1.87 tff(4550,plain,
% 1.64/1.87 ($false),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[9, 4549])).
% 1.64/1.87 tff(4551,plain,((~(s(s(s(z))) = elem!1)) | b(s(s(s(z))), s(z)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.87 tff(4552,plain,
% 1.64/1.87 (~(s(s(s(z))) = elem!1)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4551, 9, 4344])).
% 1.64/1.87 tff(4553,plain,
% 1.64/1.87 (s(s(s(z))) = elem!1),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[231, 1414])).
% 1.64/1.87 tff(4554,plain,
% 1.64/1.87 ($false),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1483, 4553])).
% 1.64/1.87 tff(4555,plain,((~(elem!1 = s(s(s(z))))) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.87 tff(4556,plain,
% 1.64/1.87 (~(elem!1 = s(s(s(z))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4555, 4552])).
% 1.64/1.87 tff(4557,plain,
% 1.64/1.87 (r(elem!1, s(s(s(z))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[2304, 4556, 3])).
% 1.64/1.87 tff(4558,plain,
% 1.64/1.87 (~r(s(s(s(z))), z)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[2312, 4557, 4546])).
% 1.64/1.87 tff(4559,plain,
% 1.64/1.87 (b(s(s(s(z))), z)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[2197, 4558])).
% 1.64/1.87 tff(4560,plain,
% 1.64/1.87 (~r(z, s(s(s(z))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[3392, 4557, 4546])).
% 1.64/1.87 tff(4561,plain,
% 1.64/1.87 (b(z, s(s(s(z))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[2415, 43, 4560, 2405])).
% 1.64/1.87 tff(4562,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z)))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(4563,plain,
% 1.64/1.87 (((~b(s(s(s(z))), z)) | (~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), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z)))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(4564,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[4563])).
% 1.64/1.87 tff(4565,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z)))),
% 1.64/1.87 inference(transitivity,[status(thm)],[4564, 4562])).
% 1.64/1.87 tff(4566,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(4567,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[4566, 4565])).
% 1.64/1.87 tff(4568,plain,
% 1.64/1.87 ($false),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4567, 306, 8, 1531, 859, 247])).
% 1.64/1.87 tff(4569,plain,((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.87 tff(4570,plain,
% 1.64/1.87 (~b(s(z), z)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4569, 4561, 8, 4559])).
% 1.64/1.87 tff(4571,plain,
% 1.64/1.87 (r(s(z), z)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[221, 4570])).
% 1.64/1.87 tff(4572,plain,
% 1.64/1.87 (~r(s(z), elem!1)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1049, 4571, 4546])).
% 1.64/1.87 tff(4573,plain,
% 1.64/1.87 (b(s(z), elem!1)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1500, 43, 4572, 90])).
% 1.64/1.87 tff(4574,assumption,(s(s(s(s(s(s(z)))))) = s(s(s(z)))), introduced(assumption)).
% 1.64/1.87 tff(4575,plain,
% 1.64/1.87 (s(s(s(z))) = s(s(s(s(s(s(z))))))),
% 1.64/1.87 inference(symmetry,[status(thm)],[4574])).
% 1.64/1.87 tff(4576,plain,
% 1.64/1.87 ($false),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[556, 4575])).
% 1.64/1.87 tff(4577,plain,(~(s(s(s(s(s(s(z)))))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.87 tff(4578,plain,
% 1.64/1.87 (~(z = elem!1)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1618, 4545])).
% 1.64/1.87 tff(4579,plain,
% 1.64/1.87 (b(z, elem!1)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[835, 4578, 7])).
% 1.64/1.87 tff(4580,plain,
% 1.64/1.87 (~b(s(z), z)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4569, 859, 8, 1531])).
% 1.64/1.87 tff(4581,plain,
% 1.64/1.87 (r(s(z), z)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[221, 4580])).
% 1.64/1.87 tff(4582,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(4583,plain,
% 1.64/1.87 (((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z))) <=> ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(4584,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[4583])).
% 1.64/1.88 tff(4585,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[4584, 4582])).
% 1.64/1.88 tff(4586,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(4587,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[4586, 4585])).
% 1.64/1.88 tff(4588,plain,
% 1.64/1.88 (~b(s(s(s(s(s(s(z)))))), z)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4587, 306, 838, 1531, 859, 1330])).
% 1.64/1.88 tff(4589,plain,
% 1.64/1.88 (r(s(s(s(s(s(s(z)))))), z)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4232, 4588])).
% 1.64/1.88 tff(4590,plain,
% 1.64/1.88 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4324, 4589, 4581])).
% 1.64/1.88 tff(4591,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(4592,plain,
% 1.64/1.88 (((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(4593,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[4592])).
% 1.64/1.88 tff(4594,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[4593, 4591])).
% 1.64/1.88 tff(4595,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(4596,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[4595, 4594])).
% 1.64/1.88 tff(4597,plain,
% 1.64/1.88 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4596, 306, 838, 8, 1531, 1330])).
% 1.64/1.88 tff(4598,plain,
% 1.64/1.88 ($false),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[651, 43, 2844, 4597, 4590])).
% 1.64/1.88 tff(4599,plain,((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.88 tff(4600,plain,
% 1.64/1.88 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4599, 4579, 4559, 4561, 8])).
% 1.64/1.88 tff(4601,plain,
% 1.64/1.88 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(s(z)))) | b(s(s(s(s(s(s(z)))))), s(s(s(z)))) | r(s(s(s(s(s(s(z)))))), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(s(z)))) | b(s(s(s(s(s(s(z)))))), s(s(s(z)))) | r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(4602,plain,
% 1.64/1.88 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(s(z)))) | b(s(s(s(s(s(s(z)))))), s(s(s(z)))) | r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(4603,plain,
% 1.64/1.88 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(s(z)))) | b(s(s(s(s(s(s(z)))))), s(s(s(z)))) | r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[4602, 4601])).
% 1.64/1.88 tff(4604,plain,
% 1.64/1.88 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4603, 43, 4600, 4577])).
% 1.64/1.88 tff(4605,plain,
% 1.64/1.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(4606,plain,
% 1.64/1.88 (((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), elem!1))) <=> ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(4607,plain,
% 1.64/1.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), elem!1))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[4606])).
% 1.64/1.88 tff(4608,plain,
% 1.64/1.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.64/1.88 inference(transitivity,[status(thm)],[4607, 4605])).
% 1.64/1.88 tff(4609,plain,
% 1.64/1.88 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(4610,plain,
% 1.64/1.88 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), elem!1))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[4609, 4608])).
% 1.64/1.88 tff(4611,plain,
% 1.64/1.88 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4610, 124, 4557, 4604])).
% 1.64/1.88 tff(4612,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(4613,plain,
% 1.64/1.88 (((~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), z))) <=> ((~b(s(z), s(s(s(z))))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(4614,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), elem!1))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[4613])).
% 1.64/1.88 tff(4615,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.64/1.88 inference(transitivity,[status(thm)],[4614, 4612])).
% 1.64/1.88 tff(4616,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(4617,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), elem!1))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[4616, 4615])).
% 1.64/1.88 tff(4618,plain,
% 1.64/1.88 (~b(s(s(s(s(s(s(z)))))), z)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4617, 306, 838, 8, 4346, 2812])).
% 1.64/1.88 tff(4619,plain,
% 1.64/1.88 (r(s(s(s(s(s(s(z)))))), z)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4232, 4618])).
% 1.64/1.88 tff(4620,plain,
% 1.64/1.88 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4324, 4619, 204])).
% 1.64/1.88 tff(4621,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(4622,plain,
% 1.64/1.88 (((~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(4623,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[4622])).
% 1.64/1.88 tff(4624,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.64/1.88 inference(transitivity,[status(thm)],[4623, 4621])).
% 1.64/1.88 tff(4625,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(4626,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[4625, 4624])).
% 1.64/1.88 tff(4627,plain,
% 1.64/1.88 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4626, 306, 8, 2831, 4346, 2812])).
% 1.64/1.88 tff(4628,plain,
% 1.64/1.88 ($false),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[651, 43, 2844, 4627, 4620])).
% 1.64/1.88 tff(4629,plain,((~b(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.88 tff(4630,plain,
% 1.64/1.88 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4629, 4571, 8, 4573, 4344, 4579])).
% 1.64/1.88 tff(4631,plain,
% 1.64/1.88 (s(s(s(s(s(s(z)))))) = elem!1),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1144, 4630, 4611])).
% 1.64/1.88 tff(4632,plain,
% 1.64/1.88 (~(s(s(elem!1)) = elem!1)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4284, 4631])).
% 1.64/1.88 tff(4633,plain,
% 1.64/1.88 (b(s(s(elem!1)), elem!1)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[47, 4632, 6])).
% 1.64/1.88 tff(4634,plain,
% 1.64/1.88 (~b(s(s(elem!1)), s(z))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4380, 4633, 4344, 4573])).
% 1.64/1.88 tff(4635,plain,
% 1.64/1.88 (r(s(s(elem!1)), s(z))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[3989, 4634])).
% 1.64/1.88 tff(4636,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(4637,plain,
% 1.64/1.88 (((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(4638,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(z, s(s(s(z)))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[4637])).
% 1.64/1.88 tff(4639,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[4638, 4636])).
% 1.64/1.88 tff(4640,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(4641,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(z, s(s(s(z)))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[4640, 4639])).
% 1.64/1.88 tff(4642,plain,
% 1.64/1.88 (~b(z, s(z))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4641, 306, 4579, 8, 4559, 4561])).
% 1.64/1.88 tff(4643,plain,
% 1.64/1.88 (r(z, s(z))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[2263, 4642])).
% 1.64/1.88 tff(4644,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(4645,plain,
% 1.64/1.88 (((~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z))) <=> ((~b(s(z), s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(4646,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z)))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[4645])).
% 1.64/1.88 tff(4647,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))))),
% 1.64/1.89 inference(transitivity,[status(thm)],[4646, 4644])).
% 1.64/1.89 tff(4648,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(4649,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z)))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[4648, 4647])).
% 1.64/1.89 tff(4650,plain,
% 1.64/1.89 (~b(s(s(elem!1)), z)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4649, 306, 4579, 4633, 8, 4344])).
% 1.64/1.89 tff(4651,plain,
% 1.64/1.89 (r(s(s(elem!1)), z)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[476, 4650])).
% 1.64/1.89 tff(4652,plain,
% 1.64/1.89 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(4653,plain,
% 1.64/1.89 (((~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z))) <=> ((~r(s(s(elem!1)), z)) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(4654,plain,
% 1.64/1.89 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z)))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[4653])).
% 1.64/1.89 tff(4655,plain,
% 1.64/1.89 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))))),
% 1.64/1.89 inference(transitivity,[status(thm)],[4654, 4652])).
% 1.64/1.89 tff(4656,plain,
% 1.64/1.89 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(4657,plain,
% 1.64/1.89 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z)))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[4656, 4655])).
% 1.64/1.89 tff(4658,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4657, 124, 4651, 4643, 4635])).
% 1.64/1.89 tff(4659,plain,(b(s(s(s(z))), s(z)) | (~b(s(z), s(s(s(z))))) | r(s(s(elem!1)), elem!1) | b(elem!1, s(s(s(z)))) | r(z, elem!1) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(4660,plain,
% 1.64/1.89 (b(s(s(s(z))), s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4659, 3, 6, 8, 7, 2])).
% 1.64/1.89 tff(4661,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(4662,plain,
% 1.64/1.89 (((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(4663,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(elem!1, s(z))) | (~b(s(s(s(z))), elem!1))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[4662])).
% 1.64/1.89 tff(4664,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.64/1.89 inference(transitivity,[status(thm)],[4663, 4661])).
% 1.64/1.89 tff(4665,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(4666,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[4665, 4664])).
% 1.64/1.89 tff(4667,plain,
% 1.64/1.89 (~b(s(s(s(z))), elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4666, 306, 4660, 8, 4344])).
% 1.64/1.89 tff(4668,plain,
% 1.64/1.89 (s(elem!1) = s(z)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[2251, 1502])).
% 1.64/1.89 tff(4669,plain,
% 1.64/1.89 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[2724, 4668])).
% 1.64/1.89 tff(4670,plain,
% 1.64/1.89 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[152, 4669])).
% 1.64/1.89 tff(4671,plain,
% 1.64/1.89 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[159, 4670])).
% 1.64/1.89 tff(4672,plain,
% 1.64/1.89 ((~b(elem!1, s(s(s(z))))) <=> (~b(z, s(s(s(elem!1)))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[1582])).
% 1.64/1.89 tff(4673,plain,
% 1.64/1.89 (~b(z, s(s(s(elem!1))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[3, 4672])).
% 1.64/1.89 tff(4674,plain,
% 1.64/1.89 (r(z, s(s(s(elem!1))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[585, 4673])).
% 1.64/1.89 tff(4675,plain,
% 1.64/1.89 (~(s(elem!1) = elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[2698, 1502])).
% 1.64/1.89 tff(4676,plain,
% 1.64/1.89 (b(z, s(elem!1))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4412, 1502, 4346])).
% 1.64/1.89 tff(4677,plain,
% 1.64/1.89 (b(elem!1, s(elem!1))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[4676, 4406])).
% 1.64/1.89 tff(4678,plain,
% 1.64/1.89 (~b(s(s(s(z))), elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4666, 306, 2284, 8, 4346])).
% 1.64/1.89 tff(4679,plain,
% 1.64/1.89 (~b(s(s(s(elem!1))), elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[2215, 1502, 4678])).
% 1.64/1.89 tff(4680,plain,
% 1.64/1.89 (r(s(s(s(elem!1))), elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1636, 3171, 4679])).
% 1.64/1.89 tff(4681,plain,
% 1.64/1.89 (~(elem!1 = s(s(elem!1)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1168, 4669])).
% 1.64/1.89 tff(4682,plain,
% 1.64/1.89 (~(s(s(elem!1)) = elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1174, 4681])).
% 1.64/1.89 tff(4683,plain,
% 1.64/1.89 (b(s(s(elem!1)), elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[47, 4682, 6])).
% 1.64/1.89 tff(4684,plain,
% 1.64/1.89 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1284, 4669])).
% 1.64/1.89 tff(4685,plain,
% 1.64/1.89 (~(s(s(elem!1)) = s(elem!1))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[195, 4675])).
% 1.64/1.89 tff(4686,assumption,(s(elem!1) = s(s(elem!1))), introduced(assumption)).
% 1.64/1.89 tff(4687,plain,
% 1.64/1.89 (s(s(elem!1)) = s(elem!1)),
% 1.64/1.89 inference(symmetry,[status(thm)],[4686])).
% 1.64/1.89 tff(4688,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[403, 4687])).
% 1.64/1.89 tff(4689,plain,((~(s(elem!1) = s(s(elem!1)))) | (s(s(elem!1)) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(4690,plain,
% 1.64/1.89 (~(s(elem!1) = s(s(elem!1)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4689, 4685])).
% 1.64/1.89 tff(4691,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(4692,plain,
% 1.64/1.89 (((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(4693,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1)))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[4692])).
% 1.64/1.89 tff(4694,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))))),
% 1.64/1.89 inference(transitivity,[status(thm)],[4693, 4691])).
% 1.64/1.89 tff(4695,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(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)))))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(4696,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1)))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[4695, 4694])).
% 1.64/1.89 tff(4697,plain,
% 1.64/1.89 (~b(s(elem!1), s(s(elem!1)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4696, 306, 30, 816, 815])).
% 1.64/1.89 tff(4698,plain,
% 1.64/1.89 (r(s(elem!1), s(s(elem!1)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1684, 43, 4697, 4690])).
% 1.64/1.89 tff(4699,plain,
% 1.64/1.89 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4458, 4698, 815, 30, 1512, 4684, 816])).
% 1.64/1.89 tff(4700,plain,
% 1.64/1.89 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1736, 4699, 1550])).
% 1.64/1.89 tff(4701,plain,
% 1.64/1.89 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(z))), s(elem!1))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[1726])).
% 1.64/1.89 tff(4702,plain,
% 1.64/1.89 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.64/1.89 inference(symmetry,[status(thm)],[4701])).
% 1.64/1.89 tff(4703,plain,
% 1.64/1.89 (b(s(s(s(z))), s(z)) <=> b(s(s(s(z))), s(elem!1))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[1503])).
% 1.64/1.89 tff(4704,plain,
% 1.64/1.89 (b(s(s(s(z))), s(elem!1))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[2284, 4703])).
% 1.64/1.89 tff(4705,plain,
% 1.64/1.89 (b(s(s(s(elem!1))), s(elem!1))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[4704, 4702])).
% 1.64/1.89 tff(4706,plain,
% 1.64/1.89 (b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1))))) <=> b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[1898])).
% 1.64/1.89 tff(4707,plain,
% 1.64/1.89 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))),
% 1.64/1.89 inference(symmetry,[status(thm)],[4706])).
% 1.64/1.89 tff(4708,plain,
% 1.64/1.89 ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = s(s(s(s(z)))))),
% 1.64/1.89 inference(commutativity,[status(thm)],[])).
% 1.64/1.89 tff(4709,plain,
% 1.64/1.89 ((s(s(s(s(elem!1)))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(z)))) = s(s(s(s(s(s(z)))))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[1898])).
% 1.64/1.89 tff(4710,plain,
% 1.64/1.89 ((s(s(s(s(elem!1)))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = s(s(s(s(z)))))),
% 1.64/1.89 inference(transitivity,[status(thm)],[4709, 4708])).
% 1.64/1.89 tff(4711,plain,
% 1.64/1.89 ((~(s(s(s(s(elem!1)))) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(s(s(s(s(z)))))) = s(s(s(s(z))))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[4710])).
% 1.64/1.89 tff(4712,plain,
% 1.64/1.89 (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1719, 4684])).
% 1.64/1.89 tff(4713,plain,
% 1.64/1.89 (~(s(s(s(s(elem!1)))) = s(s(s(s(s(s(z)))))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[3709, 4712, 1502])).
% 1.64/1.89 tff(4714,plain,
% 1.64/1.89 (~(s(s(s(s(s(s(z)))))) = s(s(s(s(z)))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[4713, 4711])).
% 1.64/1.89 tff(4715,plain,
% 1.64/1.89 (r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1))))) <=> r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[1898])).
% 1.64/1.89 tff(4716,plain,
% 1.64/1.89 ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) <=> (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[4715])).
% 1.64/1.89 tff(4717,plain,
% 1.64/1.89 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(4718,plain,
% 1.64/1.89 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(4719,plain,
% 1.64/1.89 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1))))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[4718, 4717])).
% 1.64/1.89 tff(4720,plain,
% 1.64/1.89 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4719, 124, 1289, 2858])).
% 1.64/1.89 tff(4721,plain,
% 1.64/1.89 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[4720, 4716])).
% 1.64/1.89 tff(4722,plain,
% 1.64/1.89 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(4723,plain,
% 1.64/1.89 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(4724,plain,
% 1.64/1.89 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[4723, 4722])).
% 1.64/1.89 tff(4725,plain,
% 1.64/1.89 ((s(s(s(s(s(s(z)))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4724, 43])).
% 1.64/1.89 tff(4726,plain,
% 1.64/1.89 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4725, 4721, 4714])).
% 1.64/1.89 tff(4727,plain,
% 1.64/1.89 (b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[4726, 4707])).
% 1.64/1.89 tff(4728,plain,
% 1.64/1.89 (b(s(s(s(s(elem!1)))), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.64/1.89 inference(symmetry,[status(thm)],[1727])).
% 1.64/1.89 tff(4729,plain,
% 1.64/1.89 (r(s(s(s(z))), z)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1631, 1627, 1619])).
% 1.64/1.89 tff(4730,plain,
% 1.64/1.89 (r(s(s(s(s(z)))), z) <=> r(s(s(s(s(z)))), elem!1)),
% 1.64/1.89 inference(monotonicity,[status(thm)],[1502])).
% 1.64/1.89 tff(4731,plain,
% 1.64/1.89 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), z)),
% 1.64/1.89 inference(symmetry,[status(thm)],[4730])).
% 1.64/1.89 tff(4732,plain,
% 1.64/1.89 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 1.64/1.89 inference(monotonicity,[status(thm)],[1508])).
% 1.64/1.89 tff(4733,plain,
% 1.64/1.89 (r(s(s(s(s(elem!1)))), elem!1) <=> r(s(s(s(s(z)))), elem!1)),
% 1.64/1.89 inference(symmetry,[status(thm)],[4732])).
% 1.64/1.89 tff(4734,plain,
% 1.64/1.89 (r(s(s(s(s(elem!1)))), elem!1) <=> r(s(s(s(s(z)))), z)),
% 1.64/1.89 inference(transitivity,[status(thm)],[4733, 4731])).
% 1.64/1.89 tff(4735,plain,
% 1.64/1.89 (r(s(s(s(s(z)))), z)),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[1289, 4734])).
% 1.64/1.89 tff(4736,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4464, 124, 205, 1033, 397])).
% 1.64/1.89 tff(4737,plain,((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(4738,plain,
% 1.64/1.89 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4737, 4735, 4729])).
% 1.64/1.89 tff(4739,plain,
% 1.64/1.89 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4471, 4738])).
% 1.64/1.89 tff(4740,plain,
% 1.64/1.89 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[4739, 1724])).
% 1.64/1.89 tff(4741,plain,
% 1.64/1.89 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[4740, 4728])).
% 1.64/1.89 tff(4742,plain,
% 1.64/1.89 ((~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) <=> (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[2869])).
% 1.64/1.89 tff(4743,plain,
% 1.64/1.89 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(4744,plain,
% 1.64/1.89 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(4745,plain,
% 1.64/1.89 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[4744, 4743])).
% 1.64/1.89 tff(4746,plain,
% 1.64/1.89 (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4745, 124, 1627, 2858])).
% 1.64/1.89 tff(4747,plain,
% 1.64/1.89 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[4746, 4742])).
% 1.64/1.89 tff(4748,plain,
% 1.64/1.89 (b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[2880, 4747, 1502])).
% 1.64/1.89 tff(4749,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(4750,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(4751,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1))))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[4750, 4749])).
% 1.64/1.89 tff(4752,plain,
% 1.64/1.89 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4751, 306, 759, 816, 4748, 4741])).
% 1.64/1.89 tff(4753,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4752, 4727])).
% 1.64/1.89 tff(4754,plain,((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~(z = elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(4755,plain,
% 1.64/1.89 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4754, 816, 4705, 1502, 4700, 1627])).
% 1.64/1.89 tff(4756,plain,
% 1.64/1.89 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1144, 4755, 3170])).
% 1.64/1.89 tff(4757,plain,
% 1.64/1.89 (r(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[1726, 1898])).
% 1.64/1.89 tff(4758,plain,
% 1.64/1.89 ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) <=> (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[4757])).
% 1.64/1.89 tff(4759,plain,
% 1.64/1.89 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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)))))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(4760,plain,
% 1.64/1.89 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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)))))))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(4761,plain,
% 1.64/1.89 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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))))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[4760, 4759])).
% 1.64/1.89 tff(4762,plain,
% 1.64/1.89 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4761, 124, 1627, 4700])).
% 1.64/1.89 tff(4763,plain,
% 1.64/1.89 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[4762, 4758])).
% 1.64/1.89 tff(4764,plain,
% 1.64/1.89 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4481, 4763])).
% 1.64/1.89 tff(4765,plain,
% 1.64/1.89 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[4764, 2088])).
% 1.64/1.89 tff(4766,plain,
% 1.64/1.89 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[1506, 1508])).
% 1.64/1.89 tff(4767,plain,
% 1.64/1.89 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[1506, 1508])).
% 1.64/1.89 tff(4768,plain,
% 1.64/1.89 (r(s(s(elem!1)), s(s(s(s(elem!1))))) <=> r(s(s(z)), s(s(s(s(z)))))),
% 1.64/1.89 inference(symmetry,[status(thm)],[4767])).
% 1.64/1.89 tff(4769,plain,
% 1.64/1.89 ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) <=> (~r(s(s(z)), s(s(s(s(z))))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[4768])).
% 1.64/1.89 tff(4770,plain,
% 1.64/1.89 (r(s(s(s(s(z)))), z)),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[4700, 4734])).
% 1.64/1.89 tff(4771,plain,
% 1.64/1.89 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4737, 4770, 4729])).
% 1.64/1.89 tff(4772,plain,
% 1.64/1.89 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4471, 4771])).
% 1.64/1.89 tff(4773,plain,
% 1.64/1.89 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[4772, 1724])).
% 1.64/1.89 tff(4774,plain,
% 1.64/1.89 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[4773, 4728])).
% 1.64/1.90 tff(4775,plain,
% 1.64/1.90 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(z))))),
% 1.64/1.90 inference(monotonicity,[status(thm)],[1726])).
% 1.64/1.90 tff(4776,plain,
% 1.64/1.90 (b(s(elem!1), s(s(s(z)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 1.64/1.90 inference(symmetry,[status(thm)],[4775])).
% 1.64/1.90 tff(4777,plain,
% 1.64/1.90 (b(s(z), s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 1.64/1.90 inference(monotonicity,[status(thm)],[1503])).
% 1.64/1.90 tff(4778,plain,
% 1.64/1.90 (b(s(elem!1), s(s(s(z))))),
% 1.64/1.90 inference(modus_ponens,[status(thm)],[8, 4777])).
% 1.64/1.90 tff(4779,plain,
% 1.64/1.90 (b(s(elem!1), s(s(s(elem!1))))),
% 1.64/1.90 inference(modus_ponens,[status(thm)],[4778, 4776])).
% 1.64/1.90 tff(4780,plain,
% 1.64/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.64/1.90 inference(rewrite,[status(thm)],[])).
% 1.64/1.90 tff(4781,plain,
% 1.64/1.90 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.64/1.90 inference(rewrite,[status(thm)],[])).
% 1.64/1.90 tff(4782,plain,
% 1.64/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1)))))))),
% 1.64/1.90 inference(monotonicity,[status(thm)],[4781])).
% 1.64/1.90 tff(4783,plain,
% 1.64/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.64/1.90 inference(transitivity,[status(thm)],[4782, 4780])).
% 1.64/1.90 tff(4784,plain,
% 1.64/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(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))))),
% 1.64/1.90 inference(quant_inst,[status(thm)],[])).
% 1.64/1.90 tff(4785,plain,
% 1.64/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1)))))),
% 1.64/1.90 inference(modus_ponens,[status(thm)],[4784, 4783])).
% 1.64/1.90 tff(4786,plain,
% 1.64/1.90 ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.64/1.90 inference(unit_resolution,[status(thm)],[4785, 306, 4705, 816, 4779])).
% 1.64/1.90 tff(4787,plain,
% 1.64/1.90 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4786, 4774])).
% 1.74/1.90 tff(4788,plain,
% 1.74/1.90 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1767, 43, 1512, 4787])).
% 1.74/1.90 tff(4789,plain,
% 1.74/1.90 (~b(s(s(elem!1)), s(elem!1))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[2776, 816, 8, 2284, 4668, 564, 30])).
% 1.74/1.90 tff(4790,plain,
% 1.74/1.90 (r(s(s(elem!1)), s(elem!1))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[994, 4789, 4685])).
% 1.74/1.90 tff(4791,plain,
% 1.74/1.90 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(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))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(4792,plain,
% 1.74/1.90 (((~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(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(4793,plain,
% 1.74/1.90 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(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)))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[4792])).
% 1.74/1.90 tff(4794,plain,
% 1.74/1.90 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(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))))),
% 1.74/1.90 inference(transitivity,[status(thm)],[4793, 4791])).
% 1.74/1.90 tff(4795,plain,
% 1.74/1.90 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(4796,plain,
% 1.74/1.90 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[4795, 4794])).
% 1.74/1.90 tff(4797,plain,
% 1.74/1.90 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4796, 124, 4790, 4788])).
% 1.74/1.90 tff(4798,plain,
% 1.74/1.90 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[4797, 4769])).
% 1.74/1.90 tff(4799,plain,
% 1.74/1.90 (b(s(s(z)), s(s(s(s(z)))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4510, 4798])).
% 1.74/1.90 tff(4800,plain,
% 1.74/1.90 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[4799, 4766])).
% 1.74/1.90 tff(4801,plain,
% 1.74/1.90 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(4802,plain,
% 1.74/1.90 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(4803,plain,
% 1.74/1.90 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[4802, 4801])).
% 1.74/1.90 tff(4804,plain,
% 1.74/1.90 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4803, 124, 4790, 4788])).
% 1.74/1.90 tff(4805,plain,
% 1.74/1.90 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1302, 4804, 4684])).
% 1.74/1.90 tff(4806,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(4807,plain,
% 1.74/1.90 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(4808,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), 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(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[4807])).
% 1.74/1.90 tff(4809,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), 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(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.74/1.90 inference(transitivity,[status(thm)],[4808, 4806])).
% 1.74/1.90 tff(4810,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), 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(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(4811,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[4810, 4809])).
% 1.74/1.90 tff(4812,plain,
% 1.74/1.90 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4811, 306, 30, 4805, 4800, 4765])).
% 1.74/1.90 tff(4813,plain,
% 1.74/1.90 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[610, 4812, 4671])).
% 1.74/1.90 tff(4814,plain,
% 1.74/1.90 (~r(z, s(s(elem!1)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[950, 4813, 564])).
% 1.74/1.90 tff(4815,plain,
% 1.74/1.90 (b(z, s(s(elem!1)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[460, 4814])).
% 1.74/1.90 tff(4816,plain,
% 1.74/1.90 (b(elem!1, s(s(elem!1)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[2757, 4815, 1502])).
% 1.74/1.90 tff(4817,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(4818,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(4819,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1)))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[4818, 4817])).
% 1.74/1.90 tff(4820,plain,
% 1.74/1.90 (~b(s(s(s(s(s(s(z)))))), s(elem!1))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4819, 306, 30, 4816, 816, 4756])).
% 1.74/1.90 tff(4821,plain,
% 1.74/1.90 (r(s(s(s(s(s(s(z)))))), s(elem!1))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[3220, 43, 3217, 4820])).
% 1.74/1.90 tff(4822,plain,
% 1.74/1.90 (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[3716, 306, 30, 4816, 4756])).
% 1.74/1.90 tff(4823,plain,
% 1.74/1.90 (r(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[3247, 43, 3244, 4822])).
% 1.74/1.90 tff(4824,plain,
% 1.74/1.90 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(4825,plain,
% 1.74/1.90 (((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1)))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(4826,plain,
% 1.74/1.90 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1))))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[4825])).
% 1.74/1.90 tff(4827,plain,
% 1.74/1.90 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))))),
% 1.74/1.90 inference(transitivity,[status(thm)],[4826, 4824])).
% 1.74/1.90 tff(4828,plain,
% 1.74/1.90 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(4829,plain,
% 1.74/1.90 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[4828, 4827])).
% 1.74/1.90 tff(4830,plain,
% 1.74/1.90 ($false),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4829, 124, 4698, 4823, 4821])).
% 1.74/1.90 tff(4831,plain,((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~(z = elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.90 tff(4832,plain,
% 1.74/1.90 (~b(s(elem!1), elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4831, 4683, 1502, 4680, 4674, 4677, 8, 2284])).
% 1.74/1.90 tff(4833,plain,
% 1.74/1.90 (r(s(elem!1), elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[813, 4832, 4675])).
% 1.74/1.90 tff(4834,plain,
% 1.74/1.90 (r(s(elem!1), elem!1) <=> r(s(z), elem!1)),
% 1.74/1.90 inference(symmetry,[status(thm)],[1551])).
% 1.74/1.90 tff(4835,plain,
% 1.74/1.90 (r(s(z), elem!1)),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[4833, 4834])).
% 1.74/1.90 tff(4836,plain,
% 1.74/1.90 (~b(elem!1, s(s(elem!1)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[3810, 4835, 1502, 4705, 4683, 4678, 4669, 4833])).
% 1.74/1.90 tff(4837,plain,
% 1.74/1.90 (~b(z, s(s(elem!1)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[2757, 4836, 1502])).
% 1.74/1.90 tff(4838,plain,
% 1.74/1.90 (r(z, s(s(elem!1)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[460, 4837])).
% 1.74/1.90 tff(4839,plain,
% 1.74/1.90 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[950, 4838, 4674])).
% 1.74/1.90 tff(4840,plain,
% 1.74/1.90 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[610, 4839, 4671])).
% 1.74/1.90 tff(4841,plain,
% 1.74/1.90 (r(elem!1, s(s(elem!1)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[516, 4836, 4681])).
% 1.74/1.90 tff(4842,plain,
% 1.74/1.90 (r(s(s(s(z))), z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1631, 4680, 1619])).
% 1.74/1.90 tff(4843,plain,
% 1.74/1.90 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[3230, 4833, 4705, 1502, 4779, 4842])).
% 1.74/1.90 tff(4844,plain,
% 1.74/1.90 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1144, 4843, 3170])).
% 1.74/1.90 tff(4845,plain,
% 1.74/1.90 (r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z))))))) <=> r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[1898])).
% 1.74/1.90 tff(4846,plain,
% 1.74/1.90 (r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) <=> r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))),
% 1.74/1.90 inference(symmetry,[status(thm)],[4845])).
% 1.74/1.90 tff(4847,plain,
% 1.74/1.90 ((s(s(s(s(s(s(z)))))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(s(s(s(z)))))))),
% 1.74/1.90 inference(symmetry,[status(thm)],[4708])).
% 1.74/1.90 tff(4848,plain,
% 1.74/1.90 ((s(s(s(s(elem!1)))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(z)))) = s(s(s(s(s(s(z)))))))),
% 1.74/1.90 inference(transitivity,[status(thm)],[4710, 4847])).
% 1.74/1.90 tff(4849,plain,
% 1.74/1.90 ((~(s(s(s(s(elem!1)))) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(s(s(z)))) = s(s(s(s(s(s(z))))))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[4848])).
% 1.74/1.90 tff(4850,plain,
% 1.74/1.90 (~(s(s(s(s(z)))) = s(s(s(s(s(s(z)))))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[4713, 4849])).
% 1.74/1.90 tff(4851,plain,
% 1.74/1.90 (b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z))))))) <=> b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[1898])).
% 1.74/1.90 tff(4852,plain,
% 1.74/1.90 ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))) <=> (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[4851])).
% 1.74/1.90 tff(4853,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(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(s(s(z)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(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(s(s(z)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(4854,plain,
% 1.74/1.90 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z))))))))) <=> ((~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(s(s(z)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(4855,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(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(s(s(z)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z))))))))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[4854])).
% 1.74/1.90 tff(4856,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(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(s(s(z)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))))),
% 1.74/1.90 inference(transitivity,[status(thm)],[4855, 4853])).
% 1.74/1.90 tff(4857,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(4858,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(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(s(s(z)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z))))))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[4857, 4856])).
% 1.74/1.90 tff(4859,plain,
% 1.74/1.90 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4858, 306, 2076, 815, 2812, 3222])).
% 1.74/1.90 tff(4860,plain,
% 1.74/1.90 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[4859, 4852])).
% 1.74/1.90 tff(4861,plain,
% 1.74/1.90 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(4862,plain,
% 1.74/1.90 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(4863,plain,
% 1.74/1.90 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[4862, 4861])).
% 1.74/1.90 tff(4864,plain,
% 1.74/1.90 ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4863, 43])).
% 1.74/1.90 tff(4865,plain,
% 1.74/1.90 (r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4864, 4860, 4850])).
% 1.74/1.90 tff(4866,plain,
% 1.74/1.90 (r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[4865, 4846])).
% 1.74/1.90 tff(4867,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(4868,plain,
% 1.74/1.91 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1))))) <=> ((~b(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(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(4869,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), elem!1))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[4868])).
% 1.74/1.91 tff(4870,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.74/1.91 inference(transitivity,[status(thm)],[4869, 4867])).
% 1.74/1.91 tff(4871,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(4872,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), elem!1))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[4871, 4870])).
% 1.74/1.91 tff(4873,plain,
% 1.74/1.91 (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4872, 306, 30, 815, 2812, 3222])).
% 1.74/1.91 tff(4874,plain,
% 1.74/1.91 (r(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[3247, 43, 3244, 4873])).
% 1.74/1.91 tff(4875,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(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)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(4876,plain,
% 1.74/1.91 (((~b(s(elem!1), s(s(s(elem!1))))) | (~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))))) <=> ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(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)))), s(s(elem!1)))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(4877,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[4876])).
% 1.74/1.91 tff(4878,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.74/1.91 inference(transitivity,[status(thm)],[4877, 4875])).
% 1.74/1.91 tff(4879,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~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)))))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(4880,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[4879, 4878])).
% 1.74/1.91 tff(4881,plain,
% 1.74/1.91 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4880, 306, 30, 2076, 815, 3222])).
% 1.74/1.91 tff(4882,plain,
% 1.74/1.91 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1302, 4881, 4684])).
% 1.74/1.91 tff(4883,plain,
% 1.74/1.91 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[3749, 124, 4882, 4874])).
% 1.74/1.91 tff(4884,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4883, 4866])).
% 1.74/1.91 tff(4885,plain,((~b(s(s(s(s(elem!1)))), elem!1)) | (~(z = elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(4886,plain,
% 1.74/1.91 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4885, 1502, 4677, 4844, 4779, 4683])).
% 1.74/1.91 tff(4887,plain,
% 1.74/1.91 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1736, 4886, 1550])).
% 1.74/1.91 tff(4888,plain,
% 1.74/1.91 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[3804, 124, 1627, 1289])).
% 1.74/1.91 tff(4889,plain,
% 1.74/1.91 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1297, 1289, 970])).
% 1.74/1.91 tff(4890,plain,
% 1.74/1.91 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1302, 4889, 1717])).
% 1.74/1.91 tff(4891,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(4892,plain,
% 1.74/1.91 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(4893,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(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(elem!1)))), s(s(elem!1))))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[4892])).
% 1.74/1.91 tff(4894,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(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(elem!1)))), s(s(elem!1)))))),
% 1.74/1.91 inference(transitivity,[status(thm)],[4893, 4891])).
% 1.74/1.91 tff(4895,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(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))))))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(4896,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[4895, 4894])).
% 1.74/1.91 tff(4897,plain,
% 1.74/1.91 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4896, 306, 759, 1590, 601, 4890])).
% 1.74/1.91 tff(4898,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1958, 43, 3476, 4897, 4888])).
% 1.74/1.91 tff(4899,plain,((~r(s(s(s(s(elem!1)))), elem!1)) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(4900,plain,
% 1.74/1.91 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4899, 4887, 4705, 4680, 1955, 4841, 4684, 4840])).
% 1.74/1.91 tff(4901,plain,
% 1.74/1.91 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[891, 4900, 4670])).
% 1.74/1.91 tff(4902,plain,
% 1.74/1.91 ((~b(elem!1, s(s(s(z))))) <=> (~b(elem!1, s(s(s(elem!1)))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[1581])).
% 1.74/1.91 tff(4903,plain,
% 1.74/1.91 (~b(elem!1, s(s(s(elem!1))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[3, 4902])).
% 1.74/1.91 tff(4904,plain,
% 1.74/1.91 (r(elem!1, s(s(s(elem!1))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1260, 43, 4903, 1519])).
% 1.74/1.91 tff(4905,plain,
% 1.74/1.91 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(4906,plain,
% 1.74/1.91 (((~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(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(4907,plain,
% 1.74/1.91 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[4906])).
% 1.74/1.91 tff(4908,plain,
% 1.74/1.91 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.74/1.91 inference(transitivity,[status(thm)],[4907, 4905])).
% 1.74/1.91 tff(4909,plain,
% 1.74/1.91 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(4910,plain,
% 1.74/1.91 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[4909, 4908])).
% 1.74/1.91 tff(4911,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4910, 124, 4904, 4841, 4901])).
% 1.74/1.91 tff(4912,plain,((~(z = elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | b(elem!1, s(s(s(z)))) | r(s(s(elem!1)), elem!1) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(4913,plain,
% 1.74/1.91 (~(z = elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4912, 4660, 8, 3, 6, 4344])).
% 1.74/1.91 tff(4914,plain,
% 1.74/1.91 (~(elem!1 = z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2172, 4913])).
% 1.74/1.91 tff(4915,plain,
% 1.74/1.91 (r(elem!1, z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[174, 4914, 2])).
% 1.74/1.91 tff(4916,plain,
% 1.74/1.91 (~(s(z) = elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4206, 4667, 4660])).
% 1.74/1.91 tff(4917,plain,
% 1.74/1.91 (b(z, elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[835, 4913, 7])).
% 1.74/1.91 tff(4918,plain,
% 1.74/1.91 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4284, 1171])).
% 1.74/1.91 tff(4919,plain,
% 1.74/1.91 (r(s(s(s(z))), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1489, 1444, 1])).
% 1.74/1.91 tff(4920,plain,
% 1.74/1.91 (~r(s(s(s(z))), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2561, 4919, 246])).
% 1.74/1.91 tff(4921,plain,
% 1.74/1.91 (b(s(s(s(z))), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2197, 4920])).
% 1.74/1.91 tff(4922,plain,
% 1.74/1.91 (~(elem!1 = s(s(s(z))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4555, 1444])).
% 1.74/1.91 tff(4923,plain,
% 1.74/1.91 (r(elem!1, s(s(s(z))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2304, 4922, 3])).
% 1.74/1.91 tff(4924,plain,
% 1.74/1.91 (~r(z, s(s(s(z))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[3392, 4923, 246])).
% 1.74/1.91 tff(4925,plain,
% 1.74/1.91 (b(z, s(s(s(z))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2415, 43, 4924, 2405])).
% 1.74/1.91 tff(4926,plain,
% 1.74/1.91 (~b(s(z), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4569, 4925, 8, 4921])).
% 1.74/1.91 tff(4927,plain,
% 1.74/1.91 (r(s(z), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[221, 4926])).
% 1.74/1.91 tff(4928,plain,
% 1.74/1.91 (~r(s(z), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1049, 4927, 246])).
% 1.74/1.91 tff(4929,plain,
% 1.74/1.91 (b(s(z), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1500, 43, 4928, 3094])).
% 1.74/1.91 tff(4930,plain,
% 1.74/1.91 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4629, 4929, 8, 838, 4346, 4927])).
% 1.74/1.91 tff(4931,plain,
% 1.74/1.91 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1144, 4930, 4918])).
% 1.74/1.91 tff(4932,plain,
% 1.74/1.91 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2862, 124, 4919, 4931])).
% 1.74/1.91 tff(4933,plain,
% 1.74/1.91 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4599, 4925, 838, 4921, 8])).
% 1.74/1.91 tff(4934,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4603, 43, 4933, 4932, 4577])).
% 1.74/1.91 tff(4935,plain,((~(s(s(elem!1)) = elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (s(z) = elem!1) | (~r(elem!1, z)) | b(elem!1, s(s(s(z)))) | b(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(4936,plain,
% 1.74/1.91 (~(s(s(elem!1)) = elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4935, 4917, 8, 4344, 4916, 4915, 3, 4667])).
% 1.74/1.91 tff(4937,plain,
% 1.74/1.91 (b(s(s(elem!1)), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[47, 4936, 6])).
% 1.74/1.91 tff(4938,plain,
% 1.74/1.91 (~b(z, s(s(s(z))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4569, 1531, 8, 247])).
% 1.74/1.91 tff(4939,plain,
% 1.74/1.91 (~(elem!1 = s(s(s(z))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1534, 1531, 2])).
% 1.74/1.91 tff(4940,plain,
% 1.74/1.91 (r(elem!1, s(s(s(z))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2304, 4939, 3])).
% 1.74/1.91 tff(4941,plain,
% 1.74/1.91 (~r(z, s(s(s(z))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[3392, 4940, 246])).
% 1.74/1.91 tff(4942,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2415, 43, 4941, 4938, 2405])).
% 1.74/1.91 tff(4943,plain,((~b(s(s(s(z))), z)) | (~r(elem!1, z)) | b(elem!1, s(s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(4944,plain,
% 1.74/1.91 (~b(s(s(s(z))), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4943, 247, 3, 8, 246, 2])).
% 1.74/1.91 tff(4945,plain,
% 1.74/1.91 (r(s(s(s(z))), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2197, 4944])).
% 1.74/1.91 tff(4946,plain,
% 1.74/1.91 (~r(elem!1, s(s(s(z))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2312, 4945, 246])).
% 1.74/1.91 tff(4947,plain,
% 1.74/1.91 (elem!1 = s(s(s(z)))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2304, 4946, 3])).
% 1.74/1.91 tff(4948,plain,
% 1.74/1.91 (b(z, s(s(s(z))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[842, 4947, 838])).
% 1.74/1.91 tff(4949,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(4950,plain,
% 1.74/1.91 (((~b(s(z), s(s(s(z))))) | (~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), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(4951,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), z))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[4950])).
% 1.74/1.91 tff(4952,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)))),
% 1.74/1.91 inference(transitivity,[status(thm)],[4951, 4949])).
% 1.74/1.91 tff(4953,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(4954,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), z))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[4953, 4952])).
% 1.74/1.91 tff(4955,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4954, 306, 2284, 8, 4948, 247])).
% 1.74/1.91 tff(4956,plain,((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, elem!1)) | b(elem!1, s(s(s(z)))) | (~r(elem!1, z)) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(4957,plain,
% 1.74/1.91 (~b(s(z), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4956, 4660, 8, 4917, 3, 4915, 2])).
% 1.74/1.91 tff(4958,plain,
% 1.74/1.91 (r(s(z), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[221, 4957])).
% 1.74/1.91 tff(4959,plain,
% 1.74/1.91 (~r(s(z), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1049, 4958, 4915])).
% 1.74/1.91 tff(4960,plain,
% 1.74/1.91 (b(s(z), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1500, 43, 4959, 4916])).
% 1.74/1.91 tff(4961,plain,
% 1.74/1.91 (~b(s(s(elem!1)), s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4380, 4960, 4344, 4937])).
% 1.74/1.91 tff(4962,plain,
% 1.74/1.91 (r(s(s(elem!1)), s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[3989, 4961])).
% 1.74/1.91 tff(4963,plain,
% 1.74/1.91 (~b(s(s(elem!1)), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4649, 306, 4917, 4937, 8, 4344])).
% 1.74/1.91 tff(4964,plain,
% 1.74/1.91 (r(s(s(elem!1)), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[476, 4963])).
% 1.74/1.91 tff(4965,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[3981, 124, 4964, 4958, 4962])).
% 1.74/1.91 tff(4966,plain,(b(elem!1, s(s(s(z)))) | (~b(s(z), s(s(s(z))))) | b(elem!1, z) | r(s(s(elem!1)), elem!1) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(4967,plain,
% 1.74/1.91 (b(elem!1, s(s(s(z))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4966, 8, 2, 6, 7])).
% 1.74/1.91 tff(4968,plain,
% 1.74/1.91 (~r(s(s(s(z))), s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4544, 1619, 4346, 8, 6])).
% 1.74/1.91 tff(4969,plain,
% 1.74/1.91 (b(s(s(s(z))), s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[113, 4968])).
% 1.74/1.91 tff(4970,plain,
% 1.74/1.91 (b(s(s(s(z))), s(elem!1))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[4969, 4703])).
% 1.74/1.91 tff(4971,plain,
% 1.74/1.91 (b(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[4970, 4702])).
% 1.74/1.91 tff(4972,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(4973,plain,
% 1.74/1.91 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(4974,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1)))))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[4973])).
% 1.74/1.92 tff(4975,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[4974, 4972])).
% 1.74/1.92 tff(4976,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(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))))))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(4977,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1)))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[4976, 4975])).
% 1.74/1.92 tff(4978,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[4977, 306, 4971, 1638, 4677, 4779])).
% 1.74/1.92 tff(4979,plain,((~(z = elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(4980,plain,
% 1.74/1.92 (~(z = elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[4979, 4967, 8, 4344, 6])).
% 1.74/1.92 tff(4981,plain,
% 1.74/1.92 (b(z, elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[835, 4980, 7])).
% 1.74/1.92 tff(4982,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(z))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(4983,plain,
% 1.74/1.92 (((~b(z, elem!1)) | (~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(s(z), s(s(s(z))))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(z))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(4984,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(z)))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[4983])).
% 1.74/1.92 tff(4985,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(z))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[4984, 4982])).
% 1.74/1.92 tff(4986,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~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))))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(4987,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(z)))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[4986, 4985])).
% 1.74/1.92 tff(4988,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[4987, 306, 838, 8, 4346, 1531, 1470])).
% 1.74/1.92 tff(4989,plain,((~b(s(s(s(z))), z)) | (~b(z, elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(4990,plain,
% 1.74/1.92 (~b(s(s(s(z))), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[4989, 4981, 8, 4344, 4967])).
% 1.74/1.92 tff(4991,plain,
% 1.74/1.92 (~(s(s(s(z))) = elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1472, 4967])).
% 1.74/1.92 tff(4992,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(4993,plain,
% 1.74/1.92 (((~b(elem!1, s(z))) | (~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(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(4994,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[4993])).
% 1.74/1.92 tff(4995,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.74/1.92 inference(transitivity,[status(thm)],[4994, 4992])).
% 1.74/1.92 tff(4996,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~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))))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(4997,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[4996, 4995])).
% 1.74/1.92 tff(4998,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[4997, 306, 8, 1967, 4346, 1470])).
% 1.74/1.92 tff(4999,plain,((~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(5000,plain,
% 1.74/1.92 (~b(s(s(s(z))), elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[4999, 8, 4344, 4967])).
% 1.74/1.92 tff(5001,plain,
% 1.74/1.92 (r(s(s(s(z))), elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1489, 5000, 4991])).
% 1.74/1.92 tff(5002,plain,
% 1.74/1.92 (~(elem!1 = z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2172, 4980])).
% 1.74/1.92 tff(5003,plain,
% 1.74/1.92 (r(elem!1, z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[174, 5002, 2])).
% 1.74/1.92 tff(5004,plain,
% 1.74/1.92 (~r(s(s(s(z))), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2561, 5003, 5001])).
% 1.74/1.92 tff(5005,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2197, 5004, 4990])).
% 1.74/1.92 tff(5006,plain,((~b(s(z), s(s(s(z))))) | b(elem!1, z) | r(z, elem!1) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(5007,plain,
% 1.74/1.92 (~b(s(z), s(s(s(z))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[5006, 7, 2, 6])).
% 1.74/1.92 tff(5008,plain,
% 1.74/1.92 (r(s(z), s(s(s(z))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[3302, 5007])).
% 1.74/1.92 tff(5009,plain,
% 1.74/1.92 (b(s(z), elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[4196, 3062, 5, 7, 6, 2])).
% 1.74/1.92 tff(5010,plain,
% 1.74/1.92 (b(s(z), z)),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[5009, 3074])).
% 1.74/1.92 tff(5011,plain,
% 1.74/1.92 (b(elem!1, s(s(s(z)))) <=> b(z, s(s(s(z))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[3063])).
% 1.74/1.92 tff(5012,plain,
% 1.74/1.92 (b(elem!1, s(z)) <=> b(s(s(s(z))), s(z))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[231])).
% 1.74/1.92 tff(5013,plain,
% 1.74/1.92 (b(s(s(s(z))), s(z)) <=> b(elem!1, s(z))),
% 1.74/1.92 inference(symmetry,[status(thm)],[5012])).
% 1.74/1.92 tff(5014,plain,
% 1.74/1.92 (b(elem!1, s(z))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[2284, 5013])).
% 1.74/1.92 tff(5015,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[5, 5014])).
% 1.74/1.92 tff(5016,plain,((~(elem!1 = s(s(s(z))))) | b(elem!1, s(z)) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(5017,plain,
% 1.74/1.92 (~(elem!1 = s(s(s(z))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[5016, 2283, 5])).
% 1.74/1.92 tff(5018,plain,
% 1.74/1.92 (r(elem!1, s(s(s(z))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2304, 5017, 3])).
% 1.74/1.92 tff(5019,plain,
% 1.74/1.92 (~r(elem!1, s(z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[3293, 5018, 1034])).
% 1.74/1.92 tff(5020,plain,
% 1.74/1.92 (elem!1 = s(z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[97, 5019])).
% 1.74/1.92 tff(5021,plain,
% 1.74/1.92 (s(elem!1) = s(s(z))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[5020])).
% 1.74/1.92 tff(5022,plain,
% 1.74/1.92 (s(s(elem!1)) = s(s(s(z)))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[5021])).
% 1.74/1.92 tff(5023,plain,
% 1.74/1.92 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[5022])).
% 1.74/1.92 tff(5024,plain,
% 1.74/1.92 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[5023, 5022])).
% 1.74/1.92 tff(5025,plain,
% 1.74/1.92 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(s(z))) = s(s(s(s(z)))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[5022, 5023])).
% 1.74/1.92 tff(5026,plain,
% 1.74/1.92 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[5025, 339])).
% 1.74/1.92 tff(5027,plain,
% 1.74/1.92 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 1.74/1.92 inference(symmetry,[status(thm)],[5026])).
% 1.74/1.92 tff(5028,plain,
% 1.74/1.92 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 1.74/1.92 inference(transitivity,[status(thm)],[5027, 2425])).
% 1.74/1.92 tff(5029,plain,
% 1.74/1.92 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(elem!1))) = s(s(elem!1))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[5028])).
% 1.74/1.92 tff(5030,plain,
% 1.74/1.92 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[4470, 5029])).
% 1.74/1.92 tff(5031,plain,
% 1.74/1.92 (s(z) = elem!1),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[3096, 5020])).
% 1.74/1.92 tff(5032,plain,
% 1.74/1.92 (~b(s(z), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[4298, 5020, 2])).
% 1.74/1.92 tff(5033,plain,
% 1.74/1.92 (r(s(z), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[221, 5032])).
% 1.74/1.92 tff(5034,plain,
% 1.74/1.92 (r(elem!1, z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[3089, 5033, 5031])).
% 1.74/1.92 tff(5035,plain,
% 1.74/1.92 (~(s(elem!1) = elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2654, 5033, 5, 5034])).
% 1.74/1.92 tff(5036,plain,
% 1.74/1.92 (~(elem!1 = s(elem!1))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[364, 5035])).
% 1.74/1.92 tff(5037,plain,
% 1.74/1.92 (r(elem!1, s(s(elem!1))) <=> r(s(z), s(s(elem!1)))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[5020])).
% 1.74/1.92 tff(5038,plain,
% 1.74/1.92 (r(s(z), s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 1.74/1.92 inference(symmetry,[status(thm)],[5037])).
% 1.74/1.92 tff(5039,plain,
% 1.74/1.92 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(s(z))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[5022])).
% 1.74/1.92 tff(5040,plain,
% 1.74/1.92 (r(s(z), s(s(s(z)))) <=> r(s(z), s(s(elem!1)))),
% 1.74/1.92 inference(symmetry,[status(thm)],[5039])).
% 1.74/1.92 tff(5041,plain,
% 1.74/1.92 (r(s(z), s(s(s(z)))) <=> r(elem!1, s(s(elem!1)))),
% 1.74/1.92 inference(transitivity,[status(thm)],[5040, 5038])).
% 1.74/1.92 tff(5042,plain,
% 1.74/1.92 (r(elem!1, s(s(elem!1)))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[1034, 5041])).
% 1.74/1.92 tff(5043,plain,
% 1.74/1.92 (~(s(s(elem!1)) = s(elem!1))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[195, 5035])).
% 1.74/1.92 tff(5044,plain,
% 1.74/1.92 (r(z, s(s(elem!1))) <=> r(z, s(s(s(z))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[5022])).
% 1.74/1.92 tff(5045,plain,
% 1.74/1.92 (r(z, s(s(s(z)))) <=> r(z, s(s(elem!1)))),
% 1.74/1.92 inference(symmetry,[status(thm)],[5044])).
% 1.74/1.92 tff(5046,plain,
% 1.74/1.92 ((~r(z, s(s(s(z))))) <=> (~r(z, s(s(elem!1))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[5045])).
% 1.74/1.92 tff(5047,plain,
% 1.74/1.92 (~r(z, s(s(s(z))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[3392, 5034, 5018])).
% 1.74/1.92 tff(5048,plain,
% 1.74/1.92 (~r(z, s(s(elem!1)))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[5047, 5046])).
% 1.74/1.92 tff(5049,plain,
% 1.74/1.92 (b(z, s(s(elem!1)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[460, 5048])).
% 1.74/1.92 tff(5050,plain,
% 1.74/1.92 (b(s(elem!1), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2380, 288])).
% 1.74/1.92 tff(5051,plain,
% 1.74/1.92 (~r(s(s(elem!1)), s(elem!1))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1238, 255, 970])).
% 1.74/1.92 tff(5052,plain,
% 1.74/1.92 (b(s(s(elem!1)), s(elem!1))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[994, 5051, 403])).
% 1.74/1.92 tff(5053,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1218, 5052, 276, 1198, 5050])).
% 1.74/1.92 tff(5054,plain,((~r(elem!1, s(elem!1))) | (~b(z, s(s(elem!1)))) | (s(s(elem!1)) = s(elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(5055,plain,
% 1.74/1.92 (~r(elem!1, s(elem!1))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[5054, 5049, 5043, 5042, 5034])).
% 1.74/1.92 tff(5056,plain,
% 1.74/1.92 (b(elem!1, s(elem!1))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[372, 5055, 5036])).
% 1.74/1.92 tff(5057,plain,
% 1.74/1.92 (r(s(z), s(elem!1)) <=> r(s(z), s(s(z)))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[5021])).
% 1.74/1.92 tff(5058,plain,
% 1.74/1.92 (r(elem!1, s(elem!1)) <=> r(s(z), s(elem!1))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[5020])).
% 1.74/1.92 tff(5059,plain,
% 1.74/1.92 (r(elem!1, s(elem!1)) <=> r(s(z), s(s(z)))),
% 1.74/1.92 inference(transitivity,[status(thm)],[5058, 5057])).
% 1.74/1.92 tff(5060,plain,
% 1.74/1.92 ((~r(elem!1, s(elem!1))) <=> (~r(s(z), s(s(z))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[5059])).
% 1.74/1.92 tff(5061,plain,
% 1.74/1.92 (~r(s(z), s(s(z)))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[5055, 5060])).
% 1.74/1.92 tff(5062,plain,
% 1.74/1.92 (b(s(z), s(s(z)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[4434, 5061])).
% 1.74/1.92 tff(5063,plain,
% 1.74/1.92 (b(z, s(s(s(z))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2415, 43, 5047, 2405])).
% 1.74/1.92 tff(5064,plain,
% 1.74/1.92 (r(s(s(s(elem!1))), z) <=> r(s(s(s(s(z)))), z)),
% 1.74/1.92 inference(monotonicity,[status(thm)],[3589])).
% 1.74/1.92 tff(5065,plain,
% 1.74/1.92 ((~r(s(s(s(elem!1))), z)) <=> (~r(s(s(s(s(z)))), z))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[5064])).
% 1.74/1.92 tff(5066,plain,
% 1.74/1.92 ((elem!1 = s(s(s(elem!1)))) <=> (s(z) = s(s(s(elem!1))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[10])).
% 1.74/1.92 tff(5067,plain,
% 1.74/1.92 ((s(z) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 1.74/1.92 inference(symmetry,[status(thm)],[5066])).
% 1.74/1.92 tff(5068,plain,
% 1.74/1.92 ((~(s(z) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[5067])).
% 1.74/1.92 tff(5069,plain,
% 1.74/1.92 (~(elem!1 = s(s(s(elem!1))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[645, 5068])).
% 1.74/1.92 tff(5070,plain,
% 1.74/1.92 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(z))), s(z))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[15])).
% 1.74/1.92 tff(5071,plain,
% 1.74/1.92 (b(s(s(s(z))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.74/1.92 inference(symmetry,[status(thm)],[5070])).
% 1.74/1.92 tff(5072,plain,
% 1.74/1.92 (b(s(s(s(z))), s(z)) <=> b(s(s(elem!1)), elem!1)),
% 1.74/1.92 inference(transitivity,[status(thm)],[5071, 12])).
% 1.74/1.92 tff(5073,plain,
% 1.74/1.92 (b(s(s(elem!1)), elem!1)),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[2284, 5072])).
% 1.74/1.92 tff(5074,plain,
% 1.74/1.92 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 1.74/1.92 inference(transitivity,[status(thm)],[5067, 1555])).
% 1.74/1.92 tff(5075,plain,
% 1.74/1.92 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[5074])).
% 1.74/1.92 tff(5076,plain,
% 1.74/1.92 (~(s(s(s(elem!1))) = elem!1)),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[645, 5075])).
% 1.74/1.92 tff(5077,plain,
% 1.74/1.92 (~r(z, s(s(elem!1)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[978, 246, 970])).
% 1.74/1.92 tff(5078,plain,
% 1.74/1.92 (b(z, s(s(elem!1)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[460, 5077])).
% 1.74/1.92 tff(5079,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(elem!1))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(5080,plain,
% 1.74/1.92 (((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(elem!1))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(5081,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(elem!1)))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[5080])).
% 1.74/1.92 tff(5082,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(elem!1))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[5081, 5079])).
% 1.74/1.92 tff(5083,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(5084,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(elem!1)))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[5083, 5082])).
% 1.74/1.92 tff(5085,plain,
% 1.74/1.92 (~b(s(s(s(elem!1))), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[5084, 306, 30, 5078, 601, 815])).
% 1.74/1.92 tff(5086,plain,
% 1.74/1.92 (r(s(s(s(elem!1))), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[3033, 43, 579, 5085])).
% 1.74/1.92 tff(5087,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[3027, 124, 246, 5086, 1627])).
% 1.74/1.92 tff(5088,plain,((~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(5089,plain,
% 1.74/1.92 (~r(s(s(s(elem!1))), elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[5088, 601, 246, 5073, 970, 815])).
% 1.74/1.92 tff(5090,plain,
% 1.74/1.92 (b(s(s(s(elem!1))), elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1636, 5089, 5076])).
% 1.74/1.92 tff(5091,plain,
% 1.74/1.92 (~b(elem!1, s(s(s(elem!1))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1672, 5090, 5073, 601])).
% 1.74/1.92 tff(5092,plain,
% 1.74/1.92 (r(elem!1, s(s(s(elem!1))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[3284, 5091, 5069])).
% 1.74/1.92 tff(5093,plain,
% 1.74/1.92 (~r(s(s(s(elem!1))), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[851, 5092, 246])).
% 1.74/1.92 tff(5094,plain,
% 1.74/1.92 (~r(s(s(s(s(z)))), z)),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[5093, 5065])).
% 1.74/1.92 tff(5095,plain,
% 1.74/1.92 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[3589, 15])).
% 1.74/1.92 tff(5096,plain,
% 1.74/1.92 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[601, 5095])).
% 1.74/1.92 tff(5097,assumption,(b(s(z), s(s(z)))), introduced(assumption)).
% 1.74/1.92 tff(5098,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(5099,plain,
% 1.74/1.92 (((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(5100,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(z))))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[5099])).
% 1.74/1.92 tff(5101,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[5100, 5098])).
% 1.74/1.92 tff(5102,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(5103,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(z))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[5102, 5101])).
% 1.74/1.92 tff(5104,plain,
% 1.74/1.92 (~b(s(s(s(s(z)))), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[5103, 306, 2284, 859, 5097, 5096])).
% 1.74/1.92 tff(5105,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[695, 5104, 5094])).
% 1.74/1.92 tff(5106,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~(elem!1 = s(z))) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.93 tff(5107,plain,
% 1.74/1.93 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[5106, 2283, 5063, 5062, 5020, 5034, 5042, 5056])).
% 1.74/1.93 tff(5108,plain,
% 1.74/1.93 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[610, 5107, 5030])).
% 1.74/1.93 tff(5109,plain,
% 1.74/1.93 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[5108, 5024])).
% 1.74/1.93 tff(5110,plain,
% 1.74/1.93 (~r(s(s(s(s(z)))), s(z))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1040, 124, 1034, 5109])).
% 1.74/1.93 tff(5111,plain,
% 1.74/1.93 (b(s(s(s(s(z)))), s(z))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[4490, 5110])).
% 1.74/1.93 tff(5112,plain,
% 1.74/1.93 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(z)))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5023, 5021])).
% 1.74/1.93 tff(5113,plain,
% 1.74/1.93 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(z)))) = s(s(z)))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5023, 5021])).
% 1.74/1.93 tff(5114,plain,
% 1.74/1.93 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(z)) = s(s(s(s(z)))))),
% 1.74/1.93 inference(transitivity,[status(thm)],[5113, 1707])).
% 1.74/1.93 tff(5115,plain,
% 1.74/1.93 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.74/1.93 inference(symmetry,[status(thm)],[5114])).
% 1.74/1.93 tff(5116,plain,
% 1.74/1.93 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5115])).
% 1.74/1.93 tff(5117,plain,
% 1.74/1.93 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[1612, 5116])).
% 1.74/1.93 tff(5118,plain,
% 1.74/1.93 (~r(elem!1, s(z))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[3293, 3313, 1034])).
% 1.74/1.93 tff(5119,plain,
% 1.74/1.93 (elem!1 = s(z)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[97, 5118])).
% 1.74/1.93 tff(5120,plain,
% 1.74/1.93 (s(elem!1) = s(s(z))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5119])).
% 1.74/1.93 tff(5121,plain,
% 1.74/1.93 (s(s(elem!1)) = s(s(s(z)))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5120])).
% 1.74/1.93 tff(5122,plain,
% 1.74/1.93 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5121])).
% 1.74/1.93 tff(5123,plain,
% 1.74/1.93 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5122, 5121])).
% 1.74/1.93 tff(5124,plain,
% 1.74/1.93 (~b(s(z), z)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[4298, 5119, 2])).
% 1.74/1.93 tff(5125,plain,
% 1.74/1.93 (r(s(z), z)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[221, 5124])).
% 1.74/1.93 tff(5126,plain,
% 1.74/1.93 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[3431, 3149, 2284, 2, 3313, 5125, 5])).
% 1.74/1.93 tff(5127,plain,
% 1.74/1.93 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[5126, 5123])).
% 1.74/1.93 tff(5128,plain,
% 1.74/1.93 (~r(s(s(s(s(z)))), s(z))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1040, 124, 1034, 5127])).
% 1.74/1.93 tff(5129,plain,
% 1.74/1.93 (b(s(s(s(s(z)))), s(z))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[4490, 5128])).
% 1.74/1.93 tff(5130,plain,
% 1.74/1.93 (~r(s(z), s(s(s(s(z)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[3585, 124, 1034, 5127])).
% 1.74/1.93 tff(5131,assumption,(s(z) = s(s(s(s(z))))), introduced(assumption)).
% 1.74/1.93 tff(5132,plain,
% 1.74/1.93 (s(s(s(s(z)))) = s(z)),
% 1.74/1.93 inference(symmetry,[status(thm)],[5131])).
% 1.74/1.93 tff(5133,plain,
% 1.74/1.93 ($false),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[324, 5132])).
% 1.74/1.93 tff(5134,plain,(~(s(z) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.93 tff(5135,plain,
% 1.74/1.93 (b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[680, 43, 5134])).
% 1.74/1.93 tff(5136,plain,
% 1.74/1.93 (b(s(z), s(s(s(s(z)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[5135, 5130])).
% 1.74/1.93 tff(5137,plain,
% 1.74/1.93 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[3673, 3149, 5, 5125, 2, 3313, 2284, 6])).
% 1.74/1.93 tff(5138,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(5139,plain,
% 1.74/1.93 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(5140,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5139])).
% 1.74/1.93 tff(5141,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.74/1.93 inference(transitivity,[status(thm)],[5140, 5138])).
% 1.74/1.93 tff(5142,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(5143,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[5142, 5141])).
% 1.74/1.93 tff(5144,plain,
% 1.74/1.93 ($false),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[5143, 306, 2284, 5137, 5136, 5129])).
% 1.74/1.93 tff(5145,plain,(r(s(s(elem!1)), s(elem!1)) | (~b(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | b(elem!1, s(z)) | b(elem!1, z) | (~r(elem!1, s(s(s(z))))) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.93 tff(5146,plain,
% 1.74/1.93 (r(s(s(elem!1)), s(elem!1))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[5145, 2283, 1034, 5, 2, 5018, 6])).
% 1.74/1.93 tff(5147,plain,
% 1.74/1.93 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[659, 5108, 5146])).
% 1.74/1.93 tff(5148,plain,
% 1.74/1.93 (b(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[664, 5147, 5117])).
% 1.74/1.93 tff(5149,plain,
% 1.74/1.93 (b(s(s(s(s(z)))), s(s(z)))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[5148, 5112])).
% 1.74/1.93 tff(5150,plain,
% 1.74/1.93 (~r(s(z), s(s(s(s(z)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[3585, 124, 1034, 5109])).
% 1.74/1.93 tff(5151,plain,
% 1.74/1.93 (b(s(z), s(s(s(s(z)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[5135, 5150])).
% 1.74/1.93 tff(5152,plain,
% 1.74/1.93 (~r(elem!1, s(z))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[2180, 124, 246, 204])).
% 1.74/1.93 tff(5153,plain,
% 1.74/1.93 (elem!1 = s(z)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[97, 5152])).
% 1.74/1.93 tff(5154,plain,
% 1.74/1.93 (s(elem!1) = s(s(z))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5153])).
% 1.74/1.93 tff(5155,plain,
% 1.74/1.93 (s(s(elem!1)) = s(s(s(z)))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5154])).
% 1.74/1.93 tff(5156,plain,
% 1.74/1.93 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5155])).
% 1.74/1.93 tff(5157,plain,
% 1.74/1.93 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.74/1.93 inference(symmetry,[status(thm)],[5156])).
% 1.74/1.93 tff(5158,plain,
% 1.74/1.93 (s(s(s(z))) = s(s(elem!1))),
% 1.74/1.93 inference(symmetry,[status(thm)],[5155])).
% 1.74/1.93 tff(5159,plain,
% 1.74/1.93 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5156])).
% 1.74/1.93 tff(5160,plain,
% 1.74/1.93 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 1.74/1.93 inference(symmetry,[status(thm)],[5159])).
% 1.74/1.93 tff(5161,plain,
% 1.74/1.93 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5160, 5158])).
% 1.74/1.93 tff(5162,plain,
% 1.74/1.93 (r(s(s(s(s(elem!1)))), s(s(elem!1))) <=> r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.74/1.93 inference(symmetry,[status(thm)],[5161])).
% 1.74/1.93 tff(5163,plain,
% 1.74/1.93 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(z)))) = s(s(z)))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5156, 5154])).
% 1.74/1.93 tff(5164,plain,
% 1.74/1.93 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(z)) = s(s(s(s(z)))))),
% 1.74/1.93 inference(transitivity,[status(thm)],[5163, 1707])).
% 1.74/1.93 tff(5165,plain,
% 1.74/1.93 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.74/1.93 inference(symmetry,[status(thm)],[5164])).
% 1.74/1.93 tff(5166,plain,
% 1.74/1.93 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5165])).
% 1.74/1.93 tff(5167,plain,
% 1.74/1.93 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[1612, 5166])).
% 1.74/1.93 tff(5168,plain,
% 1.74/1.93 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1284, 5167])).
% 1.74/1.93 tff(5169,plain,
% 1.74/1.93 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(z)))), s(z))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5156, 5153])).
% 1.74/1.93 tff(5170,plain,
% 1.74/1.93 (s(z) = elem!1),
% 1.74/1.93 inference(symmetry,[status(thm)],[5153])).
% 1.74/1.93 tff(5171,plain,
% 1.74/1.93 ((s(z) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5170])).
% 1.74/1.93 tff(5172,plain,
% 1.74/1.93 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 1.74/1.93 inference(transitivity,[status(thm)],[5171, 1555])).
% 1.74/1.93 tff(5173,plain,
% 1.74/1.93 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5172])).
% 1.74/1.93 tff(5174,plain,
% 1.74/1.93 (~(s(s(s(elem!1))) = elem!1)),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[645, 5173])).
% 1.74/1.93 tff(5175,plain,
% 1.74/1.93 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(elem!1))), elem!1)),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5157, 5170])).
% 1.74/1.93 tff(5176,plain,
% 1.74/1.93 ((~r(s(s(s(s(z)))), s(z))) <=> (~r(s(s(s(elem!1))), elem!1))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5175])).
% 1.74/1.93 tff(5177,plain,
% 1.74/1.93 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5156, 5155])).
% 1.74/1.93 tff(5178,plain,
% 1.74/1.93 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[152, 5167])).
% 1.74/1.93 tff(5179,plain,
% 1.74/1.93 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[159, 5178])).
% 1.74/1.93 tff(5180,plain,
% 1.74/1.93 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5156, 5155])).
% 1.74/1.93 tff(5181,plain,
% 1.74/1.93 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.74/1.93 inference(symmetry,[status(thm)],[5180])).
% 1.74/1.93 tff(5182,plain,
% 1.74/1.93 ((~b(s(s(s(s(z)))), s(s(s(z))))) <=> (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5181])).
% 1.74/1.93 tff(5183,plain,
% 1.74/1.93 (s(s(z)) = s(elem!1)),
% 1.74/1.93 inference(symmetry,[status(thm)],[5154])).
% 1.74/1.93 tff(5184,plain,
% 1.74/1.93 (r(s(z), s(s(z))) <=> r(elem!1, s(elem!1))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5170, 5183])).
% 1.74/1.93 tff(5185,plain,
% 1.74/1.93 (r(elem!1, s(elem!1)) <=> r(s(z), s(s(z)))),
% 1.74/1.93 inference(symmetry,[status(thm)],[5184])).
% 1.74/1.93 tff(5186,plain,
% 1.74/1.93 ((~r(elem!1, s(elem!1))) <=> (~r(s(z), s(s(z))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5185])).
% 1.74/1.93 tff(5187,plain,
% 1.74/1.93 (r(elem!1, s(s(elem!1))) <=> r(s(z), s(s(s(z))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5153, 5155])).
% 1.74/1.93 tff(5188,plain,
% 1.74/1.93 (r(s(z), s(s(s(z)))) <=> r(elem!1, s(s(elem!1)))),
% 1.74/1.93 inference(symmetry,[status(thm)],[5187])).
% 1.74/1.93 tff(5189,plain,
% 1.74/1.93 (r(elem!1, s(s(s(z)))) <=> r(s(z), s(s(s(z))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5153])).
% 1.74/1.93 tff(5190,plain,
% 1.74/1.93 (r(s(z), s(s(s(z))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[3313, 5189])).
% 1.74/1.93 tff(5191,plain,
% 1.74/1.93 (r(elem!1, s(s(elem!1)))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[5190, 5188])).
% 1.74/1.93 tff(5192,plain,
% 1.74/1.93 (~r(elem!1, s(elem!1))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1238, 5191, 244])).
% 1.74/1.93 tff(5193,plain,
% 1.74/1.93 (~r(s(z), s(s(z)))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[5192, 5186])).
% 1.74/1.93 tff(5194,plain,
% 1.74/1.93 ((s(z) = s(s(z))) <=> (elem!1 = s(elem!1))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5170, 5183])).
% 1.74/1.93 tff(5195,plain,
% 1.74/1.93 ((s(z) = s(s(z))) <=> (s(elem!1) = elem!1)),
% 1.74/1.93 inference(transitivity,[status(thm)],[5194, 1162])).
% 1.74/1.93 tff(5196,plain,
% 1.74/1.93 ((s(elem!1) = elem!1) <=> (s(z) = s(s(z)))),
% 1.74/1.93 inference(symmetry,[status(thm)],[5195])).
% 1.74/1.93 tff(5197,plain,
% 1.74/1.93 ((~(s(elem!1) = elem!1)) <=> (~(s(z) = s(s(z))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5196])).
% 1.74/1.93 tff(5198,plain,
% 1.74/1.93 ((s(s(elem!1)) = elem!1) <=> (s(s(elem!1)) = s(z))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5153])).
% 1.74/1.93 tff(5199,plain,
% 1.74/1.93 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 1.74/1.93 inference(symmetry,[status(thm)],[5198])).
% 1.74/1.93 tff(5200,plain,
% 1.74/1.93 ((s(s(elem!1)) = s(z)) <=> (s(s(s(z))) = s(z))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5155])).
% 1.74/1.93 tff(5201,plain,
% 1.74/1.93 ((s(s(s(z))) = s(z)) <=> (s(s(elem!1)) = s(z))),
% 1.74/1.93 inference(symmetry,[status(thm)],[5200])).
% 1.74/1.93 tff(5202,plain,
% 1.74/1.93 ((s(s(s(z))) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 1.74/1.93 inference(transitivity,[status(thm)],[5201, 5199])).
% 1.74/1.93 tff(5203,plain,
% 1.74/1.93 ((~(s(s(s(z))) = s(z))) <=> (~(s(s(elem!1)) = elem!1))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5202])).
% 1.74/1.93 tff(5204,plain,
% 1.74/1.93 (~(s(s(elem!1)) = elem!1)),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[108, 5203])).
% 1.74/1.93 tff(5205,plain,
% 1.74/1.93 (~(s(elem!1) = elem!1)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[180, 5204])).
% 1.74/1.93 tff(5206,plain,
% 1.74/1.93 (~(s(z) = s(s(z)))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[5205, 5197])).
% 1.74/1.93 tff(5207,plain,
% 1.74/1.93 (b(s(z), s(s(z)))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[4433, 5206, 5193])).
% 1.74/1.93 tff(5208,plain,
% 1.74/1.93 (~r(z, s(s(s(z))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[3392, 246, 3313])).
% 1.74/1.93 tff(5209,plain,
% 1.74/1.93 ((z = s(s(s(z)))) | b(z, s(s(s(z))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[2415, 43, 5208])).
% 1.74/1.93 tff(5210,plain,
% 1.74/1.93 (b(z, s(s(s(z))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[5209, 3385])).
% 1.74/1.93 tff(5211,plain,
% 1.74/1.93 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(z)))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5156, 5154])).
% 1.74/1.93 tff(5212,plain,
% 1.74/1.93 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5155, 5156])).
% 1.74/1.93 tff(5213,plain,
% 1.74/1.93 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.74/1.93 inference(symmetry,[status(thm)],[5212])).
% 1.74/1.93 tff(5214,plain,
% 1.74/1.93 ((~b(s(s(s(z))), s(s(s(s(z)))))) <=> (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5213])).
% 1.74/1.93 tff(5215,plain,
% 1.74/1.93 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[347, 5214])).
% 1.74/1.93 tff(5216,plain,
% 1.74/1.93 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[891, 5215, 5178])).
% 1.74/1.93 tff(5217,plain,
% 1.74/1.93 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[886, 5216, 244])).
% 1.74/1.93 tff(5218,plain,
% 1.74/1.93 (b(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[664, 5217, 5167])).
% 1.74/1.93 tff(5219,plain,
% 1.74/1.93 (b(s(s(s(s(z)))), s(s(z)))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[5218, 5211])).
% 1.74/1.93 tff(5220,plain,
% 1.74/1.93 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(z)))), s(z))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[3589, 10])).
% 1.74/1.93 tff(5221,plain,
% 1.74/1.93 ((s(z) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[3595])).
% 1.74/1.93 tff(5222,plain,
% 1.74/1.93 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 1.74/1.93 inference(transitivity,[status(thm)],[5221, 1555])).
% 1.74/1.93 tff(5223,plain,
% 1.74/1.93 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5222])).
% 1.74/1.93 tff(5224,plain,
% 1.74/1.93 (~(s(s(s(elem!1))) = elem!1)),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[645, 5223])).
% 1.74/1.93 tff(5225,plain,
% 1.74/1.93 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.74/1.93 inference(symmetry,[status(thm)],[3589])).
% 1.74/1.93 tff(5226,plain,
% 1.74/1.93 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(elem!1))), elem!1)),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5225, 3595])).
% 1.74/1.93 tff(5227,plain,
% 1.74/1.93 ((~r(s(s(s(s(z)))), s(z))) <=> (~r(s(s(s(elem!1))), elem!1))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5226])).
% 1.74/1.93 tff(5228,plain,
% 1.74/1.93 (~b(s(s(s(s(z)))), z)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[5103, 306, 2284, 859, 5097, 762])).
% 1.74/1.93 tff(5229,plain,
% 1.74/1.93 (r(s(s(s(s(z)))), z)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[695, 5228])).
% 1.74/1.93 tff(5230,plain,
% 1.74/1.93 (~r(s(s(s(s(z)))), s(z))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[3408, 124, 204, 5229])).
% 1.74/1.93 tff(5231,plain,
% 1.74/1.93 (~r(s(s(s(elem!1))), elem!1)),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[5230, 5227])).
% 1.74/1.93 tff(5232,plain,
% 1.74/1.93 (b(s(s(s(elem!1))), elem!1)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1636, 5231, 5224])).
% 1.74/1.93 tff(5233,plain,
% 1.74/1.93 (b(s(s(s(s(z)))), s(z))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[5232, 5220])).
% 1.74/1.93 tff(5234,plain,
% 1.74/1.93 (~r(s(z), s(s(s(s(z)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[3419, 124, 204, 5229])).
% 1.74/1.93 tff(5235,plain,
% 1.74/1.93 ((s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[680, 43, 5234])).
% 1.74/1.93 tff(5236,plain,
% 1.74/1.93 (b(s(z), s(s(s(s(z)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[5235, 670])).
% 1.74/1.93 tff(5237,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(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)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(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)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(5238,plain,
% 1.74/1.93 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(5239,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5238])).
% 1.74/1.93 tff(5240,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.74/1.93 inference(transitivity,[status(thm)],[5239, 5237])).
% 1.74/1.93 tff(5241,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(5242,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[5241, 5240])).
% 1.74/1.93 tff(5243,plain,
% 1.74/1.93 ($false),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[5242, 306, 2284, 5236, 3455, 762, 5233])).
% 1.74/1.93 tff(5244,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~(elem!1 = s(z))) | (~r(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.93 tff(5245,plain,
% 1.74/1.93 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[5244, 5219, 2284, 5153, 204, 5210, 5207])).
% 1.74/1.93 tff(5246,plain,
% 1.74/1.93 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[5245, 5182])).
% 1.74/1.93 tff(5247,plain,
% 1.74/1.93 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[610, 5246, 5179])).
% 1.74/1.93 tff(5248,plain,
% 1.74/1.93 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[5247, 5177])).
% 1.74/1.93 tff(5249,plain,
% 1.74/1.93 (~r(s(s(s(s(z)))), s(z))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1040, 124, 5190, 5248])).
% 1.74/1.93 tff(5250,plain,
% 1.74/1.93 (~r(s(s(s(elem!1))), elem!1)),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[5249, 5176])).
% 1.74/1.93 tff(5251,plain,
% 1.74/1.93 (b(s(s(s(elem!1))), elem!1)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1636, 5250, 5174])).
% 1.74/1.93 tff(5252,plain,
% 1.74/1.93 (b(s(s(s(s(z)))), s(z))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[5251, 5169])).
% 1.74/1.93 tff(5253,plain,
% 1.74/1.93 (~r(s(z), s(s(s(s(z)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[3585, 124, 5190, 5248])).
% 1.74/1.93 tff(5254,plain,
% 1.74/1.93 ((s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[680, 43, 5253])).
% 1.74/1.93 tff(5255,plain,
% 1.74/1.93 (b(s(z), s(s(s(s(z)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[5254, 670])).
% 1.74/1.93 tff(5256,plain,
% 1.74/1.93 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[3629, 5255, 2284, 5210, 5252, 204, 5153])).
% 1.74/1.93 tff(5257,plain,
% 1.74/1.93 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[3591])).
% 1.74/1.93 tff(5258,plain,
% 1.74/1.93 (b(s(s(s(s(elem!1)))), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.74/1.93 inference(symmetry,[status(thm)],[5257])).
% 1.74/1.93 tff(5259,plain,
% 1.74/1.93 (b(s(s(s(s(elem!1)))), s(s(elem!1))) <=> b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[15])).
% 1.74/1.93 tff(5260,plain,
% 1.74/1.93 (b(s(s(s(s(elem!1)))), s(s(elem!1))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.74/1.93 inference(transitivity,[status(thm)],[5259, 5258])).
% 1.74/1.93 tff(5261,plain,
% 1.74/1.93 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[1973, 5260])).
% 1.74/1.93 tff(5262,assumption,(~b(s(s(s(s(s(z))))), s(s(s(z))))), introduced(assumption)).
% 1.74/1.93 tff(5263,plain,
% 1.74/1.93 ($false),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[5262, 5261])).
% 1.74/1.93 tff(5264,plain,((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | b(s(s(s(s(s(z))))), s(s(s(z)))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.93 tff(5265,plain,
% 1.74/1.93 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[5264, 5256, 5153])).
% 1.74/1.93 tff(5266,plain,
% 1.74/1.93 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1302, 5265, 5168])).
% 1.74/1.93 tff(5267,plain,
% 1.74/1.93 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[5266, 5162])).
% 1.74/1.93 tff(5268,plain,
% 1.74/1.93 ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[3661, 124, 5248])).
% 1.74/1.93 tff(5269,plain,
% 1.74/1.93 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[5268, 5267])).
% 1.74/1.93 tff(5270,plain,
% 1.74/1.93 (b(s(z), s(s(s(s(s(z)))))) <=> b(s(z), s(s(s(s(elem!1)))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5160])).
% 1.74/1.93 tff(5271,plain,
% 1.74/1.93 (b(s(z), s(s(s(s(elem!1))))) <=> b(s(z), s(s(s(s(s(z))))))),
% 1.74/1.93 inference(symmetry,[status(thm)],[5270])).
% 1.74/1.93 tff(5272,plain,
% 1.74/1.93 (b(elem!1, s(s(s(s(elem!1))))) <=> b(s(z), s(s(s(s(elem!1)))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5153])).
% 1.74/1.93 tff(5273,plain,
% 1.74/1.93 ((s(s(s(s(s(z))))) = s(z)) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5160, 5170])).
% 1.74/1.93 tff(5274,plain,
% 1.74/1.93 ((s(s(s(s(s(z))))) = s(z)) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.74/1.93 inference(transitivity,[status(thm)],[5273, 1542])).
% 1.74/1.93 tff(5275,plain,
% 1.74/1.93 ((~(s(s(s(s(s(z))))) = s(z))) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5274])).
% 1.74/1.93 tff(5276,plain,
% 1.74/1.93 (~(elem!1 = s(s(s(s(elem!1)))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[500, 5275])).
% 1.74/1.93 tff(5277,plain,
% 1.74/1.93 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1918, 5266, 5191])).
% 1.74/1.93 tff(5278,plain,
% 1.74/1.93 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1923, 5277, 5276])).
% 1.74/1.93 tff(5279,plain,
% 1.74/1.93 (b(s(z), s(s(s(s(elem!1)))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[5278, 5272])).
% 1.74/1.93 tff(5280,plain,
% 1.74/1.93 (b(s(z), s(s(s(s(s(z))))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[5279, 5271])).
% 1.74/1.93 tff(5281,plain,
% 1.74/1.93 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(s(s(elem!1)))), s(z))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5160])).
% 1.74/1.93 tff(5282,plain,
% 1.74/1.93 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(s(s(s(s(z))))), s(z))),
% 1.74/1.93 inference(symmetry,[status(thm)],[5281])).
% 1.74/1.93 tff(5283,plain,
% 1.74/1.93 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(elem!1)))), s(z))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5153])).
% 1.74/1.93 tff(5284,plain,
% 1.74/1.93 ((s(s(s(s(s(z))))) = s(z)) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.74/1.93 inference(transitivity,[status(thm)],[5274, 1543])).
% 1.74/1.93 tff(5285,plain,
% 1.74/1.93 ((~(s(s(s(s(s(z))))) = s(z))) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5284])).
% 1.74/1.93 tff(5286,plain,
% 1.74/1.93 (~(s(s(s(s(elem!1)))) = elem!1)),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[500, 5285])).
% 1.74/1.93 tff(5287,plain,
% 1.74/1.93 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1297, 5266, 5191])).
% 1.74/1.93 tff(5288,plain,
% 1.74/1.93 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1736, 5287, 5286])).
% 1.74/1.93 tff(5289,plain,
% 1.74/1.93 (b(s(s(s(s(elem!1)))), s(z))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[5288, 5283])).
% 1.74/1.93 tff(5290,plain,
% 1.74/1.93 (b(s(s(s(s(s(z))))), s(z))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[5289, 5282])).
% 1.74/1.93 tff(5291,plain,
% 1.74/1.93 ((~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(s(z)))))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[3652, 306, 5252])).
% 1.74/1.93 tff(5292,plain,
% 1.74/1.93 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[5291, 5290, 5280])).
% 1.74/1.93 tff(5293,plain,
% 1.74/1.93 (s(s(s(s(s(z))))) = s(s(s(s(z))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[3665, 43, 5292, 5269])).
% 1.74/1.93 tff(5294,plain,
% 1.74/1.93 (s(s(s(s(s(s(z)))))) = s(s(s(s(s(z)))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5293])).
% 1.74/1.93 tff(5295,plain,
% 1.74/1.93 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(s(z))))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5159])).
% 1.74/1.93 tff(5296,plain,
% 1.74/1.93 (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))),
% 1.74/1.93 inference(transitivity,[status(thm)],[5295, 5294, 5293, 5157])).
% 1.74/1.93 tff(5297,plain,
% 1.74/1.93 (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1719, 5168])).
% 1.74/1.93 tff(5298,plain,
% 1.74/1.93 ($false),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[5297, 5296])).
% 1.74/1.93 tff(5299,plain,((~r(elem!1, z)) | (~b(s(s(s(z))), s(z))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(elem!1))) | b(s(s(s(z))), s(s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.93 tff(5300,plain,
% 1.74/1.93 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[5299, 5146, 5034, 5018, 5033, 5, 2283])).
% 1.74/1.93 tff(5301,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(5302,plain,
% 1.74/1.93 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(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(z)))), s(s(z)))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(5303,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(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(z)))), s(s(z))))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[5302])).
% 1.74/1.94 tff(5304,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(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(z)))), s(s(z)))))),
% 1.74/1.94 inference(transitivity,[status(thm)],[5303, 5301])).
% 1.74/1.94 tff(5305,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(5306,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[5305, 5304])).
% 1.74/1.94 tff(5307,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5306, 306, 2283, 5300, 5151, 5149, 5111])).
% 1.74/1.94 tff(5308,plain,(b(elem!1, s(s(s(z)))) | (~r(s(z), s(s(s(z))))) | b(elem!1, s(z)) | b(elem!1, z) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(5309,plain,
% 1.74/1.94 (b(elem!1, s(s(s(z))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5308, 5, 5008, 2, 6])).
% 1.74/1.94 tff(5310,plain,
% 1.74/1.94 (b(z, s(s(s(z))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[5309, 5011])).
% 1.74/1.94 tff(5311,plain,
% 1.74/1.94 (s(s(elem!1)) = s(s(z))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[3069])).
% 1.74/1.94 tff(5312,plain,
% 1.74/1.94 (b(s(s(elem!1)), z) <=> b(s(s(z)), z)),
% 1.74/1.94 inference(monotonicity,[status(thm)],[5311])).
% 1.74/1.94 tff(5313,plain,
% 1.74/1.94 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), z)),
% 1.74/1.94 inference(monotonicity,[status(thm)],[3063])).
% 1.74/1.94 tff(5314,plain,
% 1.74/1.94 (b(s(s(elem!1)), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[47, 3068, 6])).
% 1.74/1.94 tff(5315,plain,
% 1.74/1.94 (b(s(s(elem!1)), z)),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[5314, 5313])).
% 1.74/1.94 tff(5316,plain,
% 1.74/1.94 (b(s(s(z)), z)),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[5315, 5312])).
% 1.74/1.94 tff(5317,plain,
% 1.74/1.94 (b(elem!1, s(s(s(z))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5308, 5, 1034, 2, 6])).
% 1.74/1.94 tff(5318,assumption,(~b(z, elem!1)), introduced(assumption)).
% 1.74/1.94 tff(5319,plain,
% 1.74/1.94 (b(s(s(s(z))), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2219, 1629, 2, 1484])).
% 1.74/1.94 tff(5320,plain,
% 1.74/1.94 (b(s(s(s(z))), z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2197, 1629])).
% 1.74/1.94 tff(5321,plain,
% 1.74/1.94 (r(s(s(s(z))), s(z)) <=> r(elem!1, s(z))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[1430])).
% 1.74/1.94 tff(5322,plain,
% 1.74/1.94 (r(elem!1, s(z)) <=> r(s(s(s(z))), s(z))),
% 1.74/1.94 inference(symmetry,[status(thm)],[5321])).
% 1.74/1.94 tff(5323,plain,
% 1.74/1.94 ((~r(elem!1, s(z))) <=> (~r(s(s(s(z))), s(z)))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[5322])).
% 1.74/1.94 tff(5324,plain,
% 1.74/1.94 (~r(s(s(s(z))), s(z))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[2607, 5323])).
% 1.74/1.94 tff(5325,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[206, 5324])).
% 1.74/1.94 tff(5326,plain,((~(s(s(s(z))) = elem!1)) | (~r(s(s(s(z))), s(z))) | r(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(5327,plain,
% 1.74/1.94 (~(s(s(s(z))) = elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5326, 2607, 114])).
% 1.74/1.94 tff(5328,plain,
% 1.74/1.94 (b(s(s(s(z))), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1489, 5327, 1484])).
% 1.74/1.94 tff(5329,plain,
% 1.74/1.94 (~(s(z) = elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2235, 5328, 9])).
% 1.74/1.94 tff(5330,plain,
% 1.74/1.94 (r(z, elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[835, 2170, 5318])).
% 1.74/1.94 tff(5331,plain,
% 1.74/1.94 (~(elem!1 = s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[3096, 3094])).
% 1.74/1.94 tff(5332,plain,
% 1.74/1.94 ((elem!1 = s(z)) | b(elem!1, s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[96, 43, 2607])).
% 1.74/1.94 tff(5333,plain,
% 1.74/1.94 (b(elem!1, s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5332, 5331])).
% 1.74/1.94 tff(5334,plain,
% 1.74/1.94 (~(s(s(s(z))) = elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5326, 2607, 206])).
% 1.74/1.94 tff(5335,plain,
% 1.74/1.94 (b(s(s(s(z))), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1489, 5334, 1484])).
% 1.74/1.94 tff(5336,assumption,(r(s(s(s(s(s(s(z)))))), s(s(s(z))))), introduced(assumption)).
% 1.74/1.94 tff(5337,plain,
% 1.74/1.94 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(5338,plain,
% 1.74/1.94 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(5339,plain,
% 1.74/1.94 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(z)))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[5338, 5337])).
% 1.74/1.94 tff(5340,plain,
% 1.74/1.94 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5339, 124, 1034, 5336])).
% 1.74/1.94 tff(5341,plain,
% 1.74/1.94 (b(s(s(s(s(s(s(z)))))), s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[651, 43, 2844, 5340])).
% 1.74/1.94 tff(5342,plain,
% 1.74/1.94 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(5343,plain,
% 1.74/1.94 (((~r(s(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(s(z))))))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(5344,plain,
% 1.74/1.94 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(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(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(z))))))))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[5343])).
% 1.74/1.94 tff(5345,plain,
% 1.74/1.94 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(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(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 1.74/1.94 inference(transitivity,[status(thm)],[5344, 5342])).
% 1.74/1.94 tff(5346,plain,
% 1.74/1.94 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(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(s(z)))))))))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(5347,plain,
% 1.74/1.94 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(z))))))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[5346, 5345])).
% 1.74/1.94 tff(5348,plain,
% 1.74/1.94 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5347, 124, 1034, 5336])).
% 1.74/1.94 tff(5349,plain,
% 1.74/1.94 ((s(z) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = s(z))),
% 1.74/1.94 inference(commutativity,[status(thm)],[])).
% 1.74/1.94 tff(5350,assumption,(s(z) = s(s(s(s(s(s(z))))))), introduced(assumption)).
% 1.74/1.94 tff(5351,plain,
% 1.74/1.94 (s(s(s(s(s(s(z)))))) = s(z)),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[5350, 5349])).
% 1.74/1.94 tff(5352,assumption,(~(s(s(s(s(s(s(z)))))) = s(z))), introduced(assumption)).
% 1.74/1.94 tff(5353,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5352, 5351])).
% 1.74/1.94 tff(5354,plain,((~(s(z) = s(s(s(s(s(s(z)))))))) | (s(s(s(s(s(s(z)))))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(5355,plain,
% 1.74/1.94 (~(s(z) = s(s(s(s(s(s(z)))))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5354, 2844])).
% 1.74/1.94 tff(5356,plain,
% 1.74/1.94 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(s(s(z))))))) | b(s(z), s(s(s(s(s(s(z))))))) | r(s(z), s(s(s(s(s(s(z))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(s(s(z))))))) | b(s(z), s(s(s(s(s(s(z))))))) | r(s(z), s(s(s(s(s(s(z))))))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(5357,plain,
% 1.74/1.94 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(s(s(z))))))) | b(s(z), s(s(s(s(s(s(z))))))) | r(s(z), s(s(s(s(s(s(z))))))))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(5358,plain,
% 1.74/1.94 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(s(s(z))))))) | b(s(z), s(s(s(s(s(s(z))))))) | r(s(z), s(s(s(s(s(s(z)))))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[5357, 5356])).
% 1.74/1.94 tff(5359,plain,
% 1.74/1.94 (b(s(z), s(s(s(s(s(s(z)))))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5358, 43, 5355, 5348])).
% 1.74/1.94 tff(5360,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(5361,plain,
% 1.74/1.94 (((~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(5362,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[5361])).
% 1.74/1.94 tff(5363,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.74/1.94 inference(transitivity,[status(thm)],[5362, 5360])).
% 1.74/1.94 tff(5364,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(5365,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[5364, 5363])).
% 1.74/1.94 tff(5366,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5365, 306, 4346, 2812, 5359, 5341])).
% 1.74/1.94 tff(5367,plain,((~r(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(5368,plain,
% 1.74/1.94 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5367, 2812, 1034, 4346])).
% 1.74/1.94 tff(5369,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(5370,plain,
% 1.74/1.94 (((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(5371,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), elem!1))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[5370])).
% 1.74/1.94 tff(5372,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.74/1.94 inference(transitivity,[status(thm)],[5371, 5369])).
% 1.74/1.94 tff(5373,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(5374,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), elem!1))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[5373, 5372])).
% 1.74/1.94 tff(5375,plain,
% 1.74/1.94 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5374, 306, 2831, 1967, 4346, 2812])).
% 1.74/1.94 tff(5376,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[4603, 43, 5375, 5368, 4577])).
% 1.74/1.94 tff(5377,plain,((~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(5378,plain,
% 1.74/1.94 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5377, 2831, 1967, 4346, 1034])).
% 1.74/1.94 tff(5379,plain,
% 1.74/1.94 ((s(s(z)) = s(s(s(s(s(s(z))))))) <=> (s(s(z)) = elem!1)),
% 1.74/1.94 inference(monotonicity,[status(thm)],[4273])).
% 1.74/1.94 tff(5380,plain,
% 1.74/1.94 ((~(s(s(z)) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(z)) = elem!1))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[5379])).
% 1.74/1.94 tff(5381,plain,
% 1.74/1.94 (~(s(s(z)) = elem!1)),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[2826, 5380])).
% 1.74/1.94 tff(5382,plain,
% 1.74/1.94 (s(s(z)) = elem!1),
% 1.74/1.94 inference(transitivity,[status(thm)],[103, 2353, 135])).
% 1.74/1.94 tff(5383,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2448, 5382])).
% 1.74/1.94 tff(5384,plain,((~(s(elem!1) = s(s(s(z))))) | (s(s(z)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(5385,plain,
% 1.74/1.94 (~(s(elem!1) = s(s(s(z))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5384, 5381])).
% 1.74/1.94 tff(5386,plain,
% 1.74/1.94 (s(elem!1) = s(s(s(elem!1)))),
% 1.74/1.94 inference(symmetry,[status(thm)],[2597])).
% 1.74/1.94 tff(5387,plain,
% 1.74/1.94 (s(s(elem!1)) = elem!1),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[143, 2597])).
% 1.74/1.94 tff(5388,plain,
% 1.74/1.94 (elem!1 = s(s(elem!1))),
% 1.74/1.94 inference(symmetry,[status(thm)],[5387])).
% 1.74/1.94 tff(5389,plain,
% 1.74/1.94 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 1.74/1.94 inference(transitivity,[status(thm)],[4273, 5388])).
% 1.74/1.94 tff(5390,plain,
% 1.74/1.94 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(elem!1)))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[5389])).
% 1.74/1.94 tff(5391,plain,
% 1.74/1.94 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 1.74/1.94 inference(transitivity,[status(thm)],[2823, 5390, 66, 5386, 155])).
% 1.74/1.94 tff(5392,plain,
% 1.74/1.94 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(elem!1)))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[5391])).
% 1.74/1.94 tff(5393,plain,
% 1.74/1.94 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.74/1.94 inference(transitivity,[status(thm)],[497, 5392, 66, 5386, 155])).
% 1.74/1.94 tff(5394,plain,
% 1.74/1.94 (inj_0(s(s(s(s(z))))) = inj_0(s(s(elem!1)))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[5393])).
% 1.74/1.94 tff(5395,plain,
% 1.74/1.94 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(z)))))),
% 1.74/1.94 inference(symmetry,[status(thm)],[5394])).
% 1.74/1.94 tff(5396,plain,
% 1.74/1.94 (s(s(elem!1)) = s(s(s(z)))),
% 1.74/1.94 inference(transitivity,[status(thm)],[2598, 2597, 67, 5395, 320])).
% 1.74/1.94 tff(5397,plain,
% 1.74/1.94 (s(elem!1) = s(s(elem!1))),
% 1.74/1.94 inference(transitivity,[status(thm)],[5386, 155])).
% 1.74/1.94 tff(5398,plain,
% 1.74/1.94 ((s(elem!1) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[5397])).
% 1.74/1.94 tff(5399,plain,
% 1.74/1.94 ((~(s(elem!1) = s(s(s(z))))) <=> (~(s(s(elem!1)) = s(s(s(z)))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[5398])).
% 1.74/1.94 tff(5400,plain,
% 1.74/1.94 (~(s(elem!1) = s(s(s(z))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2356, 5387])).
% 1.74/1.94 tff(5401,plain,
% 1.74/1.94 (~(s(s(elem!1)) = s(s(s(z))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[5400, 5399])).
% 1.74/1.94 tff(5402,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5401, 5396])).
% 1.74/1.94 tff(5403,plain,((~(s(s(s(s(s(s(z)))))) = elem!1)) | (~(s(s(s(elem!1))) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(5404,plain,
% 1.74/1.94 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5403, 4273])).
% 1.74/1.94 tff(5405,plain,
% 1.74/1.94 (~(s(elem!1) = elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2436, 5404])).
% 1.74/1.94 tff(5406,plain,
% 1.74/1.94 (b(s(elem!1), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[813, 5405, 808])).
% 1.74/1.94 tff(5407,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(5408,plain,
% 1.74/1.95 (((~b(s(z), elem!1)) | (~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(s(z), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(5409,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[5408])).
% 1.74/1.95 tff(5410,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.74/1.95 inference(transitivity,[status(thm)],[5409, 5407])).
% 1.74/1.95 tff(5411,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~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))))))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(5412,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[5411, 5410])).
% 1.74/1.95 tff(5413,plain,
% 1.74/1.95 (~b(s(elem!1), s(s(s(z))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[5412, 306, 5406, 2831, 1967, 4346])).
% 1.74/1.95 tff(5414,plain,
% 1.74/1.95 (r(s(elem!1), s(s(s(z))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2367, 43, 5413, 5385])).
% 1.74/1.95 tff(5415,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(5416,plain,
% 1.74/1.95 (((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), elem!1))) <=> ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(5417,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z)))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[5416])).
% 1.74/1.95 tff(5418,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[5417, 5415])).
% 1.74/1.95 tff(5419,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), elem!1)))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(5420,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z)))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[5419, 5418])).
% 1.74/1.95 tff(5421,plain,
% 1.74/1.95 ($false),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[5420, 306, 816, 2831, 4346, 2647])).
% 1.74/1.95 tff(5422,plain,((~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.95 tff(5423,plain,
% 1.74/1.95 (~b(s(elem!1), s(z))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[5422, 5406, 2831, 4346])).
% 1.74/1.95 tff(5424,plain,
% 1.74/1.95 (r(s(elem!1), s(z))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2964, 5423, 2249])).
% 1.74/1.95 tff(5425,plain,
% 1.74/1.95 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(5426,plain,
% 1.74/1.95 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(5427,plain,
% 1.74/1.95 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z)))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[5426, 5425])).
% 1.74/1.95 tff(5428,plain,
% 1.74/1.95 ($false),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[5427, 124, 206, 5424, 5414])).
% 1.74/1.95 tff(5429,plain,((~(s(s(s(s(s(s(z)))))) = elem!1)) | (~r(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (s(elem!1) = s(z)) | r(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.95 tff(5430,plain,
% 1.74/1.95 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[5429, 808, 2831, 1967, 4346, 3099, 206])).
% 1.74/1.95 tff(5431,plain,
% 1.74/1.95 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1144, 5430, 5378])).
% 1.74/1.95 tff(5432,plain,
% 1.74/1.95 ((z = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = z)),
% 1.74/1.95 inference(commutativity,[status(thm)],[])).
% 1.74/1.95 tff(5433,plain,
% 1.74/1.95 ((s(s(s(s(s(s(z)))))) = z) <=> (z = s(s(s(s(s(s(z)))))))),
% 1.74/1.95 inference(symmetry,[status(thm)],[5432])).
% 1.74/1.95 tff(5434,plain,
% 1.74/1.95 ((~(s(s(s(s(s(s(z)))))) = z)) <=> (~(z = s(s(s(s(s(s(z))))))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[5433])).
% 1.74/1.95 tff(5435,plain,
% 1.74/1.95 (~(z = s(s(s(s(s(s(z)))))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[554, 5434])).
% 1.74/1.95 tff(5436,plain,
% 1.74/1.95 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(5437,plain,
% 1.74/1.95 (((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(s(z))))))))) <=> ((~r(z, elem!1)) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(5438,plain,
% 1.74/1.95 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), elem!1))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[5437])).
% 1.74/1.95 tff(5439,plain,
% 1.74/1.95 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.74/1.95 inference(transitivity,[status(thm)],[5438, 5436])).
% 1.74/1.95 tff(5440,plain,
% 1.74/1.95 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(5441,plain,
% 1.74/1.95 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), elem!1))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[5440, 5439])).
% 1.74/1.95 tff(5442,plain,
% 1.74/1.95 (~r(z, s(s(s(s(s(s(z)))))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[5441, 124, 374, 2858])).
% 1.74/1.95 tff(5443,plain,
% 1.74/1.95 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(s(s(z))))))) | b(z, s(s(s(s(s(s(z))))))) | r(z, s(s(s(s(s(s(z))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(s(s(z))))))) | b(z, s(s(s(s(s(s(z))))))) | r(z, s(s(s(s(s(s(z))))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(5444,plain,
% 1.74/1.95 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(s(s(z))))))) | b(z, s(s(s(s(s(s(z))))))) | r(z, s(s(s(s(s(s(z))))))))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(5445,plain,
% 1.74/1.95 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(s(s(z))))))) | b(z, s(s(s(s(s(s(z))))))) | r(z, s(s(s(s(s(s(z)))))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[5444, 5443])).
% 1.74/1.95 tff(5446,plain,
% 1.74/1.95 ((z = s(s(s(s(s(s(z))))))) | b(z, s(s(s(s(s(s(z)))))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[5445, 43, 5442])).
% 1.74/1.95 tff(5447,plain,
% 1.74/1.95 (b(z, s(s(s(s(s(s(z)))))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[5446, 5435])).
% 1.74/1.95 tff(5448,plain,
% 1.74/1.95 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), z)))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(5449,plain,
% 1.74/1.95 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), z)))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(5450,plain,
% 1.74/1.95 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), z))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[5449, 5448])).
% 1.74/1.95 tff(5451,plain,
% 1.74/1.95 ($false),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[5450, 124, 374, 2858, 3194])).
% 1.74/1.95 tff(5452,plain,((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(z)))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.95 tff(5453,plain,
% 1.74/1.95 (~r(s(s(s(s(s(s(z)))))), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[5452, 2858, 374])).
% 1.74/1.95 tff(5454,plain,
% 1.74/1.95 (b(s(s(s(s(s(s(z)))))), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[4232, 5453])).
% 1.74/1.95 tff(5455,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(5456,plain,
% 1.74/1.95 (((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(5457,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z))))))))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[5456])).
% 1.74/1.95 tff(5458,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[5457, 5455])).
% 1.74/1.95 tff(5459,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(5460,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z))))))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[5459, 5458])).
% 1.74/1.95 tff(5461,plain,
% 1.74/1.95 ($false),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[5460, 306, 1531, 1330, 5454, 5447])).
% 1.74/1.95 tff(5462,plain,((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.95 tff(5463,plain,
% 1.74/1.95 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[5462, 5431, 1531, 374])).
% 1.74/1.95 tff(5464,plain,
% 1.74/1.95 (((~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(5465,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z))))))))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[5464])).
% 1.74/1.95 tff(5466,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[5465, 5455])).
% 1.74/1.95 tff(5467,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(5468,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z))))))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[5467, 5466])).
% 1.74/1.95 tff(5469,plain,
% 1.74/1.95 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[5468, 306, 1531, 5454, 5447])).
% 1.74/1.95 tff(5470,plain,
% 1.74/1.95 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[4603, 43, 5469, 4577])).
% 1.74/1.95 tff(5471,plain,
% 1.74/1.95 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[5339, 124, 1034, 5470])).
% 1.74/1.95 tff(5472,plain,
% 1.74/1.95 (b(s(s(s(s(s(s(z)))))), s(z))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[651, 43, 2844, 5471])).
% 1.74/1.95 tff(5473,plain,
% 1.74/1.95 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[5347, 124, 1034, 5470])).
% 1.74/1.95 tff(5474,plain,
% 1.74/1.95 (b(s(z), s(s(s(s(s(s(z)))))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[5358, 43, 5355, 5473])).
% 1.74/1.95 tff(5475,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(5476,plain,
% 1.74/1.95 (((~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), z))) <=> ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(5477,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z))))))))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[5476])).
% 1.74/1.95 tff(5478,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[5477, 5475])).
% 1.74/1.95 tff(5479,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), z)))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(5480,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z))))))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[5479, 5478])).
% 1.74/1.96 tff(5481,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[5480, 306, 2831, 247, 5474, 5472, 5447])).
% 1.74/1.96 tff(5482,plain,((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(5483,plain,
% 1.74/1.96 (~b(s(z), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[5482, 5431, 2831, 1034, 1531, 374])).
% 1.74/1.96 tff(5484,plain,
% 1.74/1.96 (r(s(z), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[221, 5483])).
% 1.74/1.96 tff(5485,plain,
% 1.74/1.96 (~(s(s(z)) = elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[2398, 176, 87])).
% 1.74/1.96 tff(5486,plain,
% 1.74/1.96 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[4603, 43, 2885, 4577])).
% 1.74/1.96 tff(5487,plain,
% 1.74/1.96 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(5488,plain,
% 1.74/1.96 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(5489,plain,
% 1.74/1.96 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[5488, 5487])).
% 1.74/1.96 tff(5490,plain,
% 1.74/1.96 (~r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[5489, 124, 2516, 5336])).
% 1.74/1.96 tff(5491,plain,
% 1.74/1.96 (b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[2829, 43, 2826, 5490])).
% 1.74/1.96 tff(5492,plain,
% 1.74/1.96 (~r(s(s(z)), s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[3833, 2516, 1034])).
% 1.74/1.96 tff(5493,plain,
% 1.74/1.96 (b(s(s(z)), s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[2476, 5492])).
% 1.74/1.96 tff(5494,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(5495,plain,
% 1.74/1.96 (((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(5496,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[5495])).
% 1.74/1.96 tff(5497,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.74/1.96 inference(transitivity,[status(thm)],[5496, 5494])).
% 1.74/1.96 tff(5498,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(5499,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[5498, 5497])).
% 1.74/1.96 tff(5500,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[5499, 306, 2831, 4346, 5493, 5341, 5491])).
% 1.74/1.96 tff(5501,plain,((~r(s(s(z)), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(5502,plain,
% 1.74/1.96 (~r(s(s(z)), s(s(s(z))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[5501, 5486, 4346, 2831, 1034])).
% 1.74/1.96 tff(5503,plain,
% 1.74/1.96 (b(s(s(z)), s(s(s(z))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[2514, 5502])).
% 1.74/1.96 tff(5504,plain,
% 1.74/1.96 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[5403, 2434])).
% 1.74/1.96 tff(5505,plain,
% 1.74/1.96 (~(elem!1 = s(s(s(s(s(s(z)))))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[5504, 3893])).
% 1.74/1.96 tff(5506,plain,
% 1.74/1.96 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[5339, 124, 1034, 5486])).
% 1.74/1.96 tff(5507,plain,
% 1.74/1.96 (b(s(s(s(s(s(s(z)))))), s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[651, 43, 2844, 5506])).
% 1.74/1.96 tff(5508,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(5509,plain,
% 1.74/1.96 (((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(s(s(z))))))))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(5510,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(elem!1, s(s(s(s(s(s(z))))))))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[5509])).
% 1.74/1.96 tff(5511,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.74/1.96 inference(transitivity,[status(thm)],[5510, 5508])).
% 1.74/1.96 tff(5512,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(5513,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(elem!1, s(s(s(s(s(s(z))))))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[5512, 5511])).
% 1.74/1.96 tff(5514,plain,
% 1.74/1.96 (~b(elem!1, s(s(s(s(s(s(z)))))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[5513, 306, 2831, 4346, 5507])).
% 1.74/1.96 tff(5515,plain,
% 1.74/1.96 ((elem!1 = s(s(s(s(s(s(z))))))) | r(elem!1, s(s(s(s(s(s(z)))))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[3921, 43, 5514])).
% 1.74/1.96 tff(5516,plain,
% 1.74/1.96 (r(elem!1, s(s(s(s(s(s(z)))))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[5515, 5505])).
% 1.74/1.96 tff(5517,plain,
% 1.74/1.96 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1144, 5504, 5378])).
% 1.74/1.96 tff(5518,plain,
% 1.74/1.96 (~r(z, s(s(s(s(s(s(z)))))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[5441, 124, 374, 5517])).
% 1.74/1.96 tff(5519,plain,
% 1.74/1.96 ((z = s(s(s(s(s(s(z))))))) | b(z, s(s(s(s(s(s(z)))))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[5445, 43, 5518])).
% 1.74/1.96 tff(5520,plain,
% 1.74/1.96 (b(z, s(s(s(s(s(s(z)))))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[5519, 5435])).
% 1.74/1.96 tff(5521,plain,
% 1.74/1.96 (~r(s(s(s(s(s(s(z)))))), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[5452, 5517, 374])).
% 1.74/1.96 tff(5522,plain,
% 1.74/1.96 (b(s(s(s(s(s(s(z)))))), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[4232, 5521])).
% 1.74/1.96 tff(5523,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(5524,plain,
% 1.74/1.96 (((~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(5525,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[5524])).
% 1.74/1.96 tff(5526,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.74/1.96 inference(transitivity,[status(thm)],[5525, 5523])).
% 1.74/1.96 tff(5527,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(5528,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[5527, 5526])).
% 1.74/1.96 tff(5529,plain,
% 1.74/1.96 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[5528, 306, 1531, 5522, 5520])).
% 1.74/1.96 tff(5530,plain,
% 1.74/1.96 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[3207, 5529])).
% 1.74/1.96 tff(5531,plain,
% 1.74/1.96 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(5532,plain,
% 1.74/1.96 (((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(z)))))) <=> ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(5533,plain,
% 1.74/1.96 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(s(s(z))))))))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[5532])).
% 1.74/1.96 tff(5534,plain,
% 1.74/1.96 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.74/1.96 inference(transitivity,[status(thm)],[5533, 5531])).
% 1.74/1.96 tff(5535,plain,
% 1.74/1.96 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(z))))))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(5536,plain,
% 1.74/1.96 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(s(s(z))))))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[5535, 5534])).
% 1.74/1.96 tff(5537,plain,
% 1.74/1.96 (~r(elem!1, s(s(s(z))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[5536, 124, 5530, 5516])).
% 1.74/1.96 tff(5538,plain,
% 1.74/1.96 (b(elem!1, s(s(s(z))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[2304, 5537, 2301])).
% 1.74/1.96 tff(5539,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(5540,plain,
% 1.74/1.96 (((~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1))) <=> ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(5541,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[5540])).
% 1.74/1.96 tff(5542,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 1.74/1.96 inference(transitivity,[status(thm)],[5541, 5539])).
% 1.74/1.96 tff(5543,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(5544,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[5543, 5542])).
% 1.74/1.96 tff(5545,plain,
% 1.74/1.96 (~b(s(s(z)), elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[5544, 306, 1967, 4346, 5538, 5503])).
% 1.74/1.96 tff(5546,assumption,(~r(s(s(z)), elem!1)), introduced(assumption)).
% 1.74/1.96 tff(5547,plain,
% 1.74/1.96 (~r(s(s(z)), s(elem!1))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[5546, 2452])).
% 1.74/1.96 tff(5548,plain,
% 1.74/1.96 (b(s(s(z)), s(elem!1)) <=> b(s(s(z)), elem!1)),
% 1.74/1.96 inference(monotonicity,[status(thm)],[176])).
% 1.74/1.96 tff(5549,plain,
% 1.74/1.96 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(elem!1))),
% 1.74/1.96 inference(symmetry,[status(thm)],[5548])).
% 1.74/1.96 tff(5550,plain,
% 1.74/1.96 ((~b(s(s(z)), elem!1)) <=> (~b(s(s(z)), s(elem!1)))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[5549])).
% 1.74/1.96 tff(5551,assumption,(~b(s(s(z)), elem!1)), introduced(assumption)).
% 1.74/1.96 tff(5552,plain,
% 1.74/1.96 (~b(s(s(z)), s(elem!1))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[5551, 5550])).
% 1.74/1.96 tff(5553,plain,
% 1.74/1.96 ((s(s(z)) = s(elem!1)) | b(s(s(z)), s(elem!1)) | r(s(s(z)), s(elem!1))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[2496, 43])).
% 1.74/1.96 tff(5554,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[5553, 5552, 2449, 5547])).
% 1.74/1.96 tff(5555,plain,(b(s(s(z)), elem!1) | r(s(s(z)), elem!1) | (~(s(elem!1) = elem!1)) | (s(s(z)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(5556,plain,
% 1.74/1.96 (r(s(s(z)), elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[5555, 5545, 176, 5485])).
% 1.74/1.96 tff(5557,plain,
% 1.74/1.96 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[5347, 124, 1034, 5486])).
% 1.74/1.96 tff(5558,plain,
% 1.74/1.96 (b(s(z), s(s(s(s(s(s(z)))))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[5358, 43, 5355, 5557])).
% 1.74/1.96 tff(5559,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(5560,plain,
% 1.74/1.97 (((~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(z)))) <=> ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(5561,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z))))))))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[5560])).
% 1.74/1.97 tff(5562,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 1.74/1.97 inference(transitivity,[status(thm)],[5561, 5559])).
% 1.74/1.97 tff(5563,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(z))))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(5564,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z))))))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[5563, 5562])).
% 1.74/1.97 tff(5565,plain,
% 1.74/1.97 (~b(z, s(z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5564, 306, 2831, 5558, 5507, 5520])).
% 1.74/1.97 tff(5566,plain,
% 1.74/1.97 (r(z, s(z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[2263, 5565])).
% 1.74/1.97 tff(5567,plain,
% 1.74/1.97 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(5568,plain,
% 1.74/1.97 (((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(5569,plain,
% 1.74/1.97 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z)))))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[5568])).
% 1.74/1.97 tff(5570,plain,
% 1.74/1.97 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))))),
% 1.74/1.97 inference(transitivity,[status(thm)],[5569, 5567])).
% 1.74/1.97 tff(5571,plain,
% 1.74/1.97 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(5572,plain,
% 1.74/1.97 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z)))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[5571, 5570])).
% 1.74/1.97 tff(5573,plain,
% 1.74/1.97 (~r(z, s(s(s(z))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5572, 124, 206, 5566])).
% 1.74/1.97 tff(5574,plain,
% 1.74/1.97 (b(z, s(s(s(z))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[2415, 43, 5573, 2405])).
% 1.74/1.97 tff(5575,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(5576,plain,
% 1.74/1.97 (((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z))) <=> ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(5577,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[5576])).
% 1.74/1.97 tff(5578,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.74/1.97 inference(transitivity,[status(thm)],[5577, 5575])).
% 1.74/1.97 tff(5579,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(5580,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[5579, 5578])).
% 1.74/1.97 tff(5581,plain,
% 1.74/1.97 ($false),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5580, 306, 1967, 2061, 859, 1470, 2454])).
% 1.74/1.97 tff(5582,plain,((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.97 tff(5583,plain,
% 1.74/1.97 (~b(s(s(z)), z)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5582, 5503, 5574, 1967, 5538])).
% 1.74/1.97 tff(5584,plain,
% 1.74/1.97 (r(s(s(z)), z)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[2531, 5583])).
% 1.74/1.97 tff(5585,plain,
% 1.74/1.97 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(5586,plain,
% 1.74/1.97 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(5587,plain,
% 1.74/1.97 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[5586, 5585])).
% 1.74/1.97 tff(5588,plain,
% 1.74/1.97 ($false),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5587, 124, 374, 5584, 5556])).
% 1.74/1.97 tff(5589,plain,((~(s(elem!1) = elem!1)) | (~r(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (elem!1 = s(s(s(z)))) | (~r(s(s(s(z))), s(z))) | b(s(s(s(s(s(s(z)))))), s(s(s(z)))) | (~b(s(s(s(z))), z)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.97 tff(5590,plain,
% 1.74/1.97 (~(s(elem!1) = elem!1)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5589, 2885, 1967, 4346, 2831, 1034, 4939, 206, 374, 1531, 87])).
% 1.74/1.97 tff(5591,plain,
% 1.74/1.97 (b(s(elem!1), elem!1)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[813, 5590, 808])).
% 1.74/1.97 tff(5592,plain,
% 1.74/1.97 (~b(s(elem!1), s(z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5422, 5591, 2831, 4346])).
% 1.74/1.97 tff(5593,plain,
% 1.74/1.97 (~(s(s(elem!1)) = s(elem!1))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[195, 5590])).
% 1.74/1.97 tff(5594,plain,
% 1.74/1.97 (r(s(elem!1), s(z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[2964, 5592, 3099])).
% 1.74/1.97 tff(5595,plain,
% 1.74/1.97 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(elem!1))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(5596,plain,
% 1.74/1.97 (((~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(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(elem!1))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(5597,plain,
% 1.74/1.97 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(elem!1)))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[5596])).
% 1.74/1.97 tff(5598,plain,
% 1.74/1.97 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(elem!1))))),
% 1.74/1.97 inference(transitivity,[status(thm)],[5597, 5595])).
% 1.74/1.97 tff(5599,plain,
% 1.74/1.97 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(elem!1))))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(5600,plain,
% 1.74/1.97 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(elem!1)))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[5599, 5598])).
% 1.74/1.97 tff(5601,plain,
% 1.74/1.97 (~r(s(s(s(z))), s(elem!1))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5600, 124, 206, 5594])).
% 1.74/1.97 tff(5602,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(5603,plain,
% 1.74/1.97 (((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1)))) <=> ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(5604,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1)))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[5603])).
% 1.74/1.97 tff(5605,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.74/1.97 inference(transitivity,[status(thm)],[5604, 5602])).
% 1.74/1.97 tff(5606,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~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))))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(5607,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1)))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[5606, 5605])).
% 1.74/1.97 tff(5608,plain,
% 1.74/1.97 (~b(s(s(s(z))), s(elem!1))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5607, 306, 5591, 2831, 1967, 4346])).
% 1.74/1.97 tff(5609,plain,
% 1.74/1.97 ((s(s(s(z))) = s(elem!1)) | r(s(s(s(z))), s(elem!1))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[4132, 43, 5608])).
% 1.74/1.97 tff(5610,plain,
% 1.74/1.97 (s(s(s(z))) = s(elem!1)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5609, 5601])).
% 1.74/1.97 tff(5611,plain,
% 1.74/1.97 (~(s(s(s(elem!1))) = elem!1)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[4128, 5610])).
% 1.74/1.97 tff(5612,plain,
% 1.74/1.97 (r(elem!1, z)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[174, 3103, 2])).
% 1.74/1.97 tff(5613,plain,
% 1.74/1.97 (~(elem!1 = s(elem!1))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[364, 5590])).
% 1.74/1.97 tff(5614,plain,
% 1.74/1.97 (~r(s(elem!1), s(s(s(z))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5427, 124, 206, 5594])).
% 1.74/1.97 tff(5615,plain,
% 1.74/1.97 (~b(s(elem!1), s(s(s(z))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5412, 306, 5591, 2831, 1967, 4346])).
% 1.74/1.97 tff(5616,plain,
% 1.74/1.97 ((s(elem!1) = s(s(s(z)))) | r(s(elem!1), s(s(s(z))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[2367, 43, 5615])).
% 1.74/1.97 tff(5617,plain,
% 1.74/1.97 (s(elem!1) = s(s(s(z)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5616, 5614])).
% 1.74/1.97 tff(5618,plain,
% 1.74/1.97 (~(s(s(elem!1)) = elem!1)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[2356, 5617])).
% 1.74/1.97 tff(5619,plain,
% 1.74/1.97 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[610, 160, 3314])).
% 1.74/1.97 tff(5620,plain,
% 1.74/1.97 (b(s(elem!1), elem!1)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[813, 181, 808])).
% 1.74/1.97 tff(5621,plain,
% 1.74/1.97 (~(elem!1 = s(elem!1))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[364, 181])).
% 1.74/1.97 tff(5622,plain,
% 1.74/1.97 (r(elem!1, s(elem!1))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[372, 367, 5621])).
% 1.74/1.97 tff(5623,plain,
% 1.74/1.97 (((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(5624,plain,
% 1.74/1.97 (((~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)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(5625,plain,
% 1.74/1.97 (((~![X0: $i, X2: $i, X1: $i] : ((~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)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1)), s(elem!1)))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[5624])).
% 1.74/1.97 tff(5626,plain,
% 1.74/1.97 (((~![X0: $i, X2: $i, X1: $i] : ((~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)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1)), s(elem!1))))),
% 1.74/1.97 inference(transitivity,[status(thm)],[5625, 5623])).
% 1.74/1.97 tff(5627,plain,
% 1.74/1.97 ((~![X0: $i, X2: $i, X1: $i] : ((~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)))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(5628,plain,
% 1.74/1.97 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1)))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[5627, 5626])).
% 1.74/1.97 tff(5629,plain,
% 1.74/1.97 ($false),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5628, 124, 255, 1730, 244])).
% 1.74/1.97 tff(5630,plain,((~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,[]))).
% 1.74/1.97 tff(5631,plain,
% 1.74/1.97 (~r(s(s(elem!1)), s(elem!1))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5630, 1730, 255])).
% 1.74/1.97 tff(5632,plain,
% 1.74/1.97 (b(s(s(elem!1)), s(elem!1))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[994, 5631, 403])).
% 1.74/1.97 tff(5633,plain,
% 1.74/1.97 (~r(elem!1, z)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[265, 791, 255])).
% 1.74/1.97 tff(5634,plain,
% 1.74/1.97 (b(elem!1, z)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[174, 5633, 3103])).
% 1.74/1.97 tff(5635,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(5636,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(5637,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[5636, 5635])).
% 1.74/1.97 tff(5638,plain,
% 1.74/1.97 ($false),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5637, 306, 4012, 759, 1005, 601, 816])).
% 1.74/1.97 tff(5639,plain,((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.97 tff(5640,plain,
% 1.74/1.97 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5639, 5634, 1005, 601, 816])).
% 1.74/1.97 tff(5641,plain,
% 1.74/1.97 (r(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[664, 5640, 150])).
% 1.74/1.97 tff(5642,plain,
% 1.74/1.97 (~r(elem!1, s(s(s(elem!1))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[4083, 5641, 255])).
% 1.74/1.97 tff(5643,plain,
% 1.74/1.97 (elem!1 = s(s(s(elem!1)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[3284, 5642, 3282])).
% 1.74/1.97 tff(5644,plain,
% 1.74/1.97 (s(elem!1) = s(s(s(s(elem!1))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[5643])).
% 1.74/1.97 tff(5645,plain,
% 1.74/1.97 (s(s(elem!1)) = s(s(s(s(s(elem!1)))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[5644])).
% 1.74/1.97 tff(5646,plain,
% 1.74/1.97 (s(s(s(s(s(elem!1))))) = s(s(elem!1))),
% 1.74/1.97 inference(symmetry,[status(thm)],[5645])).
% 1.74/1.97 tff(5647,plain,
% 1.74/1.97 (b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))) <=> b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[5646])).
% 1.74/1.97 tff(5648,plain,
% 1.74/1.97 (b(s(s(elem!1)), s(s(s(s(elem!1))))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.74/1.97 inference(symmetry,[status(thm)],[5647])).
% 1.74/1.97 tff(5649,plain,
% 1.74/1.97 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[5644])).
% 1.74/1.97 tff(5650,plain,
% 1.74/1.97 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[1005, 5649])).
% 1.74/1.97 tff(5651,plain,
% 1.74/1.97 (b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[5650, 5648])).
% 1.74/1.97 tff(5652,plain,
% 1.74/1.97 (b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[5646])).
% 1.74/1.97 tff(5653,plain,
% 1.74/1.97 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.74/1.97 inference(symmetry,[status(thm)],[5652])).
% 1.74/1.97 tff(5654,plain,
% 1.74/1.97 (b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[601, 5653])).
% 1.74/1.97 tff(5655,plain,
% 1.74/1.97 (s(s(s(elem!1))) = elem!1),
% 1.74/1.97 inference(symmetry,[status(thm)],[5643])).
% 1.74/1.97 tff(5656,plain,
% 1.74/1.97 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 1.74/1.97 inference(monotonicity,[status(thm)],[5655])).
% 1.74/1.97 tff(5657,plain,
% 1.74/1.97 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/1.97 inference(symmetry,[status(thm)],[5656])).
% 1.74/1.97 tff(5658,plain,
% 1.74/1.97 (s(s(s(s(elem!1)))) = s(elem!1)),
% 1.74/1.97 inference(symmetry,[status(thm)],[5644])).
% 1.74/1.97 tff(5659,plain,
% 1.74/1.97 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[5658, 5643])).
% 1.74/1.97 tff(5660,plain,
% 1.74/1.97 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 1.74/1.97 inference(symmetry,[status(thm)],[5659])).
% 1.74/1.97 tff(5661,plain,
% 1.74/1.97 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[5643])).
% 1.74/1.97 tff(5662,plain,
% 1.74/1.97 (b(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[816, 5661])).
% 1.74/1.97 tff(5663,plain,
% 1.74/1.97 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[5662, 5660])).
% 1.74/1.97 tff(5664,plain,
% 1.74/1.97 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[5663, 5657])).
% 1.74/1.97 tff(5665,plain,
% 1.74/1.97 (b(z, s(s(s(s(s(elem!1)))))) <=> b(z, s(s(elem!1)))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[5646])).
% 1.74/1.97 tff(5666,plain,
% 1.74/1.97 (b(z, s(s(elem!1))) <=> b(z, s(s(s(s(s(elem!1))))))),
% 1.74/1.97 inference(symmetry,[status(thm)],[5665])).
% 1.74/1.97 tff(5667,plain,
% 1.74/1.97 ($false),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[1226, 124, 374, 791, 255])).
% 1.74/1.97 tff(5668,plain,((~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.97 tff(5669,plain,
% 1.74/1.97 (~r(z, elem!1)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5668, 791, 255])).
% 1.74/1.97 tff(5670,plain,
% 1.74/1.97 (b(z, elem!1)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[835, 5669, 2170])).
% 1.74/1.97 tff(5671,plain,
% 1.74/1.97 (~b(s(elem!1), z)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[3111, 306, 5670, 5634, 816])).
% 1.74/1.97 tff(5672,plain,
% 1.74/1.97 (s(s(elem!1)) = s(s(s(s(s(elem!1)))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[1514])).
% 1.74/1.97 tff(5673,plain,
% 1.74/1.97 (s(s(s(s(s(elem!1))))) = s(s(elem!1))),
% 1.74/1.97 inference(symmetry,[status(thm)],[5672])).
% 1.74/1.97 tff(5674,plain,
% 1.74/1.97 (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)))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[5673])).
% 1.74/1.97 tff(5675,plain,
% 1.74/1.97 (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))))))),
% 1.74/1.97 inference(symmetry,[status(thm)],[5674])).
% 1.74/1.97 tff(5676,plain,
% 1.74/1.97 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[1515, 1513])).
% 1.74/1.98 tff(5677,plain,
% 1.74/1.98 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 1.74/1.98 inference(symmetry,[status(thm)],[5676])).
% 1.74/1.98 tff(5678,plain,
% 1.74/1.98 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[1513])).
% 1.74/1.98 tff(5679,plain,
% 1.74/1.98 (b(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[816, 5678])).
% 1.74/1.98 tff(5680,plain,
% 1.74/1.98 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[5679, 5677])).
% 1.74/1.98 tff(5681,plain,
% 1.74/1.98 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[1514])).
% 1.74/1.98 tff(5682,plain,
% 1.74/1.98 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[1005, 5681])).
% 1.74/1.98 tff(5683,plain,
% 1.74/1.98 (b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))) <=> b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[5673])).
% 1.74/1.98 tff(5684,plain,
% 1.74/1.98 (b(s(s(elem!1)), s(s(s(s(elem!1))))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.74/1.98 inference(symmetry,[status(thm)],[5683])).
% 1.74/1.98 tff(5685,assumption,(b(s(s(elem!1)), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.74/1.98 tff(5686,plain,
% 1.74/1.98 (b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[5685, 5684])).
% 1.74/1.98 tff(5687,plain,
% 1.74/1.98 (b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[5673])).
% 1.74/1.98 tff(5688,plain,
% 1.74/1.98 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.74/1.98 inference(symmetry,[status(thm)],[5687])).
% 1.74/1.98 tff(5689,plain,
% 1.74/1.98 (b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[601, 5688])).
% 1.74/1.98 tff(5690,plain,
% 1.74/1.98 (s(s(s(elem!1))) = elem!1),
% 1.74/1.98 inference(symmetry,[status(thm)],[1513])).
% 1.74/1.98 tff(5691,plain,
% 1.74/1.98 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 1.74/1.98 inference(monotonicity,[status(thm)],[5690])).
% 1.74/1.98 tff(5692,plain,
% 1.74/1.98 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/1.98 inference(symmetry,[status(thm)],[5691])).
% 1.74/1.98 tff(5693,plain,
% 1.74/1.98 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[2076, 5692])).
% 1.74/1.98 tff(5694,plain,
% 1.74/1.98 (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)))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[5673])).
% 1.74/1.98 tff(5695,plain,
% 1.74/1.98 (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))))))),
% 1.74/1.98 inference(symmetry,[status(thm)],[5694])).
% 1.74/1.98 tff(5696,plain,
% 1.74/1.98 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[1973, 5695])).
% 1.74/1.98 tff(5697,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(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(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(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(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(5698,plain,
% 1.74/1.98 (((~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(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(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))))), s(s(s(s(elem!1)))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(5699,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(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))))), s(s(s(s(elem!1))))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[5698])).
% 1.74/1.98 tff(5700,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(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))))), s(s(s(s(elem!1)))))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[5699, 5697])).
% 1.74/1.98 tff(5701,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(5702,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[5701, 5700])).
% 1.74/1.98 tff(5703,plain,
% 1.74/1.98 ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5702, 306])).
% 1.74/1.98 tff(5704,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5703, 5696, 5693, 5689, 5686])).
% 1.74/1.98 tff(5705,plain,((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~(elem!1 = s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(5706,plain,
% 1.74/1.98 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5705, 5682, 1513, 601, 5680])).
% 1.74/1.98 tff(5707,plain,
% 1.74/1.98 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[1302, 5706, 1717])).
% 1.74/1.98 tff(5708,plain,
% 1.74/1.98 (r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[5707, 5675])).
% 1.74/1.98 tff(5709,plain,
% 1.74/1.98 (r(z, s(s(s(s(s(elem!1)))))) <=> r(z, s(s(elem!1)))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[5673])).
% 1.74/1.98 tff(5710,plain,
% 1.74/1.98 (r(z, s(s(elem!1))) <=> r(z, s(s(s(s(s(elem!1))))))),
% 1.74/1.98 inference(symmetry,[status(thm)],[5709])).
% 1.74/1.98 tff(5711,plain,
% 1.74/1.98 (r(z, s(s(s(s(s(elem!1))))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[437, 5710])).
% 1.74/1.98 tff(5712,plain,
% 1.74/1.98 (s(s(s(elem!1))) = elem!1),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[1641, 1513])).
% 1.74/1.98 tff(5713,plain,
% 1.74/1.98 (s(s(s(s(elem!1)))) = s(elem!1)),
% 1.74/1.98 inference(monotonicity,[status(thm)],[2184])).
% 1.74/1.98 tff(5714,plain,
% 1.74/1.98 (b(s(s(s(s(elem!1)))), z) <=> b(s(elem!1), z)),
% 1.74/1.98 inference(monotonicity,[status(thm)],[5713])).
% 1.74/1.98 tff(5715,assumption,(b(s(s(s(s(elem!1)))), z)), introduced(assumption)).
% 1.74/1.98 tff(5716,plain,
% 1.74/1.98 (b(s(elem!1), z)),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[5715, 5714])).
% 1.74/1.98 tff(5717,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[2378, 5716])).
% 1.74/1.98 tff(5718,plain,((~b(s(s(s(s(elem!1)))), z)) | b(s(elem!1), z) | (~(s(s(s(elem!1))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(5719,plain,
% 1.74/1.98 (~b(s(s(s(s(elem!1)))), z)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5718, 5712, 2378])).
% 1.74/1.98 tff(5720,plain,
% 1.74/1.98 (((~![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))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(5721,plain,
% 1.74/1.98 ((~![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))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(5722,plain,
% 1.74/1.98 ((~![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)),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[5721, 5720])).
% 1.74/1.98 tff(5723,plain,
% 1.74/1.98 (b(s(s(s(s(elem!1)))), z) | r(s(s(s(s(elem!1)))), z)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5722, 43, 1549])).
% 1.74/1.98 tff(5724,plain,
% 1.74/1.98 (r(s(s(s(s(elem!1)))), z)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5723, 5719])).
% 1.74/1.98 tff(5725,plain,
% 1.74/1.98 (((~![X0: $i, X2: $i, X1: $i] : ((~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))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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))))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(5726,plain,
% 1.74/1.98 (((~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))))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(5727,plain,
% 1.74/1.98 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~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)))))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[5726])).
% 1.74/1.98 tff(5728,plain,
% 1.74/1.98 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~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))))))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[5727, 5725])).
% 1.74/1.98 tff(5729,plain,
% 1.74/1.98 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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)))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(5730,plain,
% 1.74/1.98 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1)))))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[5729, 5728])).
% 1.74/1.98 tff(5731,plain,
% 1.74/1.98 ((~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1)))))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5730, 124, 5724])).
% 1.74/1.98 tff(5732,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5731, 5711, 5708])).
% 1.74/1.98 tff(5733,plain,((~(elem!1 = s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | b(s(elem!1), z)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(5734,plain,
% 1.74/1.98 (~r(z, s(s(elem!1)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5733, 5643, 1285, 601, 1005, 816, 5671])).
% 1.74/1.98 tff(5735,plain,
% 1.74/1.98 (b(z, s(s(elem!1)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[460, 5734])).
% 1.74/1.98 tff(5736,plain,
% 1.74/1.98 (b(z, s(s(s(s(s(elem!1))))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[5735, 5666])).
% 1.74/1.98 tff(5737,plain,
% 1.74/1.98 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(5738,plain,
% 1.74/1.98 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1))))))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(5739,plain,
% 1.74/1.98 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1)))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[5738, 5737])).
% 1.74/1.98 tff(5740,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5739, 124, 654, 791, 564])).
% 1.74/1.98 tff(5741,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(5742,plain,
% 1.74/1.98 (~r(z, s(s(s(elem!1))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5741, 5641, 791])).
% 1.74/1.98 tff(5743,plain,
% 1.74/1.98 (b(z, s(s(s(elem!1))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[585, 5742])).
% 1.74/1.98 tff(5744,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(5745,plain,
% 1.74/1.98 (((~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(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(5746,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[5745])).
% 1.74/1.98 tff(5747,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[5746, 5744])).
% 1.74/1.98 tff(5748,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(elem!1))))))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(5749,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[5748, 5747])).
% 1.74/1.98 tff(5750,plain,
% 1.74/1.98 ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5749, 306, 5743])).
% 1.74/1.98 tff(5751,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5750, 5736, 5664, 5654, 5651])).
% 1.74/1.98 tff(5752,plain,((~r(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | b(elem!1, s(s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (s(s(s(elem!1))) = s(elem!1)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(5753,plain,
% 1.74/1.98 (~r(z, s(elem!1))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5752, 5632, 601, 816, 3282, 255, 150, 2170])).
% 1.74/1.98 tff(5754,plain,
% 1.74/1.98 (b(z, s(elem!1))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[275, 5753])).
% 1.74/1.98 tff(5755,plain,
% 1.74/1.98 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[4083, 565, 255])).
% 1.74/1.98 tff(5756,plain,
% 1.74/1.98 (b(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[664, 5755, 150])).
% 1.74/1.98 tff(5757,plain,
% 1.74/1.98 (~b(elem!1, z)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5639, 5756, 1005, 601, 816])).
% 1.74/1.98 tff(5758,plain,
% 1.74/1.98 (r(elem!1, z)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[174, 5757, 1616])).
% 1.74/1.98 tff(5759,plain,
% 1.74/1.98 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(5760,plain,
% 1.74/1.98 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(5761,plain,
% 1.74/1.98 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[5760])).
% 1.74/1.98 tff(5762,plain,
% 1.74/1.98 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[5761, 5759])).
% 1.74/1.98 tff(5763,plain,
% 1.74/1.98 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(5764,plain,
% 1.74/1.98 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[5763, 5762])).
% 1.74/1.98 tff(5765,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5764, 124, 565, 1730, 878])).
% 1.74/1.98 tff(5766,plain,((~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))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(5767,plain,
% 1.74/1.98 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5766, 565, 1730])).
% 1.74/1.98 tff(5768,plain,
% 1.74/1.98 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[891, 5767, 157])).
% 1.74/1.98 tff(5769,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(5770,plain,
% 1.74/1.98 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(5771,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[5770])).
% 1.74/1.98 tff(5772,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[5771, 5769])).
% 1.74/1.98 tff(5773,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(5774,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[5773, 5772])).
% 1.74/1.98 tff(5775,plain,
% 1.74/1.98 (~b(s(s(s(elem!1))), z)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5774, 306, 1198, 5768, 601])).
% 1.74/1.98 tff(5776,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[3033, 43, 579, 852, 5775])).
% 1.74/1.98 tff(5777,plain,((~r(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(5778,plain,
% 1.74/1.98 (~b(z, s(s(elem!1)))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5777, 5758, 601, 232, 1730, 565])).
% 1.74/1.99 tff(5779,plain,
% 1.74/1.99 (r(z, s(s(elem!1)))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[460, 5778])).
% 1.74/1.99 tff(5780,plain,
% 1.74/1.99 (~r(elem!1, s(s(elem!1)))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[978, 5779, 5758])).
% 1.74/1.99 tff(5781,plain,
% 1.74/1.99 (b(elem!1, s(s(elem!1)))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[516, 5780, 360])).
% 1.74/1.99 tff(5782,plain,
% 1.74/1.99 (~r(s(s(s(elem!1))), z)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[851, 5758, 565])).
% 1.74/1.99 tff(5783,plain,
% 1.74/1.99 (b(s(s(s(elem!1))), z)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[3033, 43, 579, 5782])).
% 1.74/1.99 tff(5784,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(5785,plain,
% 1.74/1.99 (((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(5786,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[5785])).
% 1.74/1.99 tff(5787,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 1.74/1.99 inference(transitivity,[status(thm)],[5786, 5784])).
% 1.74/1.99 tff(5788,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(5789,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[5788, 5787])).
% 1.74/1.99 tff(5790,plain,
% 1.74/1.99 ($false),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5789, 306, 5756, 5783, 817, 5781, 816])).
% 1.74/1.99 tff(5791,plain,((~r(elem!1, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (elem!1 = s(s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (elem!1 = z) | (~b(s(s(elem!1)), s(elem!1))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(5792,plain,
% 1.74/1.99 (~r(elem!1, s(s(s(elem!1))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5791, 5754, 816, 360, 601, 1730, 3103, 5632, 150, 255])).
% 1.74/1.99 tff(5793,plain,
% 1.74/1.99 (elem!1 = s(s(s(elem!1)))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[3284, 5792, 3282])).
% 1.74/1.99 tff(5794,plain,
% 1.74/1.99 (s(elem!1) = s(s(s(s(elem!1))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[5793])).
% 1.74/1.99 tff(5795,plain,
% 1.74/1.99 (s(s(elem!1)) = s(s(s(s(s(elem!1)))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[5794])).
% 1.74/1.99 tff(5796,plain,
% 1.74/1.99 (s(s(s(s(s(elem!1))))) = s(s(elem!1))),
% 1.74/1.99 inference(symmetry,[status(thm)],[5795])).
% 1.74/1.99 tff(5797,plain,
% 1.74/1.99 (b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))) <=> b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[5796])).
% 1.74/1.99 tff(5798,plain,
% 1.74/1.99 (b(s(s(elem!1)), s(s(s(s(elem!1))))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.74/1.99 inference(symmetry,[status(thm)],[5797])).
% 1.74/1.99 tff(5799,plain,
% 1.74/1.99 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[5794])).
% 1.74/1.99 tff(5800,plain,
% 1.74/1.99 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[5632, 5799])).
% 1.74/1.99 tff(5801,plain,
% 1.74/1.99 (b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[5800, 5798])).
% 1.74/1.99 tff(5802,plain,
% 1.74/1.99 (b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[5796])).
% 1.74/1.99 tff(5803,plain,
% 1.74/1.99 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.74/1.99 inference(symmetry,[status(thm)],[5802])).
% 1.74/1.99 tff(5804,plain,
% 1.74/1.99 (b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[601, 5803])).
% 1.74/1.99 tff(5805,plain,
% 1.74/1.99 (s(s(s(elem!1))) = elem!1),
% 1.74/1.99 inference(symmetry,[status(thm)],[5793])).
% 1.74/1.99 tff(5806,plain,
% 1.74/1.99 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 1.74/1.99 inference(monotonicity,[status(thm)],[5805])).
% 1.74/1.99 tff(5807,plain,
% 1.74/1.99 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/1.99 inference(symmetry,[status(thm)],[5806])).
% 1.74/1.99 tff(5808,plain,
% 1.74/1.99 (s(s(s(s(elem!1)))) = s(elem!1)),
% 1.74/1.99 inference(symmetry,[status(thm)],[5794])).
% 1.74/1.99 tff(5809,plain,
% 1.74/1.99 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[5808, 5793])).
% 1.74/1.99 tff(5810,plain,
% 1.74/1.99 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 1.74/1.99 inference(symmetry,[status(thm)],[5809])).
% 1.74/1.99 tff(5811,plain,
% 1.74/1.99 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[5793])).
% 1.74/1.99 tff(5812,plain,
% 1.74/1.99 (b(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[816, 5811])).
% 1.74/1.99 tff(5813,plain,
% 1.74/1.99 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[5812, 5810])).
% 1.74/1.99 tff(5814,plain,
% 1.74/1.99 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[5813, 5807])).
% 1.74/1.99 tff(5815,plain,
% 1.74/1.99 (b(z, s(elem!1)) <=> b(z, s(s(s(s(elem!1)))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[5794])).
% 1.74/1.99 tff(5816,plain,
% 1.74/1.99 (b(z, s(s(s(s(elem!1)))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[5754, 5815])).
% 1.74/1.99 tff(5817,plain,
% 1.74/1.99 (b(z, elem!1) <=> b(z, s(s(s(elem!1))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[5793])).
% 1.74/1.99 tff(5818,plain,
% 1.74/1.99 (b(z, s(s(s(s(s(elem!1)))))) <=> b(z, s(s(elem!1)))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[5796])).
% 1.74/1.99 tff(5819,plain,
% 1.74/1.99 ((~b(z, s(s(s(s(s(elem!1))))))) <=> (~b(z, s(s(elem!1))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[5818])).
% 1.74/1.99 tff(5820,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(5821,plain,
% 1.74/1.99 (((~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(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(elem!1)))))))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(5822,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~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(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[5821])).
% 1.74/1.99 tff(5823,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~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(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.74/1.99 inference(transitivity,[status(thm)],[5822, 5820])).
% 1.74/1.99 tff(5824,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~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(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(elem!1))))))))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(5825,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[5824, 5823])).
% 1.74/1.99 tff(5826,plain,
% 1.74/1.99 ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5825, 306, 5816])).
% 1.74/1.99 tff(5827,plain,
% 1.74/1.99 (~b(z, s(s(s(s(s(elem!1))))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5826, 5814, 5804, 5801])).
% 1.74/1.99 tff(5828,plain,
% 1.74/1.99 (~b(z, s(s(elem!1)))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[5827, 5819])).
% 1.74/1.99 tff(5829,plain,
% 1.74/1.99 (r(z, s(s(elem!1)))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[460, 5828])).
% 1.74/1.99 tff(5830,plain,
% 1.74/1.99 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(5831,plain,
% 1.74/1.99 (((~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)))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(5832,plain,
% 1.74/1.99 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1))))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[5831])).
% 1.74/1.99 tff(5833,plain,
% 1.74/1.99 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))),
% 1.74/1.99 inference(transitivity,[status(thm)],[5832, 5830])).
% 1.74/1.99 tff(5834,plain,
% 1.74/1.99 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(5835,plain,
% 1.74/1.99 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[5834, 5833])).
% 1.74/1.99 tff(5836,plain,
% 1.74/1.99 ($false),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5835, 124, 374, 1730, 437])).
% 1.74/1.99 tff(5837,plain,((~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(5838,plain,
% 1.74/1.99 (~r(z, elem!1)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5837, 5829, 1730])).
% 1.74/1.99 tff(5839,plain,
% 1.74/1.99 (b(z, elem!1)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[835, 5838, 2170])).
% 1.74/1.99 tff(5840,plain,
% 1.74/1.99 (b(z, s(s(s(elem!1))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[5839, 5817])).
% 1.74/1.99 tff(5841,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(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(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(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(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(5842,plain,
% 1.74/1.99 (((~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~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(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1))))))) <=> ((~b(z, s(s(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(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(5843,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~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(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(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(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[5842])).
% 1.74/1.99 tff(5844,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~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(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(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(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.74/1.99 inference(transitivity,[status(thm)],[5843, 5841])).
% 1.74/1.99 tff(5845,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~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(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(5846,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[5845, 5844])).
% 1.74/1.99 tff(5847,plain,
% 1.74/1.99 ($false),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5846, 306, 5840, 5816, 5814, 5804, 5801])).
% 1.74/1.99 tff(5848,plain,((~r(s(s(elem!1)), elem!1)) | (z = elem!1) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | b(elem!1, s(s(s(elem!1)))) | (elem!1 = s(s(elem!1))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(elem!1, s(elem!1))) | (s(s(elem!1)) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(5849,plain,
% 1.74/1.99 (~r(s(s(elem!1)), elem!1)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5848, 3282, 601, 816, 2170, 187, 144, 5622, 196])).
% 1.74/1.99 tff(5850,plain,
% 1.74/1.99 (b(s(s(elem!1)), elem!1)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[47, 5849, 91])).
% 1.74/1.99 tff(5851,plain,
% 1.74/1.99 (~r(elem!1, s(s(elem!1)))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[1238, 244, 255])).
% 1.74/1.99 tff(5852,plain,
% 1.74/1.99 (b(elem!1, s(s(elem!1)))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[516, 5851, 360])).
% 1.74/1.99 tff(5853,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(5854,plain,
% 1.74/1.99 (((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1))) <=> ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(5855,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1))))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[5854])).
% 1.74/1.99 tff(5856,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))))),
% 1.74/1.99 inference(transitivity,[status(thm)],[5855, 5853])).
% 1.74/1.99 tff(5857,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(5858,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[5857, 5856])).
% 1.74/1.99 tff(5859,plain,
% 1.74/1.99 (~b(z, elem!1)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5858, 306, 30, 1198, 1003])).
% 1.74/1.99 tff(5860,plain,
% 1.74/1.99 (r(z, elem!1)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[835, 5859, 2170])).
% 1.74/1.99 tff(5861,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(5862,plain,
% 1.74/1.99 (((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(5863,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1))))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[5862])).
% 1.74/1.99 tff(5864,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))))),
% 1.74/1.99 inference(transitivity,[status(thm)],[5863, 5861])).
% 1.74/1.99 tff(5865,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(5866,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[5865, 5864])).
% 1.74/1.99 tff(5867,plain,
% 1.74/1.99 (~b(z, s(s(s(elem!1))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5866, 306, 30, 1198, 1003, 601])).
% 1.74/1.99 tff(5868,plain,
% 1.74/1.99 (r(z, s(s(s(elem!1))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[585, 5867])).
% 1.74/1.99 tff(5869,plain,
% 1.74/1.99 (~r(elem!1, s(s(s(elem!1))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[573, 5868, 5860])).
% 1.74/1.99 tff(5870,plain,
% 1.74/1.99 (elem!1 = s(s(s(elem!1)))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[3284, 5869, 3282])).
% 1.74/1.99 tff(5871,plain,
% 1.74/1.99 (s(s(s(elem!1))) = elem!1),
% 1.74/1.99 inference(symmetry,[status(thm)],[5870])).
% 1.74/1.99 tff(5872,plain,
% 1.74/1.99 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 1.74/1.99 inference(monotonicity,[status(thm)],[5871])).
% 1.74/1.99 tff(5873,plain,
% 1.74/2.00 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/2.00 inference(symmetry,[status(thm)],[5872])).
% 1.74/2.00 tff(5874,plain,
% 1.74/2.00 (s(elem!1) = s(s(s(s(elem!1))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5870])).
% 1.74/2.00 tff(5875,plain,
% 1.74/2.00 (s(s(s(s(elem!1)))) = s(elem!1)),
% 1.74/2.00 inference(symmetry,[status(thm)],[5874])).
% 1.74/2.00 tff(5876,plain,
% 1.74/2.00 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(elem!1), s(s(s(elem!1))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5875, 5870])).
% 1.74/2.00 tff(5877,plain,
% 1.74/2.00 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 1.74/2.00 inference(symmetry,[status(thm)],[5876])).
% 1.74/2.00 tff(5878,plain,
% 1.74/2.00 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(elem!1))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5870])).
% 1.74/2.00 tff(5879,plain,
% 1.74/2.00 (b(s(elem!1), s(s(s(elem!1))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[816, 5878])).
% 1.74/2.00 tff(5880,plain,
% 1.74/2.00 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[5879, 5877])).
% 1.74/2.00 tff(5881,plain,
% 1.74/2.00 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[5880, 5873])).
% 1.74/2.00 tff(5882,plain,
% 1.74/2.00 (r(s(s(s(elem!1))), s(z)) <=> r(elem!1, s(z))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5871])).
% 1.74/2.00 tff(5883,plain,
% 1.74/2.00 (r(elem!1, s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 1.74/2.00 inference(symmetry,[status(thm)],[5882])).
% 1.74/2.00 tff(5884,plain,
% 1.74/2.00 ((~r(elem!1, s(z))) <=> (~r(s(s(s(elem!1))), s(z)))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5883])).
% 1.74/2.00 tff(5885,plain,
% 1.74/2.00 (b(z, s(elem!1)) <=> b(z, s(s(s(s(elem!1)))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5874])).
% 1.74/2.00 tff(5886,plain,
% 1.74/2.00 (~r(z, s(elem!1))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5668, 5860, 255])).
% 1.74/2.00 tff(5887,plain,
% 1.74/2.00 (b(z, s(elem!1))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[275, 5886])).
% 1.74/2.00 tff(5888,plain,
% 1.74/2.00 (b(z, s(s(s(s(elem!1)))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[5887, 5885])).
% 1.74/2.00 tff(5889,plain,
% 1.74/2.00 ((s(z) = s(s(s(s(elem!1))))) <=> (s(z) = s(elem!1))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5875])).
% 1.74/2.00 tff(5890,plain,
% 1.74/2.00 ((s(z) = s(s(s(s(elem!1))))) <=> (s(elem!1) = s(z))),
% 1.74/2.00 inference(transitivity,[status(thm)],[5889, 4037])).
% 1.74/2.00 tff(5891,plain,
% 1.74/2.00 ((s(elem!1) = s(z)) <=> (s(z) = s(s(s(s(elem!1)))))),
% 1.74/2.00 inference(symmetry,[status(thm)],[5890])).
% 1.74/2.00 tff(5892,plain,
% 1.74/2.00 ((~(s(elem!1) = s(z))) <=> (~(s(z) = s(s(s(s(elem!1))))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5891])).
% 1.74/2.00 tff(5893,plain,
% 1.74/2.00 (~(s(z) = s(s(s(s(elem!1)))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[3099, 5892])).
% 1.74/2.00 tff(5894,plain,
% 1.74/2.00 (r(elem!1, s(s(s(s(elem!1))))) <=> r(s(s(s(elem!1))), s(elem!1))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5870, 5875])).
% 1.74/2.00 tff(5895,plain,
% 1.74/2.00 (r(s(s(s(elem!1))), s(elem!1)) <=> r(elem!1, s(s(s(s(elem!1)))))),
% 1.74/2.00 inference(symmetry,[status(thm)],[5894])).
% 1.74/2.00 tff(5896,plain,
% 1.74/2.00 (s(s(s(elem!1))) = elem!1),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[1641, 5870])).
% 1.74/2.00 tff(5897,plain,
% 1.74/2.00 (b(s(s(s(elem!1))), s(elem!1)) <=> b(elem!1, s(elem!1))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[2184])).
% 1.74/2.00 tff(5898,plain,
% 1.74/2.00 (b(elem!1, s(elem!1)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.74/2.00 inference(symmetry,[status(thm)],[5897])).
% 1.74/2.00 tff(5899,plain,
% 1.74/2.00 ((~b(elem!1, s(elem!1))) <=> (~b(s(s(s(elem!1))), s(elem!1)))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5898])).
% 1.74/2.00 tff(5900,plain,
% 1.74/2.00 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[367, 5899])).
% 1.74/2.00 tff(5901,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[759, 5900])).
% 1.74/2.00 tff(5902,plain,((~(s(s(s(elem!1))) = elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | b(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(5903,plain,
% 1.74/2.00 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5902, 5896, 367])).
% 1.74/2.00 tff(5904,plain,
% 1.74/2.00 (r(s(s(s(elem!1))), s(elem!1))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[664, 5903, 150])).
% 1.74/2.00 tff(5905,plain,
% 1.74/2.00 (r(elem!1, s(s(s(s(elem!1)))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[5904, 5895])).
% 1.74/2.00 tff(5906,plain,
% 1.74/2.00 (b(s(s(s(elem!1))), s(z)) <=> b(elem!1, s(z))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5690])).
% 1.74/2.00 tff(5907,plain,
% 1.74/2.00 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(z))),
% 1.74/2.00 inference(symmetry,[status(thm)],[3318])).
% 1.74/2.00 tff(5908,plain,
% 1.74/2.00 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(z)))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5907])).
% 1.74/2.00 tff(5909,plain,
% 1.74/2.00 (~(s(s(s(elem!1))) = s(z))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[645, 5908])).
% 1.74/2.00 tff(5910,plain,
% 1.74/2.00 (r(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> r(elem!1, s(s(s(s(elem!1)))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5690])).
% 1.74/2.00 tff(5911,plain,
% 1.74/2.00 (r(elem!1, s(s(s(s(elem!1))))) <=> r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.74/2.00 inference(symmetry,[status(thm)],[5910])).
% 1.74/2.00 tff(5912,plain,
% 1.74/2.00 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[1910, 5911])).
% 1.74/2.00 tff(5913,assumption,(r(s(z), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.74/2.00 tff(5914,plain,
% 1.74/2.00 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(5915,plain,
% 1.74/2.00 (((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z)))) <=> ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(5916,plain,
% 1.74/2.00 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(elem!1))))))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5915])).
% 1.74/2.00 tff(5917,plain,
% 1.74/2.00 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.74/2.00 inference(transitivity,[status(thm)],[5916, 5914])).
% 1.74/2.00 tff(5918,plain,
% 1.74/2.00 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(5919,plain,
% 1.74/2.00 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(elem!1))))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[5918, 5917])).
% 1.74/2.00 tff(5920,plain,
% 1.74/2.00 ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z)))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5919, 124, 5913])).
% 1.74/2.00 tff(5921,plain,
% 1.74/2.00 (~r(s(s(s(elem!1))), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5920, 5912])).
% 1.74/2.00 tff(5922,plain,
% 1.74/2.00 (((~![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)))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(5923,plain,
% 1.74/2.00 ((~![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)))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(5924,plain,
% 1.74/2.00 ((~![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))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[5923, 5922])).
% 1.74/2.00 tff(5925,plain,
% 1.74/2.00 ((s(s(s(elem!1))) = s(z)) | b(s(s(s(elem!1))), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5924, 43, 5921])).
% 1.74/2.00 tff(5926,plain,
% 1.74/2.00 (b(s(s(s(elem!1))), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5925, 5909])).
% 1.74/2.00 tff(5927,plain,
% 1.74/2.00 (b(elem!1, s(z))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[5926, 5906])).
% 1.74/2.00 tff(5928,plain,
% 1.74/2.00 (r(s(s(s(s(s(elem!1))))), s(z)) <=> r(s(s(elem!1)), s(z))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5673])).
% 1.74/2.00 tff(5929,plain,
% 1.74/2.00 ((~r(s(s(s(s(s(elem!1))))), s(z))) <=> (~r(s(s(elem!1)), s(z)))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5928])).
% 1.74/2.00 tff(5930,plain,
% 1.74/2.00 (r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))) <=> r(s(s(elem!1)), s(elem!1))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5673, 1515])).
% 1.74/2.00 tff(5931,plain,
% 1.74/2.00 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.74/2.00 inference(symmetry,[status(thm)],[5930])).
% 1.74/2.00 tff(5932,plain,
% 1.74/2.00 (r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[244, 5931])).
% 1.74/2.00 tff(5933,plain,
% 1.74/2.00 (((~![X0: $i, X2: $i, X1: $i] : ((~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(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(5934,plain,
% 1.74/2.00 (((~r(s(z), 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(s(elem!1))))), s(z)))) <=> ((~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(5935,plain,
% 1.74/2.00 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), 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(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(z)))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5934])).
% 1.74/2.00 tff(5936,plain,
% 1.74/2.00 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), 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(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 1.74/2.00 inference(transitivity,[status(thm)],[5935, 5933])).
% 1.74/2.00 tff(5937,plain,
% 1.74/2.00 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), 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(s(elem!1))))), s(z))))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(5938,plain,
% 1.74/2.00 ((~![X0: $i, X2: $i, X1: $i] : ((~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(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(z)))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[5937, 5936])).
% 1.74/2.00 tff(5939,plain,
% 1.74/2.00 ((~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(z)))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5938, 124, 5913])).
% 1.74/2.00 tff(5940,plain,
% 1.74/2.00 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5939, 5932])).
% 1.74/2.00 tff(5941,plain,
% 1.74/2.00 (~r(s(s(elem!1)), s(z))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[5940, 5929])).
% 1.74/2.00 tff(5942,plain,
% 1.74/2.00 (b(s(s(elem!1)), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[3988, 5941, 80])).
% 1.74/2.00 tff(5943,plain,
% 1.74/2.00 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), elem!1)),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5690])).
% 1.74/2.00 tff(5944,plain,
% 1.74/2.00 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(5945,plain,
% 1.74/2.00 (((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(5946,plain,
% 1.74/2.00 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1))))))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5945])).
% 1.74/2.00 tff(5947,plain,
% 1.74/2.00 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.74/2.00 inference(transitivity,[status(thm)],[5946, 5944])).
% 1.74/2.00 tff(5948,plain,
% 1.74/2.00 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(5949,plain,
% 1.74/2.00 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1))))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[5948, 5947])).
% 1.74/2.00 tff(5950,plain,
% 1.74/2.00 ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(elem!1)))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5949, 124, 5913])).
% 1.74/2.00 tff(5951,plain,
% 1.74/2.00 (~r(s(z), s(s(s(elem!1))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5950, 5912])).
% 1.74/2.00 tff(5952,plain,
% 1.74/2.00 (b(s(z), s(s(s(elem!1))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[3017, 43, 645, 5951])).
% 1.74/2.00 tff(5953,plain,
% 1.74/2.00 (b(s(z), elem!1)),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[5952, 5943])).
% 1.74/2.00 tff(5954,plain,
% 1.74/2.00 (~b(elem!1, s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[4380, 5953, 30, 5942])).
% 1.74/2.00 tff(5955,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5954, 5927])).
% 1.74/2.00 tff(5956,plain,((~r(s(z), s(s(s(s(elem!1)))))) | (~(elem!1 = s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(5957,plain,
% 1.74/2.00 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5956, 5870, 30, 244, 5905])).
% 1.74/2.00 tff(5958,plain,
% 1.74/2.00 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(elem!1))))) | b(s(z), s(s(s(s(elem!1))))) | r(s(z), s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(elem!1))))) | b(s(z), s(s(s(s(elem!1))))) | r(s(z), s(s(s(s(elem!1))))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(5959,plain,
% 1.74/2.00 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(elem!1))))) | b(s(z), s(s(s(s(elem!1))))) | r(s(z), s(s(s(s(elem!1))))))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(5960,plain,
% 1.74/2.00 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(elem!1))))) | b(s(z), s(s(s(s(elem!1))))) | r(s(z), s(s(s(s(elem!1)))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[5959, 5958])).
% 1.74/2.00 tff(5961,plain,
% 1.74/2.00 ((s(z) = s(s(s(s(elem!1))))) | b(s(z), s(s(s(s(elem!1)))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5960, 43, 5957])).
% 1.74/2.00 tff(5962,plain,
% 1.74/2.00 (b(s(z), s(s(s(s(elem!1)))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5961, 5893])).
% 1.74/2.00 tff(5963,plain,
% 1.74/2.00 (b(s(elem!1), z) <=> b(s(s(s(s(elem!1)))), z)),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5874])).
% 1.74/2.00 tff(5964,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(5965,plain,
% 1.74/2.00 (((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(5966,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1))))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5965])).
% 1.74/2.00 tff(5967,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))))),
% 1.74/2.00 inference(transitivity,[status(thm)],[5966, 5964])).
% 1.74/2.00 tff(5968,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(5969,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[5968, 5967])).
% 1.74/2.00 tff(5970,plain,
% 1.74/2.00 (~b(elem!1, z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5969, 306, 30, 1198, 1003])).
% 1.74/2.00 tff(5971,plain,
% 1.74/2.00 (r(elem!1, z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[174, 5970, 3103])).
% 1.74/2.00 tff(5972,plain,
% 1.74/2.00 (~r(s(elem!1), z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[287, 5971, 255])).
% 1.74/2.00 tff(5973,plain,
% 1.74/2.00 (b(s(elem!1), z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2380, 5972])).
% 1.74/2.00 tff(5974,plain,
% 1.74/2.00 (b(s(s(s(s(elem!1)))), z)),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[5973, 5963])).
% 1.74/2.00 tff(5975,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(5976,plain,
% 1.74/2.00 (((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(z)))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(5977,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5976])).
% 1.74/2.00 tff(5978,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.74/2.00 inference(transitivity,[status(thm)],[5977, 5975])).
% 1.74/2.00 tff(5979,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(z))))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(5980,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1))))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[5979, 5978])).
% 1.74/2.00 tff(5981,plain,
% 1.74/2.00 (~b(z, s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5980, 306, 5974, 5962, 5888])).
% 1.74/2.00 tff(5982,plain,
% 1.74/2.00 (r(z, s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[389, 43, 5981, 2260])).
% 1.74/2.00 tff(5983,plain,
% 1.74/2.00 (~r(elem!1, s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[385, 5982, 5860])).
% 1.74/2.00 tff(5984,plain,
% 1.74/2.00 (~r(s(s(s(elem!1))), s(z))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[5983, 5884])).
% 1.74/2.00 tff(5985,plain,
% 1.74/2.00 ((s(s(s(elem!1))) = s(z)) | b(s(s(s(elem!1))), s(z)) | r(s(s(s(elem!1))), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5924, 43])).
% 1.74/2.00 tff(5986,plain,
% 1.74/2.00 (b(s(s(s(elem!1))), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5985, 5909, 5984])).
% 1.74/2.00 tff(5987,plain,
% 1.74/2.00 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), elem!1)),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5871])).
% 1.74/2.00 tff(5988,plain,
% 1.74/2.00 (r(s(z), elem!1) <=> r(s(z), s(s(s(elem!1))))),
% 1.74/2.00 inference(symmetry,[status(thm)],[5987])).
% 1.74/2.00 tff(5989,plain,
% 1.74/2.00 ((~r(s(z), elem!1)) <=> (~r(s(z), s(s(s(elem!1)))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5988])).
% 1.74/2.00 tff(5990,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(5991,plain,
% 1.74/2.00 (((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), z))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(5992,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5991])).
% 1.74/2.01 tff(5993,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.74/2.01 inference(transitivity,[status(thm)],[5992, 5990])).
% 1.74/2.01 tff(5994,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), z)))),
% 1.74/2.01 inference(quant_inst,[status(thm)],[])).
% 1.74/2.01 tff(5995,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1))))))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[5994, 5993])).
% 1.74/2.01 tff(5996,plain,
% 1.74/2.01 (~b(s(z), z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[5995, 306, 5974, 5962, 5888])).
% 1.74/2.01 tff(5997,plain,
% 1.74/2.01 (r(s(z), z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[221, 5996])).
% 1.74/2.01 tff(5998,plain,
% 1.74/2.01 (~r(s(z), elem!1)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[1049, 5997, 5971])).
% 1.74/2.01 tff(5999,plain,
% 1.74/2.01 (~r(s(z), s(s(s(elem!1))))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[5998, 5989])).
% 1.74/2.01 tff(6000,plain,
% 1.74/2.01 (b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[3017, 43, 645])).
% 1.74/2.01 tff(6001,plain,
% 1.74/2.01 (b(s(z), s(s(s(elem!1))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[6000, 5999])).
% 1.74/2.01 tff(6002,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(6003,plain,
% 1.74/2.01 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(6004,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[6003])).
% 1.74/2.01 tff(6005,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.74/2.01 inference(transitivity,[status(thm)],[6004, 6002])).
% 1.74/2.01 tff(6006,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.74/2.01 inference(quant_inst,[status(thm)],[])).
% 1.74/2.01 tff(6007,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[6006, 6005])).
% 1.74/2.01 tff(6008,plain,
% 1.74/2.01 ($false),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[6007, 306, 5962, 6001, 5986, 5881])).
% 1.74/2.01 tff(6009,plain,((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | b(elem!1, s(elem!1)) | b(elem!1, s(s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (z = elem!1) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.01 tff(6010,plain,
% 1.74/2.01 (~b(z, s(s(elem!1)))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[6009, 244, 30, 816, 150, 367, 3282, 255, 2170, 5852, 601])).
% 1.74/2.01 tff(6011,plain,
% 1.74/2.01 (r(z, s(s(elem!1)))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[460, 6010])).
% 1.74/2.01 tff(6012,plain,
% 1.74/2.01 (~r(z, s(elem!1))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[799, 6011, 244])).
% 1.74/2.01 tff(6013,plain,
% 1.74/2.01 (b(z, s(elem!1))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[275, 6012])).
% 1.74/2.01 tff(6014,plain,
% 1.74/2.01 (~b(z, elem!1)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[2341, 6013, 30, 5852, 816])).
% 1.74/2.01 tff(6015,plain,
% 1.74/2.01 (r(z, elem!1)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[835, 6014, 2170])).
% 1.74/2.01 tff(6016,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(6017,plain,
% 1.74/2.01 (((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(6018,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1))))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[6017])).
% 1.74/2.01 tff(6019,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.74/2.01 inference(transitivity,[status(thm)],[6018, 6016])).
% 1.74/2.01 tff(6020,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.74/2.01 inference(quant_inst,[status(thm)],[])).
% 1.74/2.01 tff(6021,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1))))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[6020, 6019])).
% 1.74/2.01 tff(6022,plain,
% 1.74/2.01 (~b(s(elem!1), s(s(elem!1)))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[6021, 306, 30, 5852, 816])).
% 1.74/2.01 tff(6023,plain,
% 1.74/2.01 ((s(elem!1) = s(s(elem!1))) | r(s(elem!1), s(s(elem!1)))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[1684, 43, 6022])).
% 1.74/2.01 tff(6024,plain,
% 1.74/2.01 (r(s(elem!1), s(s(elem!1)))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[6023, 1659])).
% 1.74/2.01 tff(6025,plain,
% 1.74/2.01 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(6026,plain,
% 1.74/2.01 (((~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z))) <=> ((~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(6027,plain,
% 1.74/2.01 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1))))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[6026])).
% 1.74/2.01 tff(6028,plain,
% 1.74/2.01 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.74/2.01 inference(transitivity,[status(thm)],[6027, 6025])).
% 1.74/2.01 tff(6029,plain,
% 1.74/2.01 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)))),
% 1.74/2.01 inference(quant_inst,[status(thm)],[])).
% 1.74/2.01 tff(6030,plain,
% 1.74/2.01 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1))))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[6029, 6028])).
% 1.74/2.01 tff(6031,plain,
% 1.74/2.01 (~r(s(elem!1), z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[6030, 124, 6011, 6024])).
% 1.74/2.01 tff(6032,plain,
% 1.74/2.01 (b(s(elem!1), z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[2380, 6031])).
% 1.74/2.01 tff(6033,plain,
% 1.74/2.01 (~r(z, s(s(s(elem!1))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[573, 565, 374])).
% 1.74/2.01 tff(6034,plain,
% 1.74/2.01 (b(z, s(s(s(elem!1))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[585, 6033])).
% 1.74/2.01 tff(6035,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(6036,plain,
% 1.74/2.01 (((~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(6037,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1)))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[6036])).
% 1.74/2.01 tff(6038,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))))),
% 1.74/2.01 inference(transitivity,[status(thm)],[6037, 6035])).
% 1.74/2.01 tff(6039,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1))))))),
% 1.74/2.01 inference(quant_inst,[status(thm)],[])).
% 1.74/2.01 tff(6040,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1)))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[6039, 6038])).
% 1.74/2.01 tff(6041,plain,
% 1.74/2.01 ($false),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[6040, 306, 5756, 6034, 1199, 817])).
% 1.74/2.01 tff(6042,plain,((~r(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.01 tff(6043,plain,
% 1.74/2.01 (~r(elem!1, s(s(s(elem!1))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[6042, 6032, 6013, 150, 6015, 255])).
% 1.74/2.01 tff(6044,plain,
% 1.74/2.01 (elem!1 = s(s(s(elem!1)))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[3284, 6043, 3282])).
% 1.74/2.01 tff(6045,plain,
% 1.74/2.01 (s(s(s(elem!1))) = elem!1),
% 1.74/2.01 inference(symmetry,[status(thm)],[6044])).
% 1.74/2.01 tff(6046,plain,
% 1.74/2.01 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 1.74/2.01 inference(monotonicity,[status(thm)],[6045])).
% 1.74/2.01 tff(6047,plain,
% 1.74/2.01 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/2.01 inference(symmetry,[status(thm)],[6046])).
% 1.74/2.01 tff(6048,plain,
% 1.74/2.01 (s(elem!1) = s(s(s(s(elem!1))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[6044])).
% 1.74/2.01 tff(6049,plain,
% 1.74/2.01 (s(s(s(s(elem!1)))) = s(elem!1)),
% 1.74/2.01 inference(symmetry,[status(thm)],[6048])).
% 1.74/2.01 tff(6050,plain,
% 1.74/2.01 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(elem!1), s(s(s(elem!1))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[6049, 6044])).
% 1.74/2.01 tff(6051,plain,
% 1.74/2.01 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 1.74/2.01 inference(symmetry,[status(thm)],[6050])).
% 1.74/2.01 tff(6052,plain,
% 1.74/2.01 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(elem!1))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[6044])).
% 1.74/2.01 tff(6053,plain,
% 1.74/2.01 (b(s(elem!1), s(s(s(elem!1))))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[816, 6052])).
% 1.74/2.01 tff(6054,plain,
% 1.74/2.01 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[6053, 6051])).
% 1.74/2.01 tff(6055,plain,
% 1.74/2.01 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[6054, 6047])).
% 1.74/2.01 tff(6056,plain,
% 1.74/2.01 (r(s(s(s(elem!1))), s(z)) <=> r(elem!1, s(z))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[6045])).
% 1.74/2.01 tff(6057,plain,
% 1.74/2.01 (r(elem!1, s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 1.74/2.01 inference(symmetry,[status(thm)],[6056])).
% 1.74/2.01 tff(6058,plain,
% 1.74/2.01 ((~r(elem!1, s(z))) <=> (~r(s(s(s(elem!1))), s(z)))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[6057])).
% 1.74/2.01 tff(6059,plain,
% 1.74/2.01 (b(z, s(elem!1)) <=> b(z, s(s(s(s(elem!1)))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[6048])).
% 1.74/2.01 tff(6060,plain,
% 1.74/2.01 (b(z, s(s(s(s(elem!1)))))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[6013, 6059])).
% 1.74/2.01 tff(6061,assumption,(s(z) = s(s(s(s(elem!1))))), introduced(assumption)).
% 1.74/2.01 tff(6062,plain,
% 1.74/2.01 (s(s(s(s(elem!1)))) = s(z)),
% 1.74/2.01 inference(symmetry,[status(thm)],[6061])).
% 1.74/2.01 tff(6063,plain,
% 1.74/2.01 (s(elem!1) = s(z)),
% 1.74/2.01 inference(transitivity,[status(thm)],[1514, 6062])).
% 1.74/2.01 tff(6064,plain,
% 1.74/2.01 ($false),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[2249, 6063])).
% 1.74/2.01 tff(6065,plain,((~(s(z) = s(s(s(s(elem!1)))))) | (s(elem!1) = s(z)) | (~(elem!1 = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.01 tff(6066,plain,
% 1.74/2.01 (~(s(z) = s(s(s(s(elem!1)))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[6065, 6044, 3099])).
% 1.74/2.01 tff(6067,plain,
% 1.74/2.01 (r(elem!1, s(s(s(s(elem!1))))) <=> r(s(s(s(elem!1))), s(elem!1))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[6044, 6049])).
% 1.74/2.01 tff(6068,plain,
% 1.74/2.01 (r(s(s(s(elem!1))), s(elem!1)) <=> r(elem!1, s(s(s(s(elem!1)))))),
% 1.74/2.01 inference(symmetry,[status(thm)],[6067])).
% 1.74/2.01 tff(6069,plain,
% 1.74/2.01 (s(s(s(elem!1))) = elem!1),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[1641, 6044])).
% 1.74/2.01 tff(6070,plain,
% 1.74/2.01 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[5902, 6069, 367])).
% 1.74/2.01 tff(6071,plain,
% 1.74/2.01 (r(s(s(s(elem!1))), s(elem!1))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[664, 6070, 150])).
% 1.74/2.01 tff(6072,plain,
% 1.74/2.01 (r(elem!1, s(s(s(s(elem!1)))))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[6071, 6068])).
% 1.74/2.01 tff(6073,plain,
% 1.74/2.01 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[5956, 6072, 30, 244, 6044])).
% 1.74/2.01 tff(6074,assumption,(~(s(z) = s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.74/2.01 tff(6075,assumption,(~r(s(z), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.74/2.01 tff(6076,assumption,(~b(s(z), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.74/2.01 tff(6077,plain,
% 1.74/2.01 ($false),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[5960, 43, 6076, 6075, 6074])).
% 1.74/2.01 tff(6078,plain,(b(s(z), s(s(s(s(elem!1))))) | r(s(z), s(s(s(s(elem!1))))) | (s(z) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.01 tff(6079,plain,
% 1.74/2.01 (b(s(z), s(s(s(s(elem!1)))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[6078, 6073, 6066])).
% 1.74/2.01 tff(6080,plain,
% 1.74/2.01 (b(s(elem!1), z) <=> b(s(s(s(s(elem!1)))), z)),
% 1.74/2.01 inference(monotonicity,[status(thm)],[6048])).
% 1.74/2.01 tff(6081,plain,
% 1.74/2.01 (b(s(s(s(s(elem!1)))), z)),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[6032, 6080])).
% 1.74/2.01 tff(6082,plain,
% 1.74/2.01 (~b(z, s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[5980, 306, 6081, 6079, 6060])).
% 1.74/2.01 tff(6083,plain,
% 1.74/2.01 (r(z, s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[389, 43, 6082, 2260])).
% 1.74/2.01 tff(6084,plain,
% 1.74/2.01 (~r(elem!1, s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[385, 6083, 6015])).
% 1.74/2.01 tff(6085,plain,
% 1.74/2.01 (~r(s(s(s(elem!1))), s(z))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[6084, 6058])).
% 1.74/2.01 tff(6086,plain,
% 1.74/2.01 (b(s(s(s(elem!1))), s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[5985, 5909, 6085])).
% 1.74/2.01 tff(6087,plain,
% 1.74/2.01 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), elem!1)),
% 1.74/2.01 inference(monotonicity,[status(thm)],[6045])).
% 1.74/2.01 tff(6088,plain,
% 1.74/2.01 (r(s(z), elem!1) <=> r(s(z), s(s(s(elem!1))))),
% 1.74/2.01 inference(symmetry,[status(thm)],[6087])).
% 1.74/2.01 tff(6089,plain,
% 1.74/2.01 ((~r(s(z), elem!1)) <=> (~r(s(z), s(s(s(elem!1)))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[6088])).
% 1.74/2.01 tff(6090,plain,
% 1.74/2.01 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), elem!1)))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(6091,plain,
% 1.74/2.01 (((~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z)))) <=> ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), elem!1)))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(6092,plain,
% 1.74/2.01 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), elem!1))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[6091])).
% 1.74/2.01 tff(6093,plain,
% 1.74/2.01 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), elem!1)))),
% 1.74/2.01 inference(transitivity,[status(thm)],[6092, 6090])).
% 1.74/2.01 tff(6094,plain,
% 1.74/2.01 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z))))),
% 1.74/2.01 inference(quant_inst,[status(thm)],[])).
% 1.74/2.01 tff(6095,plain,
% 1.74/2.01 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), elem!1))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[6094, 6093])).
% 1.74/2.01 tff(6096,plain,
% 1.74/2.01 ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), elem!1))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[6095, 124])).
% 1.74/2.01 tff(6097,plain,
% 1.74/2.01 (~r(s(z), elem!1)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[6096, 6083, 6015])).
% 1.74/2.01 tff(6098,plain,
% 1.74/2.01 (~r(s(z), s(s(s(elem!1))))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[6097, 6089])).
% 1.74/2.01 tff(6099,plain,
% 1.74/2.01 (b(s(z), s(s(s(elem!1))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[6000, 6098])).
% 1.74/2.01 tff(6100,plain,
% 1.74/2.01 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[6007, 306, 6079, 6099, 6086])).
% 1.74/2.01 tff(6101,plain,
% 1.74/2.01 ($false),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[6100, 6055])).
% 1.74/2.01 tff(6102,plain,((~r(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | b(elem!1, s(elem!1)) | b(elem!1, s(s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (z = elem!1) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(elem!1)) = s(elem!1)) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.01 tff(6103,plain,
% 1.74/2.01 (~r(s(s(elem!1)), s(elem!1))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[6102, 5850, 816, 144, 367, 3282, 5622, 2170, 601, 196, 187])).
% 1.74/2.01 tff(6104,plain,
% 1.74/2.01 (b(s(s(elem!1)), s(elem!1))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[994, 6103, 196])).
% 1.74/2.01 tff(6105,plain,
% 1.74/2.01 (~r(z, s(elem!1))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[5752, 6104, 601, 816, 3282, 5622, 144, 2170])).
% 1.74/2.01 tff(6106,plain,
% 1.74/2.01 (b(z, s(elem!1))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[275, 6105])).
% 1.74/2.01 tff(6107,plain,
% 1.74/2.01 (~b(elem!1, s(s(elem!1)))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[1024, 6104, 816, 5850])).
% 1.74/2.01 tff(6108,plain,
% 1.74/2.01 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(elem!1))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[1505])).
% 1.74/2.01 tff(6109,plain,
% 1.74/2.01 (s(s(s(elem!1))) = elem!1),
% 1.74/2.01 inference(transitivity,[status(thm)],[1281, 6108, 135])).
% 1.74/2.01 tff(6110,plain,
% 1.74/2.01 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[6109])).
% 1.74/2.01 tff(6111,plain,
% 1.74/2.01 (b(elem!1, s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.74/2.01 inference(symmetry,[status(thm)],[6110])).
% 1.74/2.01 tff(6112,plain,
% 1.74/2.01 ((~b(elem!1, s(s(elem!1)))) <=> (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[6111])).
% 1.74/2.01 tff(6113,plain,
% 1.74/2.01 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[2754, 6112])).
% 1.74/2.01 tff(6114,plain,
% 1.74/2.01 ($false),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[601, 6113])).
% 1.74/2.01 tff(6115,plain,((~(s(s(s(s(elem!1)))) = s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | b(elem!1, s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.01 tff(6116,plain,
% 1.74/2.01 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[6115, 6107, 601])).
% 1.74/2.01 tff(6117,plain,
% 1.74/2.01 (~(elem!1 = s(s(s(elem!1))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[1518, 6116])).
% 1.74/2.01 tff(6118,plain,
% 1.74/2.01 (r(elem!1, s(s(s(elem!1))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[3284, 6117, 3282])).
% 1.74/2.01 tff(6119,plain,
% 1.74/2.01 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[4083, 6118, 5622])).
% 1.74/2.01 tff(6120,plain,
% 1.74/2.01 (b(s(s(s(elem!1))), s(elem!1))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[664, 6119, 144])).
% 1.74/2.01 tff(6121,plain,
% 1.74/2.01 (~b(elem!1, z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[5639, 6120, 6104, 601, 816])).
% 1.74/2.02 tff(6122,plain,
% 1.74/2.02 (r(elem!1, z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[174, 6121, 3103])).
% 1.74/2.02 tff(6123,plain,
% 1.74/2.02 (~r(s(elem!1), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[287, 6122, 5622])).
% 1.74/2.02 tff(6124,plain,
% 1.74/2.02 (b(s(elem!1), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2380, 6123])).
% 1.74/2.02 tff(6125,plain,
% 1.74/2.02 (r(elem!1, s(s(elem!1)))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[516, 6107, 187])).
% 1.74/2.02 tff(6126,plain,
% 1.74/2.02 (~r(z, s(s(elem!1)))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[978, 6122, 6125])).
% 1.74/2.02 tff(6127,plain,
% 1.74/2.02 (b(z, s(s(elem!1)))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[460, 6126])).
% 1.74/2.02 tff(6128,plain,
% 1.74/2.02 ($false),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[1218, 6127, 6124, 6104, 6106])).
% 1.74/2.02 tff(6129,plain,(b(elem!1, s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (z = elem!1) | b(elem!1, s(elem!1)) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.74/2.02 tff(6130,plain,
% 1.74/2.02 (b(elem!1, s(s(s(elem!1))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[6129, 367, 816, 2170, 601, 91])).
% 1.74/2.02 tff(6131,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(6132,plain,
% 1.74/2.02 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(6133,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1))))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[6132])).
% 1.74/2.02 tff(6134,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.74/2.02 inference(transitivity,[status(thm)],[6133, 6131])).
% 1.74/2.02 tff(6135,plain,
% 1.74/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.74/2.02 inference(quant_inst,[status(thm)],[])).
% 1.74/2.02 tff(6136,plain,
% 1.74/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1))),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[6135, 6134])).
% 1.74/2.02 tff(6137,plain,
% 1.74/2.02 ($false),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[6136, 306, 759, 1663, 1664, 816])).
% 1.74/2.02 tff(6138,plain,((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.02 tff(6139,plain,
% 1.74/2.02 (~b(s(s(s(elem!1))), elem!1)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[6138, 759, 1663, 816])).
% 1.74/2.02 tff(6140,plain,
% 1.74/2.02 (r(s(s(s(elem!1))), elem!1)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[1636, 6139, 1526])).
% 1.74/2.02 tff(6141,plain,
% 1.74/2.02 (~r(z, s(s(s(elem!1))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[5741, 654, 791])).
% 1.74/2.02 tff(6142,plain,
% 1.74/2.02 (b(z, s(s(s(elem!1))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[585, 6141])).
% 1.74/2.02 tff(6143,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(6144,plain,
% 1.74/2.02 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(6145,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1))))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[6144])).
% 1.74/2.02 tff(6146,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.74/2.02 inference(transitivity,[status(thm)],[6145, 6143])).
% 1.74/2.02 tff(6147,plain,
% 1.74/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))),
% 1.74/2.02 inference(quant_inst,[status(thm)],[])).
% 1.74/2.02 tff(6148,plain,
% 1.74/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1))),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[6147, 6146])).
% 1.74/2.02 tff(6149,plain,
% 1.74/2.02 ($false),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[6148, 306, 838, 4012, 818, 1664])).
% 1.74/2.02 tff(6150,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,[]))).
% 1.74/2.02 tff(6151,plain,
% 1.74/2.02 (~b(s(s(s(elem!1))), elem!1)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[6150, 6142, 838, 4012])).
% 1.74/2.02 tff(6152,plain,
% 1.74/2.02 (r(s(s(s(elem!1))), elem!1)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[1636, 6151, 1526])).
% 1.74/2.02 tff(6153,plain,
% 1.74/2.02 ($false),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[4093, 124, 654, 255, 6152])).
% 1.74/2.02 tff(6154,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (s(s(s(elem!1))) = elem!1) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.02 tff(6155,plain,
% 1.74/2.02 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[6154, 5670, 1526, 255, 5634, 791])).
% 1.74/2.02 tff(6156,plain,
% 1.74/2.02 (b(s(s(s(elem!1))), s(elem!1))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[664, 6155, 144])).
% 1.74/2.02 tff(6157,plain,
% 1.74/2.02 (~b(s(s(elem!1)), s(elem!1))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[5639, 6156, 5634, 601, 816])).
% 1.74/2.02 tff(6158,plain,
% 1.74/2.02 (r(s(s(elem!1)), s(elem!1))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[994, 6157, 196])).
% 1.74/2.02 tff(6159,plain,
% 1.74/2.02 (~r(s(s(elem!1)), elem!1)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[5630, 6158, 255])).
% 1.74/2.02 tff(6160,plain,
% 1.74/2.02 (b(s(s(elem!1)), elem!1)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[47, 6159, 91])).
% 1.74/2.02 tff(6161,plain,
% 1.74/2.02 (r(s(elem!1), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2380, 5671])).
% 1.74/2.02 tff(6162,plain,
% 1.74/2.02 (~r(s(s(elem!1)), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[471, 6158, 6161])).
% 1.74/2.02 tff(6163,plain,
% 1.74/2.02 (b(s(s(elem!1)), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[476, 6162])).
% 1.74/2.02 tff(6164,plain,
% 1.74/2.02 ($false),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[3976, 6163, 6160, 2170, 5633, 5669])).
% 1.74/2.02 tff(6165,plain,((~r(z, s(elem!1))) | (z = elem!1) | (s(s(elem!1)) = elem!1) | (~r(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.74/2.02 tff(6166,plain,
% 1.74/2.02 (~r(z, s(elem!1))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[6165, 1526, 91, 255, 601, 816, 2170])).
% 1.74/2.02 tff(6167,plain,
% 1.74/2.02 (b(z, s(elem!1))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[275, 6166])).
% 1.74/2.02 tff(6168,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(6169,plain,
% 1.74/2.02 (((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(6170,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1))))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[6169])).
% 1.74/2.02 tff(6171,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.74/2.02 inference(transitivity,[status(thm)],[6170, 6168])).
% 1.74/2.02 tff(6172,plain,
% 1.74/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1))))))),
% 1.74/2.02 inference(quant_inst,[status(thm)],[])).
% 1.74/2.02 tff(6173,plain,
% 1.74/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1))),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[6172, 6171])).
% 1.74/2.02 tff(6174,plain,
% 1.74/2.02 (~b(z, s(s(s(elem!1))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[6173, 306, 759, 1663, 6167, 816])).
% 1.74/2.02 tff(6175,plain,
% 1.74/2.02 (r(z, s(s(s(elem!1))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[585, 6174])).
% 1.74/2.02 tff(6176,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(6177,plain,
% 1.74/2.02 (((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(6178,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1))))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[6177])).
% 1.74/2.02 tff(6179,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.74/2.02 inference(transitivity,[status(thm)],[6178, 6176])).
% 1.74/2.02 tff(6180,plain,
% 1.74/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)))),
% 1.74/2.02 inference(quant_inst,[status(thm)],[])).
% 1.74/2.02 tff(6181,plain,
% 1.74/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1))),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[6180, 6179])).
% 1.74/2.02 tff(6182,plain,
% 1.74/2.02 (~b(s(s(s(elem!1))), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[6181, 306, 759, 1663, 6167, 816])).
% 1.74/2.02 tff(6183,plain,
% 1.74/2.02 (r(s(s(s(elem!1))), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[3033, 43, 579, 6182])).
% 1.74/2.02 tff(6184,plain,
% 1.74/2.02 (~r(elem!1, z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[3029, 6183, 6140])).
% 1.74/2.02 tff(6185,plain,
% 1.74/2.02 (b(elem!1, z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[174, 6184, 3103])).
% 1.74/2.02 tff(6186,plain,
% 1.74/2.02 (~b(s(s(elem!1)), s(elem!1))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[5639, 6185, 759, 601, 816])).
% 1.74/2.02 tff(6187,plain,
% 1.74/2.02 (r(s(s(elem!1)), s(elem!1))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[994, 6186, 196])).
% 1.74/2.02 tff(6188,plain,
% 1.74/2.02 (~r(s(s(elem!1)), elem!1)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[5630, 6187, 255])).
% 1.74/2.02 tff(6189,plain,
% 1.74/2.02 (b(s(s(elem!1)), elem!1)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[47, 6188, 91])).
% 1.74/2.02 tff(6190,plain,
% 1.74/2.02 (~r(elem!1, s(s(elem!1)))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[1238, 6187, 255])).
% 1.74/2.02 tff(6191,plain,
% 1.74/2.02 (b(elem!1, s(s(elem!1)))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[516, 6190, 187])).
% 1.74/2.02 tff(6192,plain,
% 1.74/2.02 (~b(z, elem!1)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2341, 6191, 6189, 6167, 816])).
% 1.74/2.02 tff(6193,plain,
% 1.74/2.02 (r(z, elem!1)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[835, 6192, 2170])).
% 1.74/2.02 tff(6194,plain,
% 1.74/2.02 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(6195,plain,
% 1.74/2.02 (((~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(6196,plain,
% 1.74/2.02 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[6195])).
% 1.74/2.02 tff(6197,plain,
% 1.74/2.02 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.74/2.02 inference(transitivity,[status(thm)],[6196, 6194])).
% 1.74/2.02 tff(6198,plain,
% 1.74/2.02 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))))),
% 1.74/2.02 inference(quant_inst,[status(thm)],[])).
% 1.74/2.02 tff(6199,plain,
% 1.74/2.02 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[6198, 6197])).
% 1.74/2.02 tff(6200,plain,
% 1.74/2.02 ($false),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[6199, 124, 6193, 6175, 6140])).
% 1.74/2.02 tff(6201,plain,((~b(s(s(s(elem!1))), s(elem!1))) | (z = elem!1) | (~b(s(elem!1), elem!1)) | (s(s(elem!1)) = elem!1) | (~r(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.74/2.02 tff(6202,plain,
% 1.74/2.02 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[6201, 1526, 816, 91, 255, 601, 1663, 2170])).
% 1.74/2.02 tff(6203,plain,
% 1.74/2.02 (r(s(s(s(elem!1))), s(elem!1))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[664, 6202, 144])).
% 1.74/2.02 tff(6204,plain,
% 1.74/2.02 (~r(s(s(s(elem!1))), elem!1)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[4093, 124, 6203, 255])).
% 1.74/2.02 tff(6205,plain,
% 1.74/2.02 (b(s(s(s(elem!1))), elem!1)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[1636, 6204, 1526])).
% 1.74/2.02 tff(6206,plain,
% 1.74/2.02 (~b(s(s(elem!1)), elem!1)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[1672, 6205, 601, 1663])).
% 1.74/2.02 tff(6207,plain,
% 1.74/2.02 (r(s(s(elem!1)), elem!1)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[47, 6206, 91])).
% 1.74/2.02 tff(6208,plain,
% 1.74/2.02 (~r(s(s(elem!1)), s(elem!1))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[5630, 6207, 255])).
% 1.74/2.02 tff(6209,plain,
% 1.74/2.02 (b(s(s(elem!1)), s(elem!1))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[994, 6208, 196])).
% 1.74/2.02 tff(6210,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.87/2.03 inference(rewrite,[status(thm)],[])).
% 1.87/2.03 tff(6211,plain,
% 1.87/2.03 (((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.87/2.03 inference(rewrite,[status(thm)],[])).
% 1.87/2.03 tff(6212,plain,
% 1.87/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1)))))),
% 1.87/2.03 inference(monotonicity,[status(thm)],[6211])).
% 1.87/2.03 tff(6213,plain,
% 1.87/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.87/2.03 inference(transitivity,[status(thm)],[6212, 6210])).
% 1.87/2.03 tff(6214,plain,
% 1.87/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))))),
% 1.87/2.03 inference(quant_inst,[status(thm)],[])).
% 1.87/2.03 tff(6215,plain,
% 1.87/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1)))),
% 1.87/2.03 inference(modus_ponens,[status(thm)],[6214, 6213])).
% 1.87/2.03 tff(6216,plain,
% 1.87/2.03 (~b(z, s(s(elem!1)))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[6215, 306, 1663, 6167, 6209, 816])).
% 1.87/2.03 tff(6217,plain,
% 1.87/2.03 (r(z, s(s(elem!1)))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[460, 6216])).
% 1.87/2.03 tff(6218,plain,
% 1.87/2.03 (~r(z, elem!1)),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[5837, 6217, 6207])).
% 1.87/2.03 tff(6219,plain,
% 1.87/2.03 (b(z, elem!1)),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[835, 6218, 2170])).
% 1.87/2.03 tff(6220,plain,
% 1.87/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.87/2.03 inference(rewrite,[status(thm)],[])).
% 1.87/2.03 tff(6221,plain,
% 1.87/2.03 (((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1)))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.87/2.03 inference(rewrite,[status(thm)],[])).
% 1.87/2.03 tff(6222,plain,
% 1.87/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1))))),
% 1.87/2.03 inference(monotonicity,[status(thm)],[6221])).
% 1.87/2.03 tff(6223,plain,
% 1.87/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.87/2.03 inference(transitivity,[status(thm)],[6222, 6220])).
% 1.87/2.03 tff(6224,plain,
% 1.87/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))),
% 1.87/2.03 inference(quant_inst,[status(thm)],[])).
% 1.87/2.03 tff(6225,plain,
% 1.87/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1))),
% 1.87/2.03 inference(modus_ponens,[status(thm)],[6224, 6223])).
% 1.87/2.03 tff(6226,plain,
% 1.87/2.03 ($false),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[6225, 306, 6219, 1663, 6167, 6205, 816])).
% 1.87/2.03 tff(6227,plain,((s(s(s(elem!1))) = elem!1) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (z = elem!1) | (~r(elem!1, s(elem!1))) | (s(s(elem!1)) = elem!1) | (~b(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.03 tff(6228,plain,
% 1.87/2.03 (s(s(s(elem!1))) = elem!1),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[6227, 6130, 816, 2170, 5622, 91, 601])).
% 1.87/2.03 tff(6229,plain,
% 1.87/2.03 (b(elem!1, s(s(s(elem!1)))) <=> b(elem!1, elem!1)),
% 1.87/2.03 inference(monotonicity,[status(thm)],[6228])).
% 1.87/2.03 tff(6230,plain,
% 1.87/2.03 (b(elem!1, elem!1) <=> b(elem!1, s(s(s(elem!1))))),
% 1.87/2.03 inference(symmetry,[status(thm)],[6229])).
% 1.87/2.03 tff(6231,plain,
% 1.87/2.03 ((~b(elem!1, elem!1)) <=> (~b(elem!1, s(s(s(elem!1)))))),
% 1.87/2.03 inference(monotonicity,[status(thm)],[6230])).
% 1.87/2.03 tff(6232,plain,
% 1.87/2.03 (~b(elem!1, s(s(s(elem!1))))),
% 1.87/2.03 inference(modus_ponens,[status(thm)],[1468, 6231])).
% 1.87/2.03 tff(6233,plain,
% 1.87/2.03 ($false),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[6130, 6232])).
% 1.87/2.03 tff(6234,plain,(b(elem!1, s(elem!1)) | (~b(s(elem!1), elem!1)) | (z = elem!1) | (s(s(elem!1)) = elem!1) | (~b(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.03 tff(6235,plain,
% 1.87/2.03 (b(elem!1, s(elem!1))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[6234, 816, 2170, 91, 601])).
% 1.87/2.03 tff(6236,assumption,(~b(s(s(s(elem!1))), s(elem!1))), introduced(assumption)).
% 1.87/2.03 tff(6237,plain,
% 1.87/2.03 (b(s(s(s(elem!1))), s(elem!1))),
% 1.87/2.03 inference(modus_ponens,[status(thm)],[815, 5898])).
% 1.87/2.03 tff(6238,plain,
% 1.87/2.03 ($false),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[6236, 6237])).
% 1.87/2.03 tff(6239,plain,((~(s(s(s(elem!1))) = elem!1)) | b(s(s(s(elem!1))), s(elem!1)) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.03 tff(6240,plain,
% 1.87/2.03 (~(s(s(s(elem!1))) = elem!1)),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[6239, 6236, 6235])).
% 1.87/2.03 tff(6241,plain,
% 1.87/2.03 (r(s(s(s(elem!1))), s(elem!1))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[664, 6236, 144])).
% 1.87/2.03 tff(6242,plain,
% 1.87/2.03 (~r(z, s(s(s(elem!1))))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[5741, 791, 654])).
% 1.87/2.03 tff(6243,plain,
% 1.87/2.03 (b(z, s(s(s(elem!1))))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[585, 6242])).
% 1.87/2.03 tff(6244,plain,
% 1.87/2.03 (~r(s(s(elem!1)), s(elem!1))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[1600, 6243, 153, 654, 791])).
% 1.87/2.03 tff(6245,plain,
% 1.87/2.03 (b(s(s(elem!1)), s(elem!1))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[994, 6244, 196])).
% 1.87/2.03 tff(6246,plain,
% 1.87/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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(elem!1))))),
% 1.87/2.03 inference(rewrite,[status(thm)],[])).
% 1.87/2.03 tff(6247,plain,
% 1.87/2.03 (((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(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))))),
% 1.87/2.03 inference(rewrite,[status(thm)],[])).
% 1.87/2.03 tff(6248,plain,
% 1.87/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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)))))),
% 1.87/2.03 inference(monotonicity,[status(thm)],[6247])).
% 1.87/2.03 tff(6249,plain,
% 1.87/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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))))),
% 1.87/2.03 inference(transitivity,[status(thm)],[6248, 6246])).
% 1.87/2.03 tff(6250,plain,
% 1.87/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 1.87/2.03 inference(quant_inst,[status(thm)],[])).
% 1.87/2.03 tff(6251,plain,
% 1.87/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1)))),
% 1.87/2.03 inference(modus_ponens,[status(thm)],[6250, 6249])).
% 1.87/2.03 tff(6252,plain,
% 1.87/2.03 (~b(s(s(elem!1)), elem!1)),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[6251, 306, 6245, 816, 6235])).
% 1.87/2.03 tff(6253,plain,
% 1.87/2.03 (r(s(s(elem!1)), elem!1)),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[47, 6252, 91])).
% 1.87/2.03 tff(6254,plain,
% 1.87/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.87/2.03 inference(rewrite,[status(thm)],[])).
% 1.87/2.03 tff(6255,plain,
% 1.87/2.03 (((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), 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(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.87/2.03 inference(rewrite,[status(thm)],[])).
% 1.87/2.03 tff(6256,plain,
% 1.87/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1)))))),
% 1.87/2.03 inference(monotonicity,[status(thm)],[6255])).
% 1.87/2.03 tff(6257,plain,
% 1.87/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.87/2.03 inference(transitivity,[status(thm)],[6256, 6254])).
% 1.87/2.03 tff(6258,plain,
% 1.87/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), 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))))))),
% 1.87/2.03 inference(quant_inst,[status(thm)],[])).
% 1.87/2.03 tff(6259,plain,
% 1.87/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1)))),
% 1.87/2.03 inference(modus_ponens,[status(thm)],[6258, 6257])).
% 1.87/2.03 tff(6260,plain,
% 1.87/2.03 ($false),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[6259, 306, 818, 1005, 1198, 601, 816])).
% 1.87/2.03 tff(6261,plain,((~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.03 tff(6262,plain,
% 1.87/2.03 (~b(z, s(s(elem!1)))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[6261, 6243, 6245, 601, 816])).
% 1.87/2.03 tff(6263,plain,
% 1.87/2.03 (r(z, s(s(elem!1)))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[460, 6262])).
% 1.87/2.03 tff(6264,plain,
% 1.87/2.03 (~r(z, elem!1)),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[5837, 6263, 6253])).
% 1.87/2.03 tff(6265,plain,
% 1.87/2.03 (b(z, elem!1)),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[835, 6264, 2170])).
% 1.87/2.03 tff(6266,plain,
% 1.87/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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)), s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 1.87/2.03 inference(rewrite,[status(thm)],[])).
% 1.87/2.03 tff(6267,plain,
% 1.87/2.03 (((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 1.87/2.03 inference(rewrite,[status(thm)],[])).
% 1.87/2.03 tff(6268,plain,
% 1.87/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1)))))),
% 1.87/2.03 inference(monotonicity,[status(thm)],[6267])).
% 1.87/2.03 tff(6269,plain,
% 1.87/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 1.87/2.03 inference(transitivity,[status(thm)],[6268, 6266])).
% 1.87/2.03 tff(6270,plain,
% 1.87/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))),
% 1.87/2.03 inference(quant_inst,[status(thm)],[])).
% 1.87/2.03 tff(6271,plain,
% 1.87/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1)))),
% 1.87/2.03 inference(modus_ponens,[status(thm)],[6270, 6269])).
% 1.87/2.03 tff(6272,plain,
% 1.87/2.03 (~b(elem!1, s(s(elem!1)))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[6271, 306, 6245, 816, 6235])).
% 1.87/2.03 tff(6273,plain,
% 1.87/2.03 (r(elem!1, s(s(elem!1)))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[516, 6272, 187])).
% 1.87/2.03 tff(6274,plain,
% 1.87/2.03 (~r(elem!1, z)),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[978, 6263, 6273])).
% 1.87/2.03 tff(6275,plain,
% 1.87/2.03 (b(elem!1, z)),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[174, 6274, 3103])).
% 1.87/2.03 tff(6276,plain,
% 1.87/2.03 (~b(s(elem!1), z)),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[4020, 6275, 6235, 6265])).
% 1.87/2.03 tff(6277,plain,
% 1.87/2.03 (r(s(elem!1), z)),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[2380, 6276])).
% 1.87/2.03 tff(6278,plain,
% 1.87/2.03 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[1284, 144])).
% 1.87/2.03 tff(6279,plain,
% 1.87/2.03 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[3437, 153])).
% 1.87/2.03 tff(6280,plain,
% 1.87/2.03 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[6115, 6272, 601])).
% 1.87/2.03 tff(6281,plain,
% 1.87/2.03 (~(elem!1 = s(s(s(elem!1))))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[1518, 6280])).
% 1.87/2.03 tff(6282,plain,
% 1.87/2.03 (~(s(s(s(elem!1))) = elem!1)),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[2187, 6281])).
% 1.87/2.03 tff(6283,plain,
% 1.87/2.03 (~b(s(s(s(elem!1))), elem!1)),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[6150, 6275, 6243, 6265])).
% 1.87/2.03 tff(6284,plain,
% 1.87/2.03 (r(s(s(s(elem!1))), elem!1)),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[1636, 6283, 6282])).
% 1.87/2.03 tff(6285,plain,
% 1.87/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), 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))))))),
% 1.87/2.03 inference(rewrite,[status(thm)],[])).
% 1.87/2.03 tff(6286,plain,
% 1.87/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), 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))))))),
% 1.87/2.03 inference(quant_inst,[status(thm)],[])).
% 1.87/2.03 tff(6287,plain,
% 1.87/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.87/2.03 inference(modus_ponens,[status(thm)],[6286, 6285])).
% 1.87/2.03 tff(6288,plain,
% 1.87/2.03 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[6287, 306, 1005, 601, 816, 4890])).
% 1.87/2.03 tff(6289,plain,
% 1.87/2.03 ($false),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[1958, 43, 3476, 4888, 6288])).
% 1.87/2.03 tff(6290,plain,((~r(s(s(s(s(elem!1)))), elem!1)) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.03 tff(6291,plain,
% 1.87/2.03 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[6290, 6284, 6245, 601, 816, 6279, 6278, 6273])).
% 1.87/2.03 tff(6292,plain,
% 1.87/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, 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)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)))),
% 1.87/2.03 inference(rewrite,[status(thm)],[])).
% 1.87/2.03 tff(6293,plain,
% 1.87/2.03 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~b(elem!1, z)) | (~b(z, 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)))),
% 1.87/2.03 inference(rewrite,[status(thm)],[])).
% 1.87/2.03 tff(6294,plain,
% 1.87/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, 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))))),
% 1.87/2.03 inference(monotonicity,[status(thm)],[6293])).
% 1.87/2.03 tff(6295,plain,
% 1.87/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, 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)))),
% 1.87/2.03 inference(transitivity,[status(thm)],[6294, 6292])).
% 1.87/2.03 tff(6296,plain,
% 1.87/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.87/2.03 inference(quant_inst,[status(thm)],[])).
% 1.87/2.03 tff(6297,plain,
% 1.87/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, 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))),
% 1.87/2.03 inference(modus_ponens,[status(thm)],[6296, 6295])).
% 1.87/2.03 tff(6298,plain,
% 1.87/2.03 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[6297, 306, 838, 4012, 816, 2076])).
% 1.87/2.03 tff(6299,plain,
% 1.87/2.03 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[1767, 43, 1516, 6298])).
% 1.87/2.03 tff(6300,plain,
% 1.87/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.87/2.03 inference(rewrite,[status(thm)],[])).
% 1.87/2.03 tff(6301,plain,
% 1.87/2.03 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.87/2.04 inference(rewrite,[status(thm)],[])).
% 1.87/2.04 tff(6302,plain,
% 1.87/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), elem!1))))),
% 1.87/2.04 inference(monotonicity,[status(thm)],[6301])).
% 1.87/2.04 tff(6303,plain,
% 1.87/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.87/2.04 inference(transitivity,[status(thm)],[6302, 6300])).
% 1.87/2.04 tff(6304,plain,
% 1.87/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.87/2.04 inference(quant_inst,[status(thm)],[])).
% 1.87/2.04 tff(6305,plain,
% 1.87/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), elem!1))),
% 1.87/2.04 inference(modus_ponens,[status(thm)],[6304, 6303])).
% 1.87/2.04 tff(6306,plain,
% 1.87/2.04 (~b(s(s(s(s(elem!1)))), z)),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[6305, 306, 838, 4012, 2076])).
% 1.87/2.04 tff(6307,plain,
% 1.87/2.04 (r(s(s(s(s(elem!1)))), z)),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[5723, 6306])).
% 1.87/2.04 tff(6308,plain,
% 1.87/2.04 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.87/2.04 inference(rewrite,[status(thm)],[])).
% 1.87/2.04 tff(6309,plain,
% 1.87/2.04 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.87/2.04 inference(quant_inst,[status(thm)],[])).
% 1.87/2.04 tff(6310,plain,
% 1.87/2.04 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.87/2.04 inference(modus_ponens,[status(thm)],[6309, 6308])).
% 1.87/2.04 tff(6311,plain,
% 1.87/2.04 ($false),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[6310, 124, 466, 6307, 6299])).
% 1.87/2.04 tff(6312,plain,((~b(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), z)) | (s(s(s(s(elem!1)))) = s(elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.04 tff(6313,plain,
% 1.87/2.04 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[6312, 6277, 6280, 6265, 6275, 816])).
% 1.87/2.04 tff(6314,plain,
% 1.87/2.04 (s(s(s(s(elem!1)))) = elem!1),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[1736, 6313, 6291])).
% 1.87/2.04 tff(6315,plain,
% 1.87/2.04 (elem!1 = s(s(s(s(elem!1))))),
% 1.87/2.04 inference(symmetry,[status(thm)],[1744])).
% 1.87/2.04 tff(6316,plain,
% 1.87/2.04 (s(z) = s(s(s(s(elem!1))))),
% 1.87/2.04 inference(transitivity,[status(thm)],[3595, 6315])).
% 1.87/2.04 tff(6317,plain,
% 1.87/2.04 (inj_0(s(z)) = inj_0(s(s(s(s(elem!1)))))),
% 1.87/2.04 inference(monotonicity,[status(thm)],[6316])).
% 1.87/2.04 tff(6318,plain,
% 1.87/2.04 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(z))),
% 1.87/2.04 inference(symmetry,[status(thm)],[6317])).
% 1.87/2.04 tff(6319,plain,
% 1.87/2.04 (s(s(s(elem!1))) = z),
% 1.87/2.04 inference(transitivity,[status(thm)],[1281, 6318, 61])).
% 1.87/2.04 tff(6320,plain,
% 1.87/2.04 ($false),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[579, 6319])).
% 1.87/2.04 tff(6321,plain,((~(elem!1 = s(z))) | (~(s(s(s(s(elem!1)))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.04 tff(6322,plain,
% 1.87/2.04 (~(elem!1 = s(z))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[6321, 6314])).
% 1.87/2.04 tff(6323,plain,
% 1.87/2.04 (~(s(z) = elem!1)),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[89, 6322])).
% 1.87/2.04 tff(6324,plain,
% 1.87/2.04 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))))),
% 1.87/2.04 inference(rewrite,[status(thm)],[])).
% 1.87/2.04 tff(6325,plain,
% 1.87/2.04 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))))),
% 1.87/2.04 inference(quant_inst,[status(thm)],[])).
% 1.87/2.04 tff(6326,plain,
% 1.87/2.04 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1))))),
% 1.87/2.04 inference(modus_ponens,[status(thm)],[6325, 6324])).
% 1.87/2.04 tff(6327,plain,
% 1.87/2.04 (~r(s(z), s(s(elem!1)))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[6326, 124, 1730, 4])).
% 1.87/2.04 tff(6328,plain,
% 1.87/2.04 (b(s(z), s(s(elem!1)))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[3997, 43, 79, 6327])).
% 1.87/2.04 tff(6329,plain,
% 1.87/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.87/2.04 inference(rewrite,[status(thm)],[])).
% 1.87/2.04 tff(6330,plain,
% 1.87/2.04 (((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.87/2.04 inference(rewrite,[status(thm)],[])).
% 1.87/2.04 tff(6331,plain,
% 1.87/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.87/2.04 inference(monotonicity,[status(thm)],[6330])).
% 1.87/2.04 tff(6332,plain,
% 1.87/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.87/2.04 inference(transitivity,[status(thm)],[6331, 6329])).
% 1.87/2.04 tff(6333,plain,
% 1.87/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.87/2.04 inference(quant_inst,[status(thm)],[])).
% 1.87/2.04 tff(6334,plain,
% 1.87/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(s(elem!1)))))),
% 1.87/2.04 inference(modus_ponens,[status(thm)],[6333, 6332])).
% 1.87/2.04 tff(6335,plain,
% 1.87/2.04 ($false),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[6334, 306, 1005, 601, 816, 6328, 3018])).
% 1.87/2.04 tff(6336,plain,((~r(s(z), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.04 tff(6337,plain,
% 1.87/2.04 (~r(s(z), elem!1)),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[6336, 6245, 601, 816, 6284, 6253])).
% 1.87/2.04 tff(6338,plain,
% 1.87/2.04 ((s(z) = elem!1) | b(s(z), elem!1)),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[1500, 43, 6337])).
% 1.87/2.04 tff(6339,plain,
% 1.87/2.04 (b(s(z), elem!1)),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[6338, 6323])).
% 1.87/2.04 tff(6340,plain,
% 1.87/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))),
% 1.87/2.04 inference(rewrite,[status(thm)],[])).
% 1.87/2.04 tff(6341,plain,
% 1.87/2.04 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))),
% 1.87/2.04 inference(rewrite,[status(thm)],[])).
% 1.87/2.04 tff(6342,plain,
% 1.87/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z))))),
% 1.87/2.04 inference(monotonicity,[status(thm)],[6341])).
% 1.87/2.04 tff(6343,plain,
% 1.87/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))),
% 1.87/2.04 inference(transitivity,[status(thm)],[6342, 6340])).
% 1.87/2.04 tff(6344,plain,
% 1.87/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))),
% 1.87/2.04 inference(quant_inst,[status(thm)],[])).
% 1.87/2.04 tff(6345,plain,
% 1.87/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z))),
% 1.87/2.04 inference(modus_ponens,[status(thm)],[6344, 6343])).
% 1.87/2.04 tff(6346,plain,
% 1.87/2.04 (~b(s(z), z)),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[6345, 306, 6265, 6275, 6339])).
% 1.87/2.04 tff(6347,plain,
% 1.87/2.04 (r(s(z), z)),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[221, 6346])).
% 1.87/2.04 tff(6348,plain,
% 1.87/2.04 (~r(s(elem!1), s(z))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[2634, 6347, 6277])).
% 1.87/2.04 tff(6349,plain,
% 1.87/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))),
% 1.87/2.04 inference(rewrite,[status(thm)],[])).
% 1.87/2.04 tff(6350,plain,
% 1.87/2.04 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z)))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))),
% 1.87/2.04 inference(rewrite,[status(thm)],[])).
% 1.87/2.04 tff(6351,plain,
% 1.87/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(elem!1), elem!1)) | (~b(s(elem!1), s(z)))))),
% 1.87/2.04 inference(monotonicity,[status(thm)],[6350])).
% 1.87/2.04 tff(6352,plain,
% 1.87/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(elem!1), elem!1)) | (~b(s(elem!1), s(z))))),
% 1.87/2.04 inference(transitivity,[status(thm)],[6351, 6349])).
% 1.87/2.04 tff(6353,plain,
% 1.87/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))),
% 1.87/2.04 inference(quant_inst,[status(thm)],[])).
% 1.87/2.04 tff(6354,plain,
% 1.87/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z)))),
% 1.87/2.04 inference(modus_ponens,[status(thm)],[6353, 6352])).
% 1.87/2.04 tff(6355,plain,
% 1.87/2.04 (~b(s(elem!1), s(z))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[6354, 306, 6265, 6275, 816, 6339])).
% 1.87/2.04 tff(6356,plain,
% 1.87/2.04 ($false),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[2612, 43, 6355, 6348, 3099])).
% 1.87/2.04 tff(6357,plain,((~r(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (z = elem!1) | (s(s(elem!1)) = elem!1) | (~r(s(s(s(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.04 tff(6358,plain,
% 1.87/2.04 (~r(z, s(elem!1))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[6357, 6241, 601, 2170, 91, 816])).
% 1.87/2.04 tff(6359,plain,
% 1.87/2.04 (b(z, s(elem!1))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[275, 6358])).
% 1.87/2.04 tff(6360,plain,
% 1.87/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))),
% 1.87/2.04 inference(rewrite,[status(thm)],[])).
% 1.87/2.04 tff(6361,plain,
% 1.87/2.04 (((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))),
% 1.87/2.04 inference(rewrite,[status(thm)],[])).
% 1.87/2.04 tff(6362,plain,
% 1.87/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1)))))),
% 1.87/2.04 inference(monotonicity,[status(thm)],[6361])).
% 1.87/2.04 tff(6363,plain,
% 1.87/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))),
% 1.87/2.04 inference(transitivity,[status(thm)],[6362, 6360])).
% 1.87/2.04 tff(6364,plain,
% 1.87/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)))),
% 1.87/2.04 inference(quant_inst,[status(thm)],[])).
% 1.87/2.04 tff(6365,plain,
% 1.87/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1)))),
% 1.87/2.04 inference(modus_ponens,[status(thm)],[6364, 6363])).
% 1.87/2.04 tff(6366,plain,
% 1.87/2.04 ($false),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[6365, 306, 4012, 817, 816, 815])).
% 1.87/2.04 tff(6367,plain,((~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.04 tff(6368,plain,
% 1.87/2.04 (~b(elem!1, z)),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[6367, 6359, 816, 6235])).
% 1.87/2.04 tff(6369,plain,
% 1.87/2.04 (r(elem!1, z)),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[174, 6368, 3103])).
% 1.87/2.04 tff(6370,plain,
% 1.87/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))),
% 1.87/2.04 inference(rewrite,[status(thm)],[])).
% 1.87/2.04 tff(6371,plain,
% 1.87/2.04 (((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, elem!1))) <=> ((~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))),
% 1.87/2.04 inference(rewrite,[status(thm)],[])).
% 1.87/2.04 tff(6372,plain,
% 1.87/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1)))))),
% 1.87/2.04 inference(monotonicity,[status(thm)],[6371])).
% 1.87/2.04 tff(6373,plain,
% 1.87/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))),
% 1.87/2.04 inference(transitivity,[status(thm)],[6372, 6370])).
% 1.87/2.04 tff(6374,plain,
% 1.87/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, elem!1)))),
% 1.87/2.04 inference(quant_inst,[status(thm)],[])).
% 1.87/2.04 tff(6375,plain,
% 1.87/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1)))),
% 1.87/2.04 inference(modus_ponens,[status(thm)],[6374, 6373])).
% 1.87/2.04 tff(6376,plain,
% 1.87/2.04 (~b(z, elem!1)),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[6375, 306, 6359, 816, 6235])).
% 1.87/2.04 tff(6377,plain,
% 1.87/2.04 (r(z, elem!1)),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[835, 6376, 2170])).
% 1.87/2.05 tff(6378,plain,
% 1.87/2.05 (~r(elem!1, s(s(elem!1)))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[978, 437, 246])).
% 1.87/2.05 tff(6379,plain,
% 1.87/2.05 (b(elem!1, s(s(elem!1)))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[516, 6378, 187])).
% 1.87/2.05 tff(6380,plain,
% 1.87/2.05 (~r(s(s(elem!1)), elem!1)),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[5837, 437, 374])).
% 1.87/2.05 tff(6381,plain,
% 1.87/2.05 (b(s(s(elem!1)), elem!1)),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[47, 6380, 91])).
% 1.87/2.05 tff(6382,plain,
% 1.87/2.05 (((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), 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(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.87/2.05 inference(rewrite,[status(thm)],[])).
% 1.87/2.05 tff(6383,plain,
% 1.87/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1))))),
% 1.87/2.05 inference(monotonicity,[status(thm)],[6382])).
% 1.87/2.05 tff(6384,plain,
% 1.87/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.87/2.05 inference(transitivity,[status(thm)],[6383, 3838])).
% 1.87/2.05 tff(6385,plain,
% 1.87/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), 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)))),
% 1.87/2.05 inference(quant_inst,[status(thm)],[])).
% 1.87/2.05 tff(6386,plain,
% 1.87/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1))),
% 1.87/2.05 inference(modus_ponens,[status(thm)],[6385, 6384])).
% 1.87/2.05 tff(6387,plain,
% 1.87/2.05 (~b(s(s(s(elem!1))), elem!1)),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[6386, 306, 6381, 6379, 601])).
% 1.87/2.05 tff(6388,plain,
% 1.87/2.05 (r(s(s(s(elem!1))), elem!1)),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[1636, 6387, 1526])).
% 1.87/2.05 tff(6389,plain,
% 1.87/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))))),
% 1.87/2.05 inference(rewrite,[status(thm)],[])).
% 1.87/2.05 tff(6390,plain,
% 1.87/2.05 (((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))))),
% 1.87/2.05 inference(rewrite,[status(thm)],[])).
% 1.87/2.05 tff(6391,plain,
% 1.87/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1))))))),
% 1.87/2.05 inference(monotonicity,[status(thm)],[6390])).
% 1.87/2.05 tff(6392,plain,
% 1.87/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))))),
% 1.87/2.05 inference(transitivity,[status(thm)],[6391, 6389])).
% 1.87/2.05 tff(6393,plain,
% 1.87/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.87/2.05 inference(quant_inst,[status(thm)],[])).
% 1.87/2.05 tff(6394,plain,
% 1.87/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1))))),
% 1.87/2.05 inference(modus_ponens,[status(thm)],[6393, 6392])).
% 1.87/2.05 tff(6395,plain,
% 1.87/2.05 (~b(elem!1, s(s(s(elem!1))))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[6394, 306, 6381, 6379, 601])).
% 1.87/2.05 tff(6396,plain,
% 1.87/2.05 (r(elem!1, s(s(s(elem!1))))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[3284, 6395, 1642])).
% 1.87/2.05 tff(6397,plain,
% 1.87/2.05 (~r(z, s(s(s(elem!1))))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[573, 6396, 374])).
% 1.87/2.05 tff(6398,plain,
% 1.87/2.05 (b(z, s(s(s(elem!1))))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[585, 6397])).
% 1.87/2.05 tff(6399,plain,
% 1.87/2.05 (~r(s(z), elem!1)),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[3042, 6398, 6388, 246])).
% 1.87/2.05 tff(6400,plain,
% 1.87/2.05 (~(s(elem!1) = s(s(elem!1)))),
% 1.87/2.05 inference(modus_ponens,[status(thm)],[196, 1658])).
% 1.87/2.05 tff(6401,plain,
% 1.87/2.05 (~b(s(elem!1), s(s(elem!1)))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[6021, 306, 6381, 6379, 816])).
% 1.87/2.05 tff(6402,plain,
% 1.87/2.05 ((s(elem!1) = s(s(elem!1))) | r(s(elem!1), s(s(elem!1)))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[1684, 43, 6401])).
% 1.87/2.05 tff(6403,plain,
% 1.87/2.05 (r(s(elem!1), s(s(elem!1)))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[6402, 6400])).
% 1.87/2.05 tff(6404,plain,
% 1.87/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))))),
% 1.87/2.05 inference(rewrite,[status(thm)],[])).
% 1.87/2.05 tff(6405,plain,
% 1.87/2.05 (((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(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), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))))),
% 1.87/2.05 inference(rewrite,[status(thm)],[])).
% 1.87/2.05 tff(6406,plain,
% 1.87/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1))))))),
% 1.87/2.05 inference(monotonicity,[status(thm)],[6405])).
% 1.87/2.05 tff(6407,plain,
% 1.87/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))))),
% 1.87/2.05 inference(transitivity,[status(thm)],[6406, 6404])).
% 1.87/2.05 tff(6408,plain,
% 1.87/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))))),
% 1.87/2.05 inference(quant_inst,[status(thm)],[])).
% 1.87/2.05 tff(6409,plain,
% 1.87/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1))))),
% 1.87/2.05 inference(modus_ponens,[status(thm)],[6408, 6407])).
% 1.87/2.05 tff(6410,plain,
% 1.87/2.05 (~b(s(z), s(s(elem!1)))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[6409, 306, 30, 1003, 2831])).
% 1.87/2.05 tff(6411,plain,
% 1.87/2.05 (r(s(z), s(s(elem!1)))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[3997, 43, 6410, 79])).
% 1.87/2.05 tff(6412,plain,
% 1.87/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))),
% 1.87/2.05 inference(rewrite,[status(thm)],[])).
% 1.87/2.05 tff(6413,plain,
% 1.87/2.05 (((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))),
% 1.87/2.05 inference(rewrite,[status(thm)],[])).
% 1.87/2.05 tff(6414,plain,
% 1.87/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z)))))),
% 1.87/2.05 inference(monotonicity,[status(thm)],[6413])).
% 1.87/2.05 tff(6415,plain,
% 1.87/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))),
% 1.87/2.05 inference(transitivity,[status(thm)],[6414, 6412])).
% 1.87/2.05 tff(6416,plain,
% 1.87/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))),
% 1.87/2.05 inference(quant_inst,[status(thm)],[])).
% 1.87/2.05 tff(6417,plain,
% 1.87/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z)))),
% 1.87/2.05 inference(modus_ponens,[status(thm)],[6416, 6415])).
% 1.87/2.05 tff(6418,plain,
% 1.87/2.05 (~b(s(elem!1), s(z))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[6417, 306, 30, 1003, 816, 2831])).
% 1.87/2.05 tff(6419,plain,
% 1.87/2.05 (r(s(elem!1), s(z))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[2612, 43, 6418, 2249])).
% 1.87/2.05 tff(6420,plain,
% 1.87/2.05 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(elem!1)))))),
% 1.87/2.05 inference(rewrite,[status(thm)],[])).
% 1.87/2.05 tff(6421,plain,
% 1.87/2.05 (((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z)))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(elem!1)))))),
% 1.87/2.05 inference(rewrite,[status(thm)],[])).
% 1.87/2.05 tff(6422,plain,
% 1.87/2.05 (((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(elem!1))))))),
% 1.87/2.05 inference(monotonicity,[status(thm)],[6421])).
% 1.87/2.05 tff(6423,plain,
% 1.87/2.05 (((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(elem!1)))))),
% 1.87/2.05 inference(transitivity,[status(thm)],[6422, 6420])).
% 1.87/2.05 tff(6424,plain,
% 1.87/2.05 ((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1), s(z))))),
% 1.87/2.05 inference(quant_inst,[status(thm)],[])).
% 1.87/2.05 tff(6425,plain,
% 1.87/2.05 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(elem!1))))),
% 1.87/2.05 inference(modus_ponens,[status(thm)],[6424, 6423])).
% 1.87/2.05 tff(6426,plain,
% 1.87/2.05 ($false),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[6425, 124, 6419, 4445, 6411])).
% 1.87/2.05 tff(6427,plain,((~b(s(z), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (s(elem!1) = s(z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.05 tff(6428,plain,
% 1.87/2.05 (~b(s(z), elem!1)),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[6427, 6403, 2249, 6381, 6379, 816])).
% 1.87/2.05 tff(6429,plain,
% 1.87/2.05 ((s(z) = elem!1) | r(s(z), elem!1)),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[1500, 43, 6428])).
% 1.87/2.05 tff(6430,plain,
% 1.87/2.05 (s(z) = elem!1),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[6429, 6399])).
% 1.87/2.05 tff(6431,plain,
% 1.87/2.05 (s(s(z)) = s(elem!1)),
% 1.87/2.05 inference(monotonicity,[status(thm)],[6430])).
% 1.87/2.05 tff(6432,plain,
% 1.87/2.05 (s(s(s(z))) = s(s(elem!1))),
% 1.87/2.05 inference(monotonicity,[status(thm)],[6431])).
% 1.87/2.05 tff(6433,plain,
% 1.87/2.05 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.87/2.05 inference(monotonicity,[status(thm)],[6432])).
% 1.87/2.05 tff(6434,plain,
% 1.87/2.05 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 1.87/2.05 inference(monotonicity,[status(thm)],[6433])).
% 1.87/2.05 tff(6435,plain,
% 1.87/2.05 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 1.87/2.05 inference(monotonicity,[status(thm)],[6434, 6431])).
% 1.87/2.05 tff(6436,plain,
% 1.87/2.05 ((s(s(s(s(elem!1)))) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(s(z)))),
% 1.87/2.05 inference(symmetry,[status(thm)],[6435])).
% 1.87/2.05 tff(6437,plain,
% 1.87/2.05 (~r(s(s(s(elem!1))), z)),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[3029, 6388, 246])).
% 1.87/2.05 tff(6438,plain,
% 1.87/2.05 (b(s(s(s(elem!1))), z)),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[3033, 43, 579, 6437])).
% 1.87/2.05 tff(6439,plain,
% 1.87/2.05 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[1958, 43, 3476, 4888])).
% 1.87/2.05 tff(6440,plain,
% 1.87/2.05 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.87/2.05 inference(rewrite,[status(thm)],[])).
% 1.87/2.05 tff(6441,plain,
% 1.87/2.05 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.87/2.05 inference(quant_inst,[status(thm)],[])).
% 1.87/2.05 tff(6442,plain,
% 1.87/2.05 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), z))),
% 1.87/2.05 inference(modus_ponens,[status(thm)],[6441, 6440])).
% 1.87/2.05 tff(6443,plain,
% 1.87/2.05 (~r(s(s(s(s(elem!1)))), z)),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[6442, 124, 374, 1289])).
% 1.87/2.05 tff(6444,plain,
% 1.87/2.05 (b(s(s(s(s(elem!1)))), z)),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[5723, 6443])).
% 1.87/2.05 tff(6445,assumption,(b(s(s(s(elem!1))), z)), introduced(assumption)).
% 1.87/2.05 tff(6446,plain,
% 1.87/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.87/2.05 inference(rewrite,[status(thm)],[])).
% 1.87/2.05 tff(6447,plain,
% 1.87/2.05 (((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(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(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.87/2.05 inference(rewrite,[status(thm)],[])).
% 1.87/2.05 tff(6448,plain,
% 1.87/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z))))),
% 1.87/2.05 inference(monotonicity,[status(thm)],[6447])).
% 1.87/2.05 tff(6449,plain,
% 1.87/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.87/2.05 inference(transitivity,[status(thm)],[6448, 6446])).
% 1.87/2.05 tff(6450,plain,
% 1.87/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.87/2.05 inference(quant_inst,[status(thm)],[])).
% 1.87/2.05 tff(6451,plain,
% 1.87/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z))),
% 1.87/2.05 inference(modus_ponens,[status(thm)],[6450, 6449])).
% 1.87/2.05 tff(6452,plain,
% 1.87/2.05 ($false),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[6451, 306, 818, 6445, 6444, 6439])).
% 1.87/2.05 tff(6453,plain,((~r(s(s(s(s(elem!1)))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.05 tff(6454,plain,
% 1.87/2.05 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[6453, 6398, 6438, 6279, 6388, 374])).
% 1.87/2.05 tff(6455,plain,
% 1.87/2.05 (elem!1 = s(z)),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[89, 6430])).
% 1.87/2.05 tff(6456,plain,
% 1.87/2.05 (~(s(s(s(s(elem!1)))) = elem!1)),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[6321, 6455])).
% 1.87/2.05 tff(6457,plain,
% 1.87/2.05 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[1736, 6456, 6454])).
% 1.87/2.05 tff(6458,plain,
% 1.87/2.05 (s(s(s(s(elem!1)))) = s(elem!1)),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[4458, 6457, 815, 6278, 816, 6381, 6403])).
% 1.87/2.05 tff(6459,plain,
% 1.87/2.05 (s(s(s(s(s(z))))) = s(s(z))),
% 1.87/2.05 inference(modus_ponens,[status(thm)],[6458, 6436])).
% 1.87/2.05 tff(6460,assumption,(s(s(s(s(s(z))))) = s(s(z))), introduced(assumption)).
% 1.87/2.05 tff(6461,plain,
% 1.87/2.05 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(z)))),
% 1.87/2.05 inference(monotonicity,[status(thm)],[6460])).
% 1.87/2.05 tff(6462,plain,
% 1.87/2.05 (s(s(s(s(z)))) = s(z)),
% 1.87/2.05 inference(transitivity,[status(thm)],[497, 6461, 546])).
% 1.87/2.05 tff(6463,plain,
% 1.87/2.05 ($false),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[324, 6462])).
% 1.87/2.05 tff(6464,plain,(~(s(s(s(s(s(z))))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.05 tff(6465,plain,
% 1.87/2.05 ($false),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[6464, 6459])).
% 1.87/2.05 tff(6466,plain,((~r(z, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~r(elem!1, z)) | (s(elem!1) = s(z)) | (~r(z, elem!1)) | (s(s(s(elem!1))) = elem!1) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.87/2.05 tff(6467,plain,
% 1.87/2.05 (~r(z, s(s(elem!1)))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[6466, 6369, 816, 6235, 3099, 6377, 6240, 601, 91])).
% 1.87/2.05 tff(6468,plain,
% 1.87/2.05 (b(z, s(s(elem!1)))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[460, 6467])).
% 1.87/2.05 tff(6469,plain,
% 1.87/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 1.87/2.05 inference(rewrite,[status(thm)],[])).
% 1.87/2.05 tff(6470,plain,
% 1.87/2.05 (((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1))))) <=> ((~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 1.87/2.05 inference(rewrite,[status(thm)],[])).
% 1.87/2.05 tff(6471,plain,
% 1.87/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1)))))),
% 1.87/2.05 inference(monotonicity,[status(thm)],[6470])).
% 1.87/2.05 tff(6472,plain,
% 1.87/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 1.87/2.05 inference(transitivity,[status(thm)],[6471, 6469])).
% 1.87/2.06 tff(6473,plain,
% 1.87/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))))),
% 1.87/2.06 inference(quant_inst,[status(thm)],[])).
% 1.87/2.06 tff(6474,plain,
% 1.87/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1)))),
% 1.87/2.06 inference(modus_ponens,[status(thm)],[6473, 6472])).
% 1.87/2.06 tff(6475,plain,
% 1.87/2.06 ($false),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[6474, 306, 817, 1005, 1198, 816, 815])).
% 1.87/2.06 tff(6476,plain,((~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.06 tff(6477,plain,
% 1.87/2.06 (~b(s(s(elem!1)), s(elem!1))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[6476, 6468, 816, 6235, 6359])).
% 1.87/2.06 tff(6478,plain,
% 1.87/2.06 (r(s(s(elem!1)), s(elem!1))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[994, 6477, 196])).
% 1.87/2.06 tff(6479,plain,
% 1.87/2.06 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[886, 6478, 6241])).
% 1.87/2.06 tff(6480,plain,
% 1.87/2.06 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[891, 6479, 153])).
% 1.87/2.06 tff(6481,assumption,(~b(s(s(elem!1)), elem!1)), introduced(assumption)).
% 1.87/2.06 tff(6482,plain,
% 1.87/2.06 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), elem!1)),
% 1.87/2.06 inference(monotonicity,[status(thm)],[2184])).
% 1.87/2.06 tff(6483,plain,
% 1.87/2.06 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.87/2.06 inference(symmetry,[status(thm)],[6482])).
% 1.87/2.06 tff(6484,plain,
% 1.87/2.06 ((~b(s(s(elem!1)), elem!1)) <=> (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.87/2.06 inference(monotonicity,[status(thm)],[6483])).
% 1.87/2.06 tff(6485,plain,
% 1.87/2.06 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.87/2.06 inference(modus_ponens,[status(thm)],[6481, 6484])).
% 1.87/2.06 tff(6486,plain,
% 1.87/2.06 ($false),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[1590, 6485])).
% 1.87/2.06 tff(6487,plain,((~(s(s(s(elem!1))) = elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | b(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.87/2.06 tff(6488,plain,
% 1.87/2.06 (~(s(s(s(elem!1))) = elem!1)),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[6487, 6481, 1590])).
% 1.87/2.06 tff(6489,plain,
% 1.87/2.06 (~(elem!1 = s(s(s(elem!1))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[1641, 6488])).
% 1.87/2.06 tff(6490,plain,
% 1.87/2.06 (r(s(s(elem!1)), elem!1)),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[47, 6481, 91])).
% 1.87/2.06 tff(6491,plain,
% 1.87/2.06 (~r(z, s(s(elem!1)))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[5837, 6490, 374])).
% 1.87/2.06 tff(6492,plain,
% 1.87/2.06 (b(z, s(s(elem!1)))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[460, 6491])).
% 1.87/2.06 tff(6493,plain,
% 1.87/2.06 (~r(elem!1, s(s(s(elem!1))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[5777, 6492, 601, 153, 246, 6490])).
% 1.87/2.06 tff(6494,plain,
% 1.87/2.06 (b(elem!1, s(s(s(elem!1))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[3284, 6493, 6489])).
% 1.87/2.06 tff(6495,plain,
% 1.87/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, 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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.87/2.06 inference(rewrite,[status(thm)],[])).
% 1.87/2.06 tff(6496,plain,
% 1.87/2.06 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.87/2.06 inference(rewrite,[status(thm)],[])).
% 1.87/2.06 tff(6497,plain,
% 1.87/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(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(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.87/2.06 inference(monotonicity,[status(thm)],[6496])).
% 1.87/2.06 tff(6498,plain,
% 1.87/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(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(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.87/2.06 inference(transitivity,[status(thm)],[6497, 6495])).
% 1.87/2.06 tff(6499,plain,
% 1.87/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(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(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))))),
% 1.87/2.06 inference(quant_inst,[status(thm)],[])).
% 1.87/2.06 tff(6500,plain,
% 1.87/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, 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)))))),
% 1.87/2.06 inference(modus_ponens,[status(thm)],[6499, 6498])).
% 1.87/2.06 tff(6501,plain,
% 1.87/2.06 (~b(elem!1, s(s(elem!1)))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[6500, 306, 6494, 1590, 601])).
% 1.87/2.06 tff(6502,plain,
% 1.87/2.06 (r(elem!1, s(s(elem!1)))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[516, 6501, 187])).
% 1.87/2.06 tff(6503,plain,
% 1.87/2.06 (~b(s(s(s(elem!1))), z)),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[5774, 306, 6492, 1590, 601])).
% 1.87/2.06 tff(6504,plain,
% 1.87/2.06 (r(s(s(s(elem!1))), z)),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[3033, 43, 579, 6503])).
% 1.87/2.06 tff(6505,plain,
% 1.87/2.06 (~r(s(s(s(elem!1))), elem!1)),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[3029, 6504, 246])).
% 1.87/2.06 tff(6506,plain,
% 1.87/2.06 (b(s(s(s(elem!1))), elem!1)),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[1636, 6505, 6488])).
% 1.87/2.06 tff(6507,plain,
% 1.87/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.87/2.06 inference(rewrite,[status(thm)],[])).
% 1.87/2.06 tff(6508,plain,
% 1.87/2.06 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~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(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.87/2.06 inference(rewrite,[status(thm)],[])).
% 1.87/2.06 tff(6509,plain,
% 1.87/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.87/2.06 inference(monotonicity,[status(thm)],[6508])).
% 1.87/2.06 tff(6510,plain,
% 1.87/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.87/2.06 inference(transitivity,[status(thm)],[6509, 6507])).
% 1.87/2.06 tff(6511,plain,
% 1.87/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~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)))),
% 1.87/2.06 inference(quant_inst,[status(thm)],[])).
% 1.87/2.06 tff(6512,plain,
% 1.87/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.87/2.06 inference(modus_ponens,[status(thm)],[6511, 6510])).
% 1.87/2.06 tff(6513,plain,
% 1.87/2.06 (~b(s(s(s(s(elem!1)))), z)),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[6512, 306, 1198, 1590, 1664, 4890])).
% 1.87/2.06 tff(6514,plain,
% 1.87/2.06 ($false),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[5723, 6513, 6443])).
% 1.87/2.06 tff(6515,plain,((~r(s(s(s(s(elem!1)))), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.06 tff(6516,plain,
% 1.87/2.06 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[6515, 6492, 1590, 6506, 374, 6278, 6502])).
% 1.87/2.06 tff(6517,plain,
% 1.87/2.06 (~(s(elem!1) = s(s(s(elem!1))))),
% 1.87/2.06 inference(modus_ponens,[status(thm)],[144, 1870])).
% 1.87/2.06 tff(6518,plain,
% 1.87/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.87/2.06 inference(rewrite,[status(thm)],[])).
% 1.87/2.06 tff(6519,plain,
% 1.87/2.06 (((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.87/2.06 inference(rewrite,[status(thm)],[])).
% 1.87/2.06 tff(6520,plain,
% 1.87/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1)))))))),
% 1.87/2.06 inference(monotonicity,[status(thm)],[6519])).
% 1.87/2.06 tff(6521,plain,
% 1.87/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.87/2.06 inference(transitivity,[status(thm)],[6520, 6518])).
% 1.87/2.06 tff(6522,plain,
% 1.87/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.87/2.06 inference(quant_inst,[status(thm)],[])).
% 1.87/2.06 tff(6523,plain,
% 1.87/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1)))))),
% 1.87/2.06 inference(modus_ponens,[status(thm)],[6522, 6521])).
% 1.87/2.06 tff(6524,plain,
% 1.87/2.06 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[6523, 306, 6494, 6506, 816])).
% 1.87/2.06 tff(6525,plain,
% 1.87/2.06 ((s(elem!1) = s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[1881, 43, 6524])).
% 1.87/2.06 tff(6526,plain,
% 1.87/2.06 (r(s(elem!1), s(s(s(elem!1))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[6525, 6517])).
% 1.87/2.06 tff(6527,plain,
% 1.87/2.06 (~b(z, s(s(s(elem!1))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[1598, 6492, 601, 1590])).
% 1.87/2.06 tff(6528,plain,
% 1.87/2.06 (r(z, s(s(s(elem!1))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[585, 6527])).
% 1.87/2.06 tff(6529,plain,
% 1.87/2.06 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))))),
% 1.87/2.06 inference(rewrite,[status(thm)],[])).
% 1.87/2.06 tff(6530,plain,
% 1.87/2.06 (((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z))) <=> ((~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))))),
% 1.87/2.06 inference(rewrite,[status(thm)],[])).
% 1.87/2.06 tff(6531,plain,
% 1.87/2.06 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1)))))))),
% 1.87/2.06 inference(monotonicity,[status(thm)],[6530])).
% 1.87/2.06 tff(6532,plain,
% 1.87/2.06 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))))),
% 1.87/2.06 inference(transitivity,[status(thm)],[6531, 6529])).
% 1.87/2.06 tff(6533,plain,
% 1.87/2.06 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)))),
% 1.87/2.06 inference(quant_inst,[status(thm)],[])).
% 1.87/2.06 tff(6534,plain,
% 1.87/2.06 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1)))))),
% 1.87/2.06 inference(modus_ponens,[status(thm)],[6533, 6532])).
% 1.87/2.06 tff(6535,plain,
% 1.87/2.06 (~r(s(elem!1), z)),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[6534, 124, 6528, 6526])).
% 1.87/2.06 tff(6536,plain,
% 1.87/2.06 (b(s(elem!1), z)),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[2380, 6535])).
% 1.87/2.06 tff(6537,plain,
% 1.87/2.06 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)))),
% 1.87/2.06 inference(rewrite,[status(thm)],[])).
% 1.87/2.06 tff(6538,plain,
% 1.87/2.06 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)))),
% 1.87/2.06 inference(quant_inst,[status(thm)],[])).
% 1.87/2.06 tff(6539,plain,
% 1.87/2.06 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z))),
% 1.87/2.06 inference(modus_ponens,[status(thm)],[6538, 6537])).
% 1.87/2.06 tff(6540,plain,
% 1.87/2.06 (~r(s(s(elem!1)), z)),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[6539, 124, 374, 6490])).
% 1.87/2.06 tff(6541,plain,
% 1.87/2.06 (b(s(s(elem!1)), z)),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[476, 6540])).
% 1.87/2.06 tff(6542,plain,
% 1.87/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 1.87/2.06 inference(rewrite,[status(thm)],[])).
% 1.87/2.06 tff(6543,plain,
% 1.87/2.06 (((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 1.87/2.06 inference(rewrite,[status(thm)],[])).
% 1.87/2.06 tff(6544,plain,
% 1.87/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z))))),
% 1.87/2.06 inference(monotonicity,[status(thm)],[6543])).
% 1.87/2.06 tff(6545,plain,
% 1.87/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 1.87/2.06 inference(transitivity,[status(thm)],[6544, 6542])).
% 1.87/2.06 tff(6546,plain,
% 1.87/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.87/2.06 inference(quant_inst,[status(thm)],[])).
% 1.87/2.06 tff(6547,plain,
% 1.87/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z))),
% 1.87/2.06 inference(modus_ponens,[status(thm)],[6546, 6545])).
% 1.87/2.06 tff(6548,plain,
% 1.87/2.06 (~b(s(elem!1), s(s(elem!1)))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[6547, 306, 6536, 817, 6541])).
% 1.87/2.06 tff(6549,plain,
% 1.87/2.06 ((s(elem!1) = s(s(elem!1))) | r(s(elem!1), s(s(elem!1)))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[1684, 43, 6548])).
% 1.87/2.06 tff(6550,plain,
% 1.87/2.06 (r(s(elem!1), s(s(elem!1)))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[6549, 6400])).
% 1.87/2.06 tff(6551,plain,
% 1.87/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)))),
% 1.87/2.06 inference(rewrite,[status(thm)],[])).
% 1.87/2.06 tff(6552,plain,
% 1.87/2.06 (((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)))),
% 1.87/2.06 inference(rewrite,[status(thm)],[])).
% 1.87/2.06 tff(6553,plain,
% 1.87/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z))))),
% 1.87/2.06 inference(monotonicity,[status(thm)],[6552])).
% 1.87/2.06 tff(6554,plain,
% 1.87/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)))),
% 1.87/2.06 inference(transitivity,[status(thm)],[6553, 6551])).
% 1.87/2.06 tff(6555,plain,
% 1.87/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))))),
% 1.87/2.06 inference(quant_inst,[status(thm)],[])).
% 1.87/2.06 tff(6556,plain,
% 1.87/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z))),
% 1.87/2.06 inference(modus_ponens,[status(thm)],[6555, 6554])).
% 1.87/2.06 tff(6557,plain,
% 1.87/2.06 (~b(s(z), s(s(elem!1)))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[6556, 306, 1199, 817, 3968, 247])).
% 1.87/2.06 tff(6558,plain,
% 1.87/2.06 (r(s(z), s(s(elem!1)))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[3997, 43, 6557, 79])).
% 1.87/2.06 tff(6559,plain,
% 1.87/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))),
% 1.87/2.06 inference(rewrite,[status(thm)],[])).
% 1.87/2.06 tff(6560,plain,
% 1.87/2.06 (((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z)))) <=> ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))),
% 1.87/2.06 inference(rewrite,[status(thm)],[])).
% 1.87/2.06 tff(6561,plain,
% 1.87/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), s(z)))))),
% 1.87/2.06 inference(monotonicity,[status(thm)],[6560])).
% 1.87/2.06 tff(6562,plain,
% 1.87/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))),
% 1.87/2.06 inference(transitivity,[status(thm)],[6561, 6559])).
% 1.87/2.07 tff(6563,plain,
% 1.87/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))),
% 1.87/2.07 inference(quant_inst,[status(thm)],[])).
% 1.87/2.07 tff(6564,plain,
% 1.87/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), s(z)))),
% 1.87/2.07 inference(modus_ponens,[status(thm)],[6563, 6562])).
% 1.87/2.07 tff(6565,plain,
% 1.87/2.07 (~b(s(elem!1), s(z))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[6564, 306, 1199, 817, 247])).
% 1.87/2.07 tff(6566,plain,
% 1.87/2.07 (r(s(elem!1), s(z))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[2612, 43, 6565, 2249])).
% 1.87/2.07 tff(6567,plain,
% 1.87/2.07 ($false),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[6425, 124, 6566, 4445, 6558])).
% 1.87/2.07 tff(6568,plain,((~b(s(z), z)) | (~r(s(elem!1), s(s(elem!1)))) | (s(elem!1) = s(z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.07 tff(6569,plain,
% 1.87/2.07 (~b(s(z), z)),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[6568, 6550, 2249, 6541, 817, 6536])).
% 1.87/2.07 tff(6570,plain,
% 1.87/2.07 (r(s(z), z)),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[221, 6569])).
% 1.87/2.07 tff(6571,plain,
% 1.87/2.07 (~r(s(z), s(s(s(elem!1))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[4074, 6528, 6570])).
% 1.87/2.07 tff(6572,plain,
% 1.87/2.07 (b(s(z), s(s(s(elem!1))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[3017, 43, 645, 6571])).
% 1.87/2.07 tff(6573,plain,
% 1.87/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.87/2.07 inference(rewrite,[status(thm)],[])).
% 1.87/2.07 tff(6574,plain,
% 1.87/2.07 (((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), elem!1))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.87/2.07 inference(rewrite,[status(thm)],[])).
% 1.87/2.07 tff(6575,plain,
% 1.87/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.87/2.07 inference(monotonicity,[status(thm)],[6574])).
% 1.87/2.07 tff(6576,plain,
% 1.87/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.87/2.07 inference(transitivity,[status(thm)],[6575, 6573])).
% 1.87/2.07 tff(6577,plain,
% 1.87/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), elem!1)))),
% 1.87/2.07 inference(quant_inst,[status(thm)],[])).
% 1.87/2.07 tff(6578,plain,
% 1.87/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1)))))),
% 1.87/2.07 inference(modus_ponens,[status(thm)],[6577, 6576])).
% 1.87/2.07 tff(6579,plain,
% 1.87/2.07 (~b(s(z), elem!1)),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[6578, 306, 6494, 6506, 6572])).
% 1.87/2.07 tff(6580,plain,
% 1.87/2.07 (~r(s(z), elem!1)),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[1049, 6570, 246])).
% 1.87/2.07 tff(6581,plain,
% 1.87/2.07 ((s(z) = elem!1) | b(s(z), elem!1)),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[1500, 43, 6580])).
% 1.87/2.07 tff(6582,plain,
% 1.87/2.07 (s(z) = elem!1),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[6581, 6579])).
% 1.87/2.07 tff(6583,plain,
% 1.87/2.07 (elem!1 = s(z)),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[89, 6582])).
% 1.87/2.07 tff(6584,plain,
% 1.87/2.07 (~(s(s(s(s(elem!1)))) = elem!1)),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[6321, 6583])).
% 1.87/2.07 tff(6585,plain,
% 1.87/2.07 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[1736, 6584, 6516])).
% 1.87/2.07 tff(6586,plain,
% 1.87/2.07 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[1776, 306, 6494, 6506, 6585])).
% 1.87/2.07 tff(6587,plain,
% 1.87/2.07 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[1958, 43, 6279, 6586])).
% 1.87/2.07 tff(6588,plain,
% 1.87/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(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(s(s(s(elem!1))), elem!1)))),
% 1.87/2.07 inference(rewrite,[status(thm)],[])).
% 1.87/2.07 tff(6589,plain,
% 1.87/2.07 (((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.87/2.07 inference(rewrite,[status(thm)],[])).
% 1.87/2.07 tff(6590,plain,
% 1.87/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1))))),
% 1.87/2.07 inference(monotonicity,[status(thm)],[6589])).
% 1.87/2.07 tff(6591,plain,
% 1.87/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.87/2.07 inference(transitivity,[status(thm)],[6590, 6588])).
% 1.87/2.07 tff(6592,plain,
% 1.87/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.87/2.07 inference(quant_inst,[status(thm)],[])).
% 1.87/2.07 tff(6593,plain,
% 1.87/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1))),
% 1.87/2.07 inference(modus_ponens,[status(thm)],[6592, 6591])).
% 1.87/2.07 tff(6594,plain,
% 1.87/2.07 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[6593, 306, 6494, 6506, 816, 6585])).
% 1.87/2.07 tff(6595,plain,
% 1.87/2.07 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[6115, 6501, 601])).
% 1.87/2.07 tff(6596,plain,
% 1.87/2.07 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[1767, 43, 6595, 6594])).
% 1.87/2.07 tff(6597,plain,
% 1.87/2.07 ($false),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[1962, 124, 654, 6596, 6587])).
% 1.87/2.07 tff(6598,plain,(b(s(s(elem!1)), 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))))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (s(elem!1) = s(z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.87/2.07 tff(6599,plain,
% 1.87/2.07 (b(s(s(elem!1)), elem!1)),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[6598, 6480, 816, 6241, 6377, 6369, 3099, 6359, 601, 91])).
% 1.87/2.07 tff(6600,plain,
% 1.87/2.07 (~(elem!1 = s(s(s(elem!1))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[1641, 6240])).
% 1.87/2.07 tff(6601,plain,
% 1.87/2.07 (~b(z, s(s(s(elem!1))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[1598, 6480, 601, 6468])).
% 1.87/2.07 tff(6602,plain,
% 1.87/2.07 (r(z, s(s(s(elem!1))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[585, 6601])).
% 1.87/2.07 tff(6603,plain,
% 1.87/2.07 (~r(elem!1, s(s(s(elem!1))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[573, 6602, 6377])).
% 1.87/2.07 tff(6604,plain,
% 1.87/2.07 (b(elem!1, s(s(s(elem!1))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[3284, 6603, 6600])).
% 1.87/2.07 tff(6605,plain,
% 1.87/2.07 (~b(s(s(s(elem!1))), elem!1)),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[1672, 6604, 601, 6599])).
% 1.87/2.07 tff(6606,plain,
% 1.87/2.07 (r(s(s(s(elem!1))), elem!1)),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[1636, 6605, 6240])).
% 1.87/2.07 tff(6607,plain,
% 1.87/2.07 ($false),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[6199, 124, 6377, 6602, 6606])).
% 1.87/2.07 tff(6608,plain,(b(s(s(s(elem!1))), s(elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (s(s(elem!1)) = elem!1) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.87/2.07 tff(6609,plain,
% 1.87/2.07 (b(s(s(s(elem!1))), s(elem!1))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[6608, 601, 816, 91, 2170])).
% 1.87/2.07 tff(6610,plain,
% 1.87/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))),
% 1.87/2.07 inference(rewrite,[status(thm)],[])).
% 1.87/2.07 tff(6611,plain,
% 1.87/2.07 (((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))),
% 1.87/2.07 inference(rewrite,[status(thm)],[])).
% 1.87/2.07 tff(6612,plain,
% 1.87/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1)))))),
% 1.87/2.07 inference(monotonicity,[status(thm)],[6611])).
% 1.87/2.07 tff(6613,plain,
% 1.87/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))),
% 1.87/2.07 inference(transitivity,[status(thm)],[6612, 6610])).
% 1.87/2.07 tff(6614,plain,
% 1.87/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(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))))))),
% 1.87/2.07 inference(quant_inst,[status(thm)],[])).
% 1.87/2.07 tff(6615,plain,
% 1.87/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1)))),
% 1.87/2.07 inference(modus_ponens,[status(thm)],[6614, 6613])).
% 1.87/2.07 tff(6616,plain,
% 1.87/2.07 ($false),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[6615, 306, 759, 1663, 816, 815])).
% 1.87/2.07 tff(6617,plain,((~b(s(s(s(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)))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.07 tff(6618,plain,
% 1.87/2.07 (~b(elem!1, s(s(s(elem!1))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[6617, 6609, 816, 6235])).
% 1.87/2.07 tff(6619,plain,
% 1.87/2.07 (b(elem!1, s(s(s(s(elem!1))))) <=> b(elem!1, s(elem!1))),
% 1.87/2.07 inference(monotonicity,[status(thm)],[5713])).
% 1.87/2.07 tff(6620,plain,
% 1.87/2.07 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 1.87/2.07 inference(symmetry,[status(thm)],[6619])).
% 1.87/2.07 tff(6621,plain,
% 1.87/2.07 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.87/2.07 inference(modus_ponens,[status(thm)],[6235, 6620])).
% 1.87/2.07 tff(6622,assumption,(b(elem!1, s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.87/2.07 tff(6623,plain,
% 1.87/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.87/2.07 inference(rewrite,[status(thm)],[])).
% 1.87/2.07 tff(6624,plain,
% 1.87/2.07 (((~b(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(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.87/2.07 inference(rewrite,[status(thm)],[])).
% 1.87/2.07 tff(6625,plain,
% 1.87/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1))))))))),
% 1.87/2.07 inference(monotonicity,[status(thm)],[6624])).
% 1.87/2.07 tff(6626,plain,
% 1.87/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.87/2.07 inference(transitivity,[status(thm)],[6625, 6623])).
% 1.87/2.07 tff(6627,plain,
% 1.87/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.87/2.07 inference(quant_inst,[status(thm)],[])).
% 1.87/2.07 tff(6628,plain,
% 1.87/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 1.87/2.07 inference(modus_ponens,[status(thm)],[6627, 6626])).
% 1.87/2.07 tff(6629,plain,
% 1.87/2.07 ($false),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[6628, 306, 759, 6622, 1005, 601, 816])).
% 1.87/2.07 tff(6630,plain,((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.07 tff(6631,plain,
% 1.87/2.07 (~b(s(s(elem!1)), s(elem!1))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[6630, 6621, 816, 6609, 601])).
% 1.87/2.07 tff(6632,plain,
% 1.87/2.07 (r(s(s(elem!1)), s(elem!1))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[994, 6631, 196])).
% 1.87/2.07 tff(6633,plain,
% 1.87/2.07 (elem!1 = s(s(s(elem!1)))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[2187, 2184])).
% 1.87/2.07 tff(6634,plain,
% 1.87/2.07 (s(s(s(s(elem!1)))) = s(elem!1)),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[1518, 6633])).
% 1.87/2.07 tff(6635,plain,
% 1.87/2.07 (b(elem!1, s(s(elem!1)))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[6115, 6634, 601])).
% 1.87/2.07 tff(6636,plain,
% 1.87/2.07 (~b(z, s(elem!1))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[6367, 4012, 816, 815])).
% 1.87/2.07 tff(6637,plain,
% 1.87/2.07 (r(z, s(elem!1))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[275, 6636])).
% 1.87/2.07 tff(6638,plain,
% 1.87/2.07 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.87/2.07 inference(rewrite,[status(thm)],[])).
% 1.87/2.07 tff(6639,plain,
% 1.87/2.07 (((~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)), z)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.87/2.07 inference(rewrite,[status(thm)],[])).
% 1.87/2.07 tff(6640,plain,
% 1.87/2.07 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1)))))),
% 1.87/2.07 inference(monotonicity,[status(thm)],[6639])).
% 1.87/2.07 tff(6641,plain,
% 1.87/2.07 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.87/2.07 inference(transitivity,[status(thm)],[6640, 6638])).
% 1.87/2.07 tff(6642,plain,
% 1.87/2.07 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)))),
% 1.87/2.07 inference(quant_inst,[status(thm)],[])).
% 1.87/2.07 tff(6643,plain,
% 1.87/2.07 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1)))),
% 1.87/2.07 inference(modus_ponens,[status(thm)],[6642, 6641])).
% 1.87/2.07 tff(6644,plain,
% 1.87/2.07 (~r(s(s(elem!1)), z)),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[6643, 124, 6637, 244])).
% 1.87/2.07 tff(6645,plain,
% 1.87/2.07 (b(s(s(elem!1)), z)),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[476, 6644])).
% 1.87/2.07 tff(6646,plain,
% 1.87/2.07 (~r(z, s(s(elem!1)))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[799, 6637, 244])).
% 1.87/2.07 tff(6647,plain,
% 1.87/2.07 (b(z, s(s(elem!1)))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[460, 6646])).
% 1.87/2.07 tff(6648,plain,
% 1.87/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 1.87/2.07 inference(rewrite,[status(thm)],[])).
% 1.87/2.07 tff(6649,plain,
% 1.87/2.07 (((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 1.87/2.07 inference(rewrite,[status(thm)],[])).
% 1.87/2.08 tff(6650,plain,
% 1.87/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z))))),
% 1.87/2.08 inference(monotonicity,[status(thm)],[6649])).
% 1.87/2.08 tff(6651,plain,
% 1.87/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 1.87/2.08 inference(transitivity,[status(thm)],[6650, 6648])).
% 1.87/2.08 tff(6652,plain,
% 1.87/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))))),
% 1.87/2.08 inference(quant_inst,[status(thm)],[])).
% 1.87/2.08 tff(6653,plain,
% 1.87/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z))),
% 1.87/2.08 inference(modus_ponens,[status(thm)],[6652, 6651])).
% 1.87/2.08 tff(6654,plain,
% 1.87/2.08 ($false),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[6653, 306, 4012, 6647, 1003, 6645])).
% 1.87/2.08 tff(6655,plain,((~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.08 tff(6656,plain,
% 1.87/2.08 (~b(elem!1, z)),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[6655, 6635, 6632, 816, 6235])).
% 1.87/2.08 tff(6657,plain,
% 1.87/2.08 (r(elem!1, z)),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[174, 6656, 3103])).
% 1.87/2.08 tff(6658,plain,
% 1.87/2.08 ((s(z) = s(s(s(elem!1)))) <=> (s(z) = elem!1)),
% 1.87/2.08 inference(monotonicity,[status(thm)],[2184])).
% 1.87/2.08 tff(6659,plain,
% 1.87/2.08 ((s(z) = s(s(s(elem!1)))) <=> (elem!1 = s(z))),
% 1.87/2.08 inference(transitivity,[status(thm)],[6658, 84])).
% 1.87/2.08 tff(6660,plain,
% 1.87/2.08 ((s(z) = s(s(s(elem!1)))) <=> (s(z) = elem!1)),
% 1.87/2.08 inference(transitivity,[status(thm)],[6659, 3092])).
% 1.87/2.08 tff(6661,plain,
% 1.87/2.08 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(z) = elem!1))),
% 1.87/2.08 inference(monotonicity,[status(thm)],[6660])).
% 1.87/2.08 tff(6662,plain,
% 1.87/2.08 (~(s(z) = elem!1)),
% 1.87/2.08 inference(modus_ponens,[status(thm)],[645, 6661])).
% 1.87/2.08 tff(6663,plain,
% 1.87/2.08 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(elem!1), elem!1)),
% 1.87/2.08 inference(monotonicity,[status(thm)],[5713])).
% 1.87/2.08 tff(6664,plain,
% 1.87/2.08 (b(s(elem!1), elem!1) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 1.87/2.08 inference(symmetry,[status(thm)],[6663])).
% 1.87/2.08 tff(6665,plain,
% 1.87/2.08 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.87/2.08 inference(modus_ponens,[status(thm)],[816, 6664])).
% 1.87/2.08 tff(6666,plain,
% 1.87/2.08 (~(s(z) = s(s(s(s(elem!1)))))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[6065, 6633, 3099])).
% 1.87/2.08 tff(6667,plain,
% 1.87/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))),
% 1.87/2.08 inference(rewrite,[status(thm)],[])).
% 1.87/2.08 tff(6668,plain,
% 1.87/2.08 (((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z))) <=> ((~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))),
% 1.87/2.08 inference(rewrite,[status(thm)],[])).
% 1.87/2.08 tff(6669,plain,
% 1.87/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1)))))),
% 1.87/2.08 inference(monotonicity,[status(thm)],[6668])).
% 1.87/2.08 tff(6670,plain,
% 1.87/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))),
% 1.87/2.08 inference(transitivity,[status(thm)],[6669, 6667])).
% 1.87/2.08 tff(6671,plain,
% 1.87/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 1.87/2.08 inference(quant_inst,[status(thm)],[])).
% 1.87/2.08 tff(6672,plain,
% 1.87/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1)))),
% 1.87/2.08 inference(modus_ponens,[status(thm)],[6671, 6670])).
% 1.87/2.08 tff(6673,plain,
% 1.87/2.08 (~b(s(elem!1), z)),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[6672, 306, 838, 816, 815])).
% 1.87/2.08 tff(6674,plain,
% 1.87/2.08 (r(s(elem!1), z)),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[2380, 6673])).
% 1.87/2.08 tff(6675,plain,
% 1.87/2.08 (~r(s(s(elem!1)), z)),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[471, 6674, 244])).
% 1.87/2.08 tff(6676,plain,
% 1.87/2.08 (b(s(s(elem!1)), z)),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[476, 6675])).
% 1.87/2.08 tff(6677,plain,
% 1.87/2.08 (((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1)))) <=> ((~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))),
% 1.87/2.08 inference(rewrite,[status(thm)],[])).
% 1.87/2.08 tff(6678,plain,
% 1.87/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1)))))),
% 1.87/2.08 inference(monotonicity,[status(thm)],[6677])).
% 1.87/2.08 tff(6679,plain,
% 1.87/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))),
% 1.87/2.08 inference(transitivity,[status(thm)],[6678, 6370])).
% 1.87/2.08 tff(6680,plain,
% 1.87/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))),
% 1.87/2.08 inference(quant_inst,[status(thm)],[])).
% 1.87/2.08 tff(6681,plain,
% 1.87/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1)))),
% 1.87/2.08 inference(modus_ponens,[status(thm)],[6680, 6679])).
% 1.87/2.08 tff(6682,plain,
% 1.87/2.08 (~b(z, s(elem!1))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[6681, 306, 838, 816, 815])).
% 1.87/2.08 tff(6683,plain,
% 1.87/2.08 (r(z, s(elem!1))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[275, 6682])).
% 1.87/2.08 tff(6684,plain,
% 1.87/2.08 (~r(z, s(s(elem!1)))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[799, 6683, 244])).
% 1.87/2.08 tff(6685,plain,
% 1.87/2.08 (b(z, s(s(elem!1)))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[460, 6684])).
% 1.87/2.08 tff(6686,plain,
% 1.87/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 1.87/2.08 inference(rewrite,[status(thm)],[])).
% 1.87/2.08 tff(6687,plain,
% 1.87/2.08 (((~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1))) <=> ((~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 1.87/2.08 inference(rewrite,[status(thm)],[])).
% 1.87/2.08 tff(6688,plain,
% 1.87/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z))))),
% 1.87/2.08 inference(monotonicity,[status(thm)],[6687])).
% 1.87/2.08 tff(6689,plain,
% 1.87/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 1.87/2.08 inference(transitivity,[status(thm)],[6688, 6686])).
% 1.87/2.08 tff(6690,plain,
% 1.87/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)))),
% 1.87/2.08 inference(quant_inst,[status(thm)],[])).
% 1.87/2.08 tff(6691,plain,
% 1.87/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z))),
% 1.87/2.08 inference(modus_ponens,[status(thm)],[6690, 6689])).
% 1.87/2.08 tff(6692,plain,
% 1.87/2.08 ($false),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[6691, 306, 838, 6685, 1003, 6676])).
% 1.87/2.08 tff(6693,plain,((~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.08 tff(6694,plain,
% 1.87/2.08 (~b(z, elem!1)),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[6693, 6635, 6632, 816, 6235])).
% 1.87/2.08 tff(6695,plain,
% 1.87/2.08 (r(z, elem!1)),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[835, 6694, 2170])).
% 1.87/2.08 tff(6696,plain,
% 1.87/2.08 (~r(s(s(elem!1)), z)),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[6539, 124, 374, 1730])).
% 1.87/2.08 tff(6697,plain,
% 1.87/2.08 (b(s(s(elem!1)), z)),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[476, 6696])).
% 1.87/2.08 tff(6698,plain,
% 1.87/2.08 (~r(z, s(s(elem!1)))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[5837, 1730, 374])).
% 1.87/2.08 tff(6699,plain,
% 1.87/2.08 (b(z, s(s(elem!1)))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[460, 6698])).
% 1.87/2.08 tff(6700,plain,
% 1.87/2.08 (((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 1.87/2.08 inference(rewrite,[status(thm)],[])).
% 1.87/2.08 tff(6701,plain,
% 1.87/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z))))),
% 1.87/2.08 inference(monotonicity,[status(thm)],[6700])).
% 1.87/2.08 tff(6702,plain,
% 1.87/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 1.87/2.08 inference(transitivity,[status(thm)],[6701, 6648])).
% 1.87/2.08 tff(6703,plain,
% 1.87/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)))),
% 1.87/2.08 inference(quant_inst,[status(thm)],[])).
% 1.87/2.08 tff(6704,plain,
% 1.87/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z))),
% 1.87/2.08 inference(modus_ponens,[status(thm)],[6703, 6702])).
% 1.87/2.08 tff(6705,plain,
% 1.87/2.08 (~b(elem!1, z)),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[6704, 306, 6699, 1003, 6697])).
% 1.87/2.08 tff(6706,plain,
% 1.87/2.08 (r(elem!1, z)),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[174, 6705, 1616])).
% 1.87/2.08 tff(6707,plain,
% 1.87/2.08 (s(elem!1) = s(s(s(s(elem!1))))),
% 1.87/2.08 inference(symmetry,[status(thm)],[5713])).
% 1.87/2.08 tff(6708,plain,
% 1.87/2.08 (r(s(z), s(elem!1)) <=> r(s(z), s(s(s(s(elem!1)))))),
% 1.87/2.08 inference(monotonicity,[status(thm)],[6707])).
% 1.87/2.08 tff(6709,plain,
% 1.87/2.08 (r(s(z), s(s(s(s(elem!1))))) <=> r(s(z), s(elem!1))),
% 1.87/2.08 inference(symmetry,[status(thm)],[6708])).
% 1.87/2.08 tff(6710,plain,
% 1.87/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.87/2.08 inference(rewrite,[status(thm)],[])).
% 1.87/2.08 tff(6711,plain,
% 1.87/2.08 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(elem!1))))))) <=> ((~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.87/2.08 inference(rewrite,[status(thm)],[])).
% 1.87/2.08 tff(6712,plain,
% 1.87/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 1.87/2.08 inference(monotonicity,[status(thm)],[6711])).
% 1.87/2.08 tff(6713,plain,
% 1.87/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.87/2.08 inference(transitivity,[status(thm)],[6712, 6710])).
% 1.87/2.08 tff(6714,plain,
% 1.87/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.87/2.08 inference(quant_inst,[status(thm)],[])).
% 1.87/2.08 tff(6715,plain,
% 1.87/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1))))))),
% 1.87/2.08 inference(modus_ponens,[status(thm)],[6714, 6713])).
% 1.87/2.08 tff(6716,plain,
% 1.87/2.08 ((~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1))))))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[6715, 306])).
% 1.87/2.08 tff(6717,plain,
% 1.87/2.08 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[6716, 2831, 2076, 6622])).
% 1.87/2.08 tff(6718,plain,
% 1.87/2.08 (r(s(z), s(s(s(s(elem!1)))))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[6078, 6717, 6074])).
% 1.87/2.08 tff(6719,plain,
% 1.87/2.08 (r(s(z), s(elem!1))),
% 1.87/2.08 inference(modus_ponens,[status(thm)],[6718, 6709])).
% 1.87/2.08 tff(6720,plain,
% 1.87/2.08 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1))))),
% 1.87/2.08 inference(rewrite,[status(thm)],[])).
% 1.87/2.08 tff(6721,plain,
% 1.87/2.08 (((~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1))))),
% 1.87/2.08 inference(rewrite,[status(thm)],[])).
% 1.87/2.08 tff(6722,plain,
% 1.87/2.08 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1)))))),
% 1.87/2.08 inference(monotonicity,[status(thm)],[6721])).
% 1.87/2.08 tff(6723,plain,
% 1.87/2.08 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1))))),
% 1.87/2.08 inference(transitivity,[status(thm)],[6722, 6720])).
% 1.87/2.08 tff(6724,plain,
% 1.87/2.08 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(elem!1)))))),
% 1.87/2.08 inference(quant_inst,[status(thm)],[])).
% 1.87/2.08 tff(6725,plain,
% 1.87/2.08 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1)))),
% 1.87/2.08 inference(modus_ponens,[status(thm)],[6724, 6723])).
% 1.87/2.08 tff(6726,plain,
% 1.87/2.08 (~r(s(z), s(s(elem!1)))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[6725, 124, 244, 6719])).
% 1.87/2.08 tff(6727,plain,
% 1.87/2.08 (b(s(z), s(s(elem!1)))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[3997, 43, 79, 6726])).
% 1.87/2.08 tff(6728,plain,
% 1.87/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 1.87/2.08 inference(rewrite,[status(thm)],[])).
% 1.87/2.08 tff(6729,plain,
% 1.87/2.08 (((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 1.87/2.08 inference(rewrite,[status(thm)],[])).
% 1.87/2.08 tff(6730,plain,
% 1.87/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z))))),
% 1.87/2.08 inference(monotonicity,[status(thm)],[6729])).
% 1.87/2.08 tff(6731,plain,
% 1.87/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 1.87/2.08 inference(transitivity,[status(thm)],[6730, 6728])).
% 1.87/2.08 tff(6732,plain,
% 1.87/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)))),
% 1.87/2.08 inference(quant_inst,[status(thm)],[])).
% 1.87/2.08 tff(6733,plain,
% 1.87/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z))),
% 1.87/2.08 inference(modus_ponens,[status(thm)],[6732, 6731])).
% 1.87/2.08 tff(6734,plain,
% 1.87/2.08 ($false),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[6733, 306, 1198, 1003, 3968, 6727, 2831])).
% 1.87/2.08 tff(6735,plain,((~b(s(z), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~(s(s(s(elem!1))) = elem!1)) | (s(z) = s(s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.08 tff(6736,plain,
% 1.87/2.08 (~b(s(z), elem!1)),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[6735, 6699, 1003, 6697, 244, 2184, 6074, 2076, 6622])).
% 1.87/2.08 tff(6737,plain,
% 1.87/2.08 (r(s(z), elem!1)),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[1500, 43, 6736, 6662])).
% 1.87/2.08 tff(6738,plain,
% 1.87/2.08 (~r(s(z), z)),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[1049, 6737, 6706])).
% 1.87/2.08 tff(6739,plain,
% 1.87/2.08 (b(s(z), z)),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[221, 6738])).
% 1.87/2.09 tff(6740,plain,
% 1.87/2.09 (~r(s(z), s(s(elem!1)))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[6326, 124, 1730, 6737])).
% 1.87/2.09 tff(6741,plain,
% 1.87/2.09 (b(s(z), s(s(elem!1)))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[3997, 43, 79, 6740])).
% 1.87/2.09 tff(6742,plain,
% 1.87/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)))),
% 1.87/2.09 inference(rewrite,[status(thm)],[])).
% 1.87/2.09 tff(6743,plain,
% 1.87/2.09 (((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)))),
% 1.87/2.09 inference(rewrite,[status(thm)],[])).
% 1.87/2.09 tff(6744,plain,
% 1.87/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z))))),
% 1.87/2.09 inference(monotonicity,[status(thm)],[6743])).
% 1.87/2.09 tff(6745,plain,
% 1.87/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)))),
% 1.87/2.09 inference(transitivity,[status(thm)],[6744, 6742])).
% 1.87/2.09 tff(6746,plain,
% 1.87/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))))),
% 1.87/2.09 inference(quant_inst,[status(thm)],[])).
% 1.87/2.09 tff(6747,plain,
% 1.87/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z))),
% 1.87/2.09 inference(modus_ponens,[status(thm)],[6746, 6745])).
% 1.87/2.09 tff(6748,plain,
% 1.87/2.09 ($false),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[6747, 306, 6699, 6697, 6741, 6739])).
% 1.87/2.09 tff(6749,plain,((~r(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~(s(s(s(elem!1))) = elem!1)) | (s(z) = s(s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (elem!1 = z) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.09 tff(6750,plain,
% 1.87/2.09 (~r(s(s(elem!1)), elem!1)),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[6749, 6695, 6632, 2184, 6666, 6665, 6621, 3103, 6635])).
% 1.87/2.09 tff(6751,plain,
% 1.87/2.09 (b(s(s(elem!1)), elem!1)),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[47, 6750, 91])).
% 1.87/2.09 tff(6752,plain,
% 1.87/2.09 (r(s(s(s(s(elem!1)))), s(s(elem!1))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.87/2.09 inference(monotonicity,[status(thm)],[5713])).
% 1.87/2.09 tff(6753,plain,
% 1.87/2.09 (b(s(s(s(s(elem!1)))), s(s(elem!1))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.87/2.09 inference(monotonicity,[status(thm)],[5713])).
% 1.87/2.09 tff(6754,plain,
% 1.87/2.09 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.87/2.09 inference(symmetry,[status(thm)],[6753])).
% 1.87/2.09 tff(6755,plain,
% 1.87/2.09 ((~b(s(elem!1), s(s(elem!1)))) <=> (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.87/2.09 inference(monotonicity,[status(thm)],[6754])).
% 1.87/2.09 tff(6756,plain,
% 1.87/2.09 (~b(s(elem!1), s(s(elem!1)))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[6021, 306, 6751, 6635, 816])).
% 1.87/2.09 tff(6757,plain,
% 1.87/2.09 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.87/2.09 inference(modus_ponens,[status(thm)],[6756, 6755])).
% 1.87/2.09 tff(6758,plain,
% 1.87/2.09 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[1302, 6757, 6278])).
% 1.87/2.09 tff(6759,plain,
% 1.87/2.09 (r(s(elem!1), s(s(elem!1)))),
% 1.87/2.09 inference(modus_ponens,[status(thm)],[6758, 6752])).
% 1.87/2.09 tff(6760,plain,
% 1.87/2.09 (~b(s(z), elem!1)),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[6427, 6759, 3099, 6751, 6635, 816])).
% 1.87/2.09 tff(6761,plain,
% 1.87/2.09 (r(s(z), elem!1)),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[1500, 43, 6760, 6662])).
% 1.87/2.09 tff(6762,plain,
% 1.87/2.09 (~r(s(z), z)),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[1049, 6761, 6657])).
% 1.87/2.09 tff(6763,plain,
% 1.87/2.09 (b(s(z), z)),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[221, 6762])).
% 1.87/2.09 tff(6764,plain,
% 1.87/2.09 (b(s(z), s(elem!1)) <=> b(s(z), s(s(s(s(elem!1)))))),
% 1.87/2.09 inference(monotonicity,[status(thm)],[6707])).
% 1.87/2.09 tff(6765,plain,
% 1.87/2.09 ((~b(s(z), s(elem!1))) <=> (~b(s(z), s(s(s(s(elem!1))))))),
% 1.87/2.09 inference(monotonicity,[status(thm)],[6764])).
% 1.87/2.09 tff(6766,plain,
% 1.87/2.09 (~r(z, s(elem!1))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[799, 437, 244])).
% 1.87/2.09 tff(6767,plain,
% 1.87/2.09 (b(z, s(elem!1))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[275, 6766])).
% 1.87/2.09 tff(6768,plain,
% 1.87/2.09 (~r(s(elem!1), z)),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[6030, 124, 437, 4445])).
% 1.87/2.09 tff(6769,plain,
% 1.87/2.09 (b(s(elem!1), z)),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[2380, 6768])).
% 1.87/2.09 tff(6770,plain,
% 1.87/2.09 (~b(s(elem!1), s(z))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[6564, 306, 6769, 6767, 3020])).
% 1.87/2.09 tff(6771,plain,
% 1.87/2.09 (r(s(elem!1), s(z))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[2612, 43, 6770, 2249])).
% 1.87/2.09 tff(6772,plain,
% 1.87/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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))), z)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.87/2.09 inference(rewrite,[status(thm)],[])).
% 1.87/2.09 tff(6773,plain,
% 1.87/2.09 (((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1)))) <=> ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.87/2.09 inference(rewrite,[status(thm)],[])).
% 1.87/2.09 tff(6774,plain,
% 1.87/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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))), z)) | (~b(s(s(s(z))), s(elem!1)))))),
% 1.87/2.09 inference(monotonicity,[status(thm)],[6773])).
% 1.87/2.09 tff(6775,plain,
% 1.87/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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))), z)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.87/2.09 inference(transitivity,[status(thm)],[6774, 6772])).
% 1.87/2.09 tff(6776,plain,
% 1.87/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.87/2.09 inference(quant_inst,[status(thm)],[])).
% 1.87/2.09 tff(6777,plain,
% 1.87/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1)))),
% 1.87/2.09 inference(modus_ponens,[status(thm)],[6776, 6775])).
% 1.87/2.09 tff(6778,plain,
% 1.87/2.09 (~b(s(s(s(z))), s(elem!1))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[6777, 306, 1199, 817, 1531])).
% 1.87/2.09 tff(6779,assumption,(~(s(s(s(z))) = s(elem!1))), introduced(assumption)).
% 1.87/2.09 tff(6780,plain,
% 1.87/2.09 (r(s(s(s(z))), s(elem!1))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[4132, 43, 6779, 6778])).
% 1.87/2.09 tff(6781,plain,
% 1.87/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)))),
% 1.87/2.09 inference(rewrite,[status(thm)],[])).
% 1.87/2.09 tff(6782,plain,
% 1.87/2.09 (((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)))),
% 1.87/2.09 inference(rewrite,[status(thm)],[])).
% 1.87/2.09 tff(6783,plain,
% 1.87/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z))))),
% 1.87/2.09 inference(monotonicity,[status(thm)],[6782])).
% 1.87/2.09 tff(6784,plain,
% 1.87/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)))),
% 1.87/2.09 inference(transitivity,[status(thm)],[6783, 6781])).
% 1.87/2.09 tff(6785,plain,
% 1.87/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 1.87/2.09 inference(quant_inst,[status(thm)],[])).
% 1.87/2.09 tff(6786,plain,
% 1.87/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z))),
% 1.87/2.09 inference(modus_ponens,[status(thm)],[6785, 6784])).
% 1.87/2.09 tff(6787,plain,
% 1.87/2.09 (~b(s(s(s(z))), s(z))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[6786, 306, 1199, 817, 1531, 247])).
% 1.87/2.09 tff(6788,plain,
% 1.87/2.09 (r(s(s(s(z))), s(z))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[113, 6787])).
% 1.87/2.09 tff(6789,plain,
% 1.87/2.09 ($false),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[5600, 124, 6788, 2626, 6780])).
% 1.87/2.09 tff(6790,plain,((~b(s(s(s(z))), z)) | (~r(s(elem!1), s(z))) | (s(s(s(z))) = s(elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.09 tff(6791,plain,
% 1.87/2.09 (~b(s(s(s(z))), z)),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[6790, 6771, 4129, 6769, 6767, 3020])).
% 1.87/2.09 tff(6792,plain,
% 1.87/2.09 ((~(s(z) = s(s(s(elem!1))))) <=> (~(elem!1 = s(z)))),
% 1.87/2.09 inference(monotonicity,[status(thm)],[6659])).
% 1.87/2.09 tff(6793,plain,
% 1.87/2.09 (~(elem!1 = s(z))),
% 1.87/2.09 inference(modus_ponens,[status(thm)],[645, 6792])).
% 1.87/2.09 tff(6794,plain,
% 1.87/2.09 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[2974, 6793])).
% 1.87/2.09 tff(6795,plain,
% 1.87/2.09 (~(s(z) = s(s(s(s(elem!1)))))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[6065, 6633, 2249])).
% 1.87/2.09 tff(6796,plain,
% 1.87/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))),
% 1.87/2.09 inference(rewrite,[status(thm)],[])).
% 1.87/2.09 tff(6797,plain,
% 1.87/2.09 (((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1)))) <=> ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))),
% 1.87/2.09 inference(rewrite,[status(thm)],[])).
% 1.87/2.09 tff(6798,plain,
% 1.87/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(z), s(elem!1)))))),
% 1.87/2.09 inference(monotonicity,[status(thm)],[6797])).
% 1.87/2.09 tff(6799,plain,
% 1.87/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))),
% 1.87/2.09 inference(transitivity,[status(thm)],[6798, 6796])).
% 1.87/2.09 tff(6800,plain,
% 1.87/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))),
% 1.87/2.09 inference(quant_inst,[status(thm)],[])).
% 1.87/2.09 tff(6801,plain,
% 1.87/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(z), s(elem!1)))),
% 1.87/2.09 inference(modus_ponens,[status(thm)],[6800, 6799])).
% 1.87/2.09 tff(6802,plain,
% 1.87/2.09 (~b(s(z), s(elem!1))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[6801, 306, 6769, 6767, 3020])).
% 1.87/2.09 tff(6803,plain,
% 1.87/2.09 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.87/2.09 inference(modus_ponens,[status(thm)],[6802, 6765])).
% 1.87/2.09 tff(6804,plain,
% 1.87/2.09 (r(s(z), s(s(s(s(elem!1)))))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[6078, 6803, 6795])).
% 1.87/2.09 tff(6805,plain,
% 1.87/2.09 (r(s(z), s(elem!1))),
% 1.87/2.09 inference(modus_ponens,[status(thm)],[6804, 6709])).
% 1.87/2.09 tff(6806,plain,
% 1.87/2.09 (~r(s(z), s(s(elem!1)))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[6725, 124, 244, 6805])).
% 1.87/2.09 tff(6807,plain,
% 1.87/2.09 (b(s(z), s(s(elem!1)))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[3997, 43, 79, 6806])).
% 1.87/2.09 tff(6808,plain,
% 1.87/2.09 (~r(z, s(z))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[6096, 4, 374])).
% 1.87/2.09 tff(6809,plain,
% 1.87/2.09 (b(z, s(z))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[389, 43, 6808, 2260])).
% 1.87/2.09 tff(6810,plain,
% 1.87/2.09 (b(s(s(s(z))), z)),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[202, 43, 169, 1629])).
% 1.87/2.09 tff(6811,plain,
% 1.87/2.09 (~(s(s(s(z))) = elem!1)),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[2204, 1629, 246])).
% 1.87/2.09 tff(6812,plain,
% 1.87/2.09 (r(s(s(s(z))), elem!1)),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[1489, 6811, 1])).
% 1.87/2.09 tff(6813,plain,
% 1.87/2.09 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))))),
% 1.87/2.09 inference(rewrite,[status(thm)],[])).
% 1.87/2.09 tff(6814,plain,
% 1.87/2.09 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))))),
% 1.87/2.09 inference(quant_inst,[status(thm)],[])).
% 1.87/2.09 tff(6815,plain,
% 1.87/2.09 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z)))),
% 1.87/2.09 inference(modus_ponens,[status(thm)],[6814, 6813])).
% 1.87/2.09 tff(6816,plain,
% 1.87/2.09 ((~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z)))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[6815, 124])).
% 1.87/2.09 tff(6817,plain,
% 1.87/2.09 (~r(s(s(s(z))), s(z))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[6816, 6812, 4])).
% 1.87/2.09 tff(6818,plain,
% 1.87/2.09 (b(s(s(s(z))), s(z))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[113, 6817])).
% 1.87/2.09 tff(6819,plain,
% 1.87/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))))),
% 1.87/2.09 inference(rewrite,[status(thm)],[])).
% 1.87/2.09 tff(6820,plain,
% 1.87/2.09 (((~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))))),
% 1.87/2.09 inference(rewrite,[status(thm)],[])).
% 1.87/2.09 tff(6821,plain,
% 1.87/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), z)) | (~b(z, s(z)))))),
% 1.87/2.09 inference(monotonicity,[status(thm)],[6820])).
% 1.87/2.09 tff(6822,plain,
% 1.87/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))))),
% 1.87/2.09 inference(transitivity,[status(thm)],[6821, 6819])).
% 1.87/2.09 tff(6823,plain,
% 1.87/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 1.87/2.09 inference(quant_inst,[status(thm)],[])).
% 1.87/2.09 tff(6824,plain,
% 1.87/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), z)) | (~b(z, s(z)))),
% 1.87/2.09 inference(modus_ponens,[status(thm)],[6823, 6822])).
% 1.87/2.09 tff(6825,plain,
% 1.87/2.09 ($false),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[6824, 306, 30, 6818, 3999, 6810, 485])).
% 1.87/2.09 tff(6826,plain,(r(s(s(s(z))), z) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~r(s(z), elem!1)) | b(s(s(s(z))), elem!1) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.09 tff(6827,plain,
% 1.87/2.09 (r(s(s(s(z))), z)),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[6826, 1, 3999, 6809, 4, 30, 246])).
% 1.87/2.09 tff(6828,plain,
% 1.87/2.09 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))),
% 1.87/2.09 inference(rewrite,[status(thm)],[])).
% 1.87/2.09 tff(6829,plain,
% 1.87/2.09 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))),
% 1.87/2.09 inference(quant_inst,[status(thm)],[])).
% 1.87/2.09 tff(6830,plain,
% 1.87/2.09 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z))),
% 1.87/2.09 inference(modus_ponens,[status(thm)],[6829, 6828])).
% 1.87/2.09 tff(6831,plain,
% 1.87/2.09 ((~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[6830, 124])).
% 1.87/2.09 tff(6832,plain,
% 1.87/2.09 ($false),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[6831, 4200, 6827, 374])).
% 1.87/2.09 tff(6833,plain,(b(s(s(s(z))), elem!1) | (~r(z, elem!1)) | (s(s(s(z))) = elem!1) | (~b(s(z), s(s(elem!1)))) | (~r(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.09 tff(6834,plain,
% 1.87/2.09 (b(s(s(s(z))), elem!1)),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[6833, 6807, 4106, 374, 4, 30, 246])).
% 1.87/2.09 tff(6835,plain,
% 1.87/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(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(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.87/2.10 inference(rewrite,[status(thm)],[])).
% 1.87/2.10 tff(6836,plain,
% 1.87/2.10 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1))))) <=> ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.87/2.10 inference(rewrite,[status(thm)],[])).
% 1.87/2.10 tff(6837,plain,
% 1.87/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(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(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 1.87/2.10 inference(monotonicity,[status(thm)],[6836])).
% 1.87/2.10 tff(6838,plain,
% 1.87/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(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(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.87/2.10 inference(transitivity,[status(thm)],[6837, 6835])).
% 1.87/2.10 tff(6839,plain,
% 1.87/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.87/2.10 inference(quant_inst,[status(thm)],[])).
% 1.87/2.10 tff(6840,plain,
% 1.87/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(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(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1))))),
% 1.87/2.10 inference(modus_ponens,[status(thm)],[6839, 6838])).
% 1.87/2.10 tff(6841,plain,
% 1.87/2.10 ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1))))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[6840, 306])).
% 1.87/2.10 tff(6842,plain,
% 1.87/2.10 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[6841, 6834, 30, 2076, 6622])).
% 1.87/2.10 tff(6843,plain,
% 1.87/2.10 (r(s(s(s(z))), s(s(elem!1)))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[2986, 43, 6842, 6794])).
% 1.87/2.10 tff(6844,plain,
% 1.87/2.10 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.87/2.10 inference(rewrite,[status(thm)],[])).
% 1.87/2.10 tff(6845,plain,
% 1.87/2.10 (((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z))) <=> ((~r(s(s(s(z))), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.87/2.10 inference(rewrite,[status(thm)],[])).
% 1.87/2.10 tff(6846,plain,
% 1.87/2.10 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1))))))),
% 1.87/2.10 inference(monotonicity,[status(thm)],[6845])).
% 1.87/2.10 tff(6847,plain,
% 1.87/2.10 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.87/2.10 inference(transitivity,[status(thm)],[6846, 6844])).
% 1.87/2.10 tff(6848,plain,
% 1.87/2.10 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)))),
% 1.87/2.10 inference(quant_inst,[status(thm)],[])).
% 1.87/2.10 tff(6849,plain,
% 1.87/2.10 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1))))),
% 1.87/2.10 inference(modus_ponens,[status(thm)],[6848, 6847])).
% 1.87/2.10 tff(6850,plain,
% 1.87/2.10 (~r(s(s(s(z))), z)),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[6849, 124, 437, 6843])).
% 1.87/2.10 tff(6851,plain,
% 1.87/2.10 ($false),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[202, 43, 169, 6850, 6791])).
% 1.87/2.10 tff(6852,plain,((~r(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), s(elem!1))) | (~(s(s(s(elem!1))) = elem!1)) | (s(elem!1) = s(z)) | (~r(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.10 tff(6853,plain,
% 1.87/2.10 (~r(z, s(s(elem!1)))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[6852, 6751, 6665, 6621, 6695, 6761, 6657, 6632, 2184, 3099, 6759])).
% 1.87/2.10 tff(6854,plain,
% 1.87/2.10 (b(z, s(s(elem!1)))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[460, 6853])).
% 1.87/2.10 tff(6855,plain,
% 1.87/2.10 (~r(z, s(z))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[6096, 6761, 6695])).
% 1.87/2.10 tff(6856,plain,
% 1.87/2.10 (b(z, s(z))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[389, 43, 6855, 2260])).
% 1.87/2.10 tff(6857,plain,
% 1.87/2.10 (~(s(s(s(z))) = elem!1)),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[4105, 2184, 3099])).
% 1.87/2.10 tff(6858,plain,
% 1.87/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)))),
% 1.87/2.10 inference(rewrite,[status(thm)],[])).
% 1.87/2.10 tff(6859,plain,
% 1.87/2.10 (((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)))),
% 1.87/2.10 inference(rewrite,[status(thm)],[])).
% 1.87/2.10 tff(6860,plain,
% 1.87/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z))))),
% 1.87/2.10 inference(monotonicity,[status(thm)],[6859])).
% 1.87/2.10 tff(6861,plain,
% 1.87/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)))),
% 1.87/2.10 inference(transitivity,[status(thm)],[6860, 6858])).
% 1.87/2.10 tff(6862,plain,
% 1.87/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))))),
% 1.87/2.10 inference(quant_inst,[status(thm)],[])).
% 1.87/2.10 tff(6863,plain,
% 1.87/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z))),
% 1.87/2.10 inference(modus_ponens,[status(thm)],[6862, 6861])).
% 1.87/2.10 tff(6864,plain,
% 1.87/2.10 (~b(s(z), s(s(elem!1)))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[6863, 306, 30, 1198, 3968, 247])).
% 1.87/2.10 tff(6865,plain,
% 1.87/2.10 (r(s(z), s(s(elem!1)))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[3997, 43, 6864, 79])).
% 1.87/2.10 tff(6866,plain,
% 1.87/2.10 (~r(s(elem!1), s(z))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[6425, 124, 4445, 6865])).
% 1.87/2.10 tff(6867,plain,
% 1.87/2.10 (b(s(elem!1), s(z))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[2612, 43, 6866, 2249])).
% 1.87/2.10 tff(6868,plain,
% 1.87/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))),
% 1.87/2.10 inference(rewrite,[status(thm)],[])).
% 1.87/2.10 tff(6869,plain,
% 1.87/2.10 (((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z))) <=> ((~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))),
% 1.87/2.10 inference(rewrite,[status(thm)],[])).
% 1.87/2.10 tff(6870,plain,
% 1.87/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z)))))),
% 1.87/2.10 inference(monotonicity,[status(thm)],[6869])).
% 1.87/2.10 tff(6871,plain,
% 1.87/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))),
% 1.87/2.10 inference(transitivity,[status(thm)],[6870, 6868])).
% 1.87/2.10 tff(6872,plain,
% 1.87/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)))),
% 1.87/2.10 inference(quant_inst,[status(thm)],[])).
% 1.87/2.10 tff(6873,plain,
% 1.87/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z)))),
% 1.87/2.10 inference(modus_ponens,[status(thm)],[6872, 6871])).
% 1.87/2.10 tff(6874,plain,
% 1.87/2.10 (~b(s(elem!1), z)),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[6873, 306, 1198, 6867, 247, 485])).
% 1.87/2.10 tff(6875,plain,
% 1.87/2.10 (r(s(elem!1), z)),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[2380, 6874])).
% 1.87/2.10 tff(6876,plain,
% 1.87/2.10 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))))),
% 1.87/2.10 inference(rewrite,[status(thm)],[])).
% 1.87/2.10 tff(6877,plain,
% 1.87/2.10 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))))),
% 1.87/2.10 inference(quant_inst,[status(thm)],[])).
% 1.87/2.10 tff(6878,plain,
% 1.87/2.10 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1)))),
% 1.87/2.10 inference(modus_ponens,[status(thm)],[6877, 6876])).
% 1.87/2.10 tff(6879,plain,
% 1.87/2.10 (~r(s(s(s(z))), s(elem!1))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[6878, 124, 466, 205])).
% 1.87/2.10 tff(6880,plain,
% 1.87/2.10 (b(s(s(s(z))), s(elem!1))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[4132, 43, 6779, 6879])).
% 1.87/2.10 tff(6881,plain,
% 1.87/2.10 ((s(s(s(z))) = elem!1) <=> (elem!1 = s(s(s(z))))),
% 1.87/2.10 inference(symmetry,[status(thm)],[1414])).
% 1.87/2.10 tff(6882,plain,
% 1.87/2.10 ((~(s(s(s(z))) = elem!1)) <=> (~(elem!1 = s(s(s(z)))))),
% 1.87/2.10 inference(monotonicity,[status(thm)],[6881])).
% 1.87/2.10 tff(6883,plain,
% 1.87/2.10 (~(elem!1 = s(s(s(z))))),
% 1.87/2.10 inference(modus_ponens,[status(thm)],[1483, 6882])).
% 1.87/2.10 tff(6884,plain,
% 1.87/2.10 (~r(elem!1, s(s(s(z))))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[2312, 205, 246])).
% 1.87/2.10 tff(6885,plain,
% 1.87/2.10 (b(elem!1, s(s(s(z))))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[131, 43, 6884, 6883])).
% 1.87/2.10 tff(6886,plain,
% 1.87/2.10 (~r(s(s(s(z))), elem!1)),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[6831, 205, 374])).
% 1.87/2.10 tff(6887,plain,
% 1.87/2.10 (b(s(s(s(z))), elem!1)),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[1489, 6886, 1483])).
% 1.87/2.10 tff(6888,plain,
% 1.87/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.87/2.10 inference(rewrite,[status(thm)],[])).
% 1.87/2.10 tff(6889,plain,
% 1.87/2.10 (((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.87/2.10 inference(rewrite,[status(thm)],[])).
% 1.87/2.10 tff(6890,plain,
% 1.87/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1)))))),
% 1.87/2.10 inference(monotonicity,[status(thm)],[6889])).
% 1.87/2.10 tff(6891,plain,
% 1.87/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.87/2.10 inference(transitivity,[status(thm)],[6890, 6888])).
% 1.87/2.10 tff(6892,plain,
% 1.87/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.87/2.10 inference(quant_inst,[status(thm)],[])).
% 1.87/2.10 tff(6893,plain,
% 1.87/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1)))),
% 1.87/2.10 inference(modus_ponens,[status(thm)],[6892, 6891])).
% 1.87/2.10 tff(6894,plain,
% 1.87/2.10 ($false),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[6893, 306, 816, 6887, 6885, 6880])).
% 1.87/2.10 tff(6895,plain,((~r(s(s(s(z))), z)) | (~b(s(elem!1), elem!1)) | (s(s(s(z))) = s(elem!1)) | (~r(s(elem!1), z)) | (s(s(s(z))) = elem!1) | (~r(z, elem!1)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.10 tff(6896,plain,
% 1.87/2.10 (~r(s(s(s(z))), z)),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[6895, 6875, 6779, 816, 1483, 374, 246])).
% 1.87/2.10 tff(6897,plain,
% 1.87/2.10 (b(s(s(s(z))), z)),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[2197, 6896])).
% 1.87/2.10 tff(6898,plain,
% 1.87/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.87/2.10 inference(rewrite,[status(thm)],[])).
% 1.87/2.10 tff(6899,plain,
% 1.87/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~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)))))),
% 1.87/2.10 inference(quant_inst,[status(thm)],[])).
% 1.87/2.10 tff(6900,plain,
% 1.87/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~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))))),
% 1.87/2.10 inference(modus_ponens,[status(thm)],[6899, 6898])).
% 1.87/2.10 tff(6901,plain,
% 1.87/2.10 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[6900, 306, 30, 1198, 3968, 6897])).
% 1.87/2.10 tff(6902,plain,
% 1.87/2.10 (r(s(s(s(z))), s(s(elem!1)))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[2986, 43, 6901, 2976])).
% 1.87/2.10 tff(6903,plain,
% 1.87/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)))),
% 1.87/2.10 inference(rewrite,[status(thm)],[])).
% 1.87/2.10 tff(6904,plain,
% 1.87/2.10 (((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)))),
% 1.87/2.10 inference(rewrite,[status(thm)],[])).
% 1.87/2.10 tff(6905,plain,
% 1.87/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z))))),
% 1.87/2.10 inference(monotonicity,[status(thm)],[6904])).
% 1.87/2.10 tff(6906,plain,
% 1.87/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)))),
% 1.87/2.10 inference(transitivity,[status(thm)],[6905, 6903])).
% 1.87/2.10 tff(6907,plain,
% 1.87/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))),
% 1.87/2.10 inference(quant_inst,[status(thm)],[])).
% 1.87/2.10 tff(6908,plain,
% 1.87/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z))),
% 1.87/2.10 inference(modus_ponens,[status(thm)],[6907, 6906])).
% 1.87/2.10 tff(6909,plain,
% 1.87/2.10 (~b(s(s(elem!1)), s(z))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[6908, 306, 30, 1198, 3968, 247])).
% 1.87/2.10 tff(6910,plain,
% 1.87/2.10 (r(s(s(elem!1)), s(z))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[3988, 6909, 80])).
% 1.87/2.10 tff(6911,plain,
% 1.87/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)))),
% 1.87/2.10 inference(rewrite,[status(thm)],[])).
% 1.87/2.10 tff(6912,plain,
% 1.87/2.10 (((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)))),
% 1.87/2.10 inference(rewrite,[status(thm)],[])).
% 1.87/2.10 tff(6913,plain,
% 1.87/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z))))),
% 1.87/2.10 inference(monotonicity,[status(thm)],[6912])).
% 1.87/2.10 tff(6914,plain,
% 1.87/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)))),
% 1.87/2.10 inference(transitivity,[status(thm)],[6913, 6911])).
% 1.87/2.11 tff(6915,plain,
% 1.87/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 1.87/2.11 inference(quant_inst,[status(thm)],[])).
% 1.87/2.11 tff(6916,plain,
% 1.87/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z))),
% 1.87/2.11 inference(modus_ponens,[status(thm)],[6915, 6914])).
% 1.87/2.11 tff(6917,plain,
% 1.87/2.11 (~b(s(s(s(z))), s(z))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[6916, 306, 30, 1198, 6897, 247])).
% 1.87/2.11 tff(6918,plain,
% 1.87/2.11 (r(s(s(s(z))), s(z))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[113, 6917])).
% 1.87/2.11 tff(6919,plain,
% 1.87/2.11 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.87/2.11 inference(rewrite,[status(thm)],[])).
% 1.87/2.11 tff(6920,plain,
% 1.87/2.11 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.87/2.11 inference(quant_inst,[status(thm)],[])).
% 1.87/2.11 tff(6921,plain,
% 1.87/2.11 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(elem!1))))),
% 1.87/2.11 inference(modus_ponens,[status(thm)],[6920, 6919])).
% 1.87/2.11 tff(6922,plain,
% 1.87/2.11 ($false),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[6921, 124, 6918, 6910, 6902])).
% 1.87/2.11 tff(6923,plain,((~b(s(s(elem!1)), z)) | (s(s(s(z))) = s(s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (s(s(s(z))) = s(elem!1)) | (~b(s(elem!1), elem!1)) | (s(s(s(z))) = elem!1) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~b(z, s(z))) | (s(elem!1) = s(z)) | (~r(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.11 tff(6924,plain,
% 1.87/2.11 (~b(s(s(elem!1)), z)),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[6923, 6794, 6751, 6854, 6763, 4129, 816, 6857, 6695, 6657, 6856, 3099, 6759])).
% 1.87/2.11 tff(6925,plain,
% 1.87/2.11 (r(s(s(elem!1)), z)),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[476, 6924])).
% 1.87/2.11 tff(6926,plain,
% 1.87/2.11 (~r(s(elem!1), z)),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[471, 6925, 6632])).
% 1.87/2.11 tff(6927,plain,
% 1.87/2.11 (b(s(elem!1), z)),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[2380, 6926])).
% 1.87/2.11 tff(6928,plain,
% 1.87/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))),
% 1.87/2.11 inference(rewrite,[status(thm)],[])).
% 1.87/2.11 tff(6929,plain,
% 1.87/2.11 (((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1)))) <=> ((~b(s(elem!1), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))),
% 1.87/2.11 inference(rewrite,[status(thm)],[])).
% 1.87/2.11 tff(6930,plain,
% 1.87/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(elem!1)))))),
% 1.87/2.11 inference(monotonicity,[status(thm)],[6929])).
% 1.87/2.11 tff(6931,plain,
% 1.87/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))),
% 1.87/2.11 inference(transitivity,[status(thm)],[6930, 6928])).
% 1.87/2.11 tff(6932,plain,
% 1.87/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))),
% 1.87/2.11 inference(quant_inst,[status(thm)],[])).
% 1.87/2.11 tff(6933,plain,
% 1.87/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(elem!1)))),
% 1.87/2.11 inference(modus_ponens,[status(thm)],[6932, 6931])).
% 1.87/2.11 tff(6934,plain,
% 1.87/2.11 (~b(s(z), s(elem!1))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[6933, 306, 6751, 6927, 6854, 6763])).
% 1.87/2.11 tff(6935,plain,
% 1.87/2.11 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.87/2.11 inference(modus_ponens,[status(thm)],[6934, 6765])).
% 1.87/2.11 tff(6936,plain,
% 1.87/2.11 (r(s(z), s(s(s(s(elem!1)))))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[6078, 6935, 6666])).
% 1.87/2.11 tff(6937,plain,
% 1.87/2.11 (r(s(z), s(elem!1))),
% 1.87/2.11 inference(modus_ponens,[status(thm)],[6936, 6709])).
% 1.87/2.11 tff(6938,plain,
% 1.87/2.11 (~r(s(z), s(s(elem!1)))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[6725, 124, 6632, 6937])).
% 1.87/2.11 tff(6939,plain,
% 1.87/2.11 (b(s(z), s(s(elem!1)))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[3997, 43, 79, 6938])).
% 1.87/2.11 tff(6940,plain,
% 1.87/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)))),
% 1.87/2.11 inference(rewrite,[status(thm)],[])).
% 1.87/2.11 tff(6941,plain,
% 1.87/2.11 (((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)))),
% 1.87/2.11 inference(rewrite,[status(thm)],[])).
% 1.87/2.11 tff(6942,plain,
% 1.87/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z))))),
% 1.87/2.11 inference(monotonicity,[status(thm)],[6941])).
% 1.87/2.11 tff(6943,plain,
% 1.87/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)))),
% 1.87/2.11 inference(transitivity,[status(thm)],[6942, 6940])).
% 1.87/2.11 tff(6944,plain,
% 1.87/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)))),
% 1.87/2.11 inference(quant_inst,[status(thm)],[])).
% 1.87/2.11 tff(6945,plain,
% 1.87/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z))),
% 1.87/2.11 inference(modus_ponens,[status(thm)],[6944, 6943])).
% 1.87/2.11 tff(6946,plain,
% 1.87/2.11 ($false),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[6945, 306, 6751, 6854, 6635, 6939, 6763])).
% 1.87/2.11 tff(6947,plain,((~(s(s(s(elem!1))) = elem!1)) | (~b(s(elem!1), elem!1)) | (s(s(elem!1)) = elem!1) | (z = elem!1) | (~b(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.11 tff(6948,plain,
% 1.87/2.11 (~(s(s(s(elem!1))) = elem!1)),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[6947, 816, 91, 2170, 601])).
% 1.87/2.11 tff(6949,plain,
% 1.87/2.11 (~(elem!1 = s(s(s(elem!1))))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[1641, 6948])).
% 1.87/2.11 tff(6950,plain,
% 1.87/2.11 (r(elem!1, s(s(s(elem!1))))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[3284, 6949, 6618])).
% 1.87/2.11 tff(6951,plain,
% 1.87/2.11 (~b(s(s(elem!1)), s(elem!1))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[5639, 4012, 6609, 601, 816])).
% 1.87/2.11 tff(6952,plain,
% 1.87/2.11 (r(s(s(elem!1)), s(elem!1))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[994, 6951, 196])).
% 1.87/2.11 tff(6953,plain,
% 1.87/2.11 (~b(z, s(elem!1))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[6367, 4012, 816, 6235])).
% 1.87/2.11 tff(6954,plain,
% 1.87/2.11 (r(z, s(elem!1))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[275, 6953])).
% 1.87/2.11 tff(6955,plain,
% 1.87/2.11 (~r(z, s(s(elem!1)))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[799, 6954, 6952])).
% 1.87/2.11 tff(6956,plain,
% 1.87/2.11 (b(z, s(s(elem!1)))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[460, 6955])).
% 1.87/2.11 tff(6957,plain,
% 1.87/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))))),
% 1.87/2.11 inference(rewrite,[status(thm)],[])).
% 1.87/2.11 tff(6958,plain,
% 1.87/2.11 (((~b(elem!1, 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(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))), elem!1)) | (~b(elem!1, s(elem!1))))),
% 1.87/2.11 inference(rewrite,[status(thm)],[])).
% 1.87/2.11 tff(6959,plain,
% 1.87/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1)))))),
% 1.87/2.11 inference(monotonicity,[status(thm)],[6958])).
% 1.87/2.11 tff(6960,plain,
% 1.87/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))))),
% 1.87/2.11 inference(transitivity,[status(thm)],[6959, 6957])).
% 1.87/2.11 tff(6961,plain,
% 1.87/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.87/2.11 inference(quant_inst,[status(thm)],[])).
% 1.87/2.11 tff(6962,plain,
% 1.87/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1)))),
% 1.87/2.11 inference(modus_ponens,[status(thm)],[6961, 6960])).
% 1.87/2.11 tff(6963,plain,
% 1.87/2.11 (~b(s(s(s(elem!1))), elem!1)),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[6962, 306, 6609, 816, 6235])).
% 1.87/2.11 tff(6964,plain,
% 1.87/2.11 (r(s(s(s(elem!1))), elem!1)),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[1636, 6948, 6963])).
% 1.87/2.11 tff(6965,plain,
% 1.87/2.11 (~b(elem!1, s(s(elem!1)))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[6655, 6952, 4012, 816, 6235])).
% 1.87/2.11 tff(6966,plain,
% 1.87/2.11 (r(elem!1, s(s(elem!1)))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[516, 6965, 187])).
% 1.87/2.11 tff(6967,assumption,(~b(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 1.87/2.11 tff(6968,plain,
% 1.87/2.11 (~(s(s(s(elem!1))) = elem!1)),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[2187, 1653])).
% 1.87/2.11 tff(6969,plain,
% 1.87/2.11 (r(s(s(s(elem!1))), elem!1)),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[1636, 6968, 6967])).
% 1.87/2.11 tff(6970,plain,
% 1.87/2.11 (~r(elem!1, z)),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[5088, 6969, 30, 601, 815, 970])).
% 1.87/2.11 tff(6971,plain,
% 1.87/2.11 (b(elem!1, z)),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[174, 6970, 3103])).
% 1.87/2.11 tff(6972,plain,
% 1.87/2.11 (~b(z, s(elem!1))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[6367, 6971, 816, 815])).
% 1.87/2.11 tff(6973,plain,
% 1.87/2.11 (r(z, s(elem!1))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[275, 6972])).
% 1.87/2.11 tff(6974,plain,
% 1.87/2.11 (~r(z, s(s(elem!1)))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[799, 6973, 244])).
% 1.87/2.11 tff(6975,plain,
% 1.87/2.11 (b(z, s(s(elem!1)))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[460, 6974])).
% 1.87/2.11 tff(6976,plain,
% 1.87/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))))),
% 1.87/2.11 inference(rewrite,[status(thm)],[])).
% 1.87/2.11 tff(6977,plain,
% 1.87/2.11 (((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))))),
% 1.87/2.11 inference(rewrite,[status(thm)],[])).
% 1.87/2.11 tff(6978,plain,
% 1.87/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1))))))),
% 1.87/2.11 inference(monotonicity,[status(thm)],[6977])).
% 1.87/2.11 tff(6979,plain,
% 1.87/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))))),
% 1.87/2.11 inference(transitivity,[status(thm)],[6978, 6976])).
% 1.87/2.11 tff(6980,plain,
% 1.87/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))),
% 1.87/2.11 inference(quant_inst,[status(thm)],[])).
% 1.87/2.11 tff(6981,plain,
% 1.87/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1))))),
% 1.87/2.11 inference(modus_ponens,[status(thm)],[6980, 6979])).
% 1.87/2.11 tff(6982,plain,
% 1.87/2.11 (~b(z, s(s(s(elem!1))))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[6981, 306, 6971, 30, 6975, 601])).
% 1.87/2.11 tff(6983,plain,
% 1.87/2.11 (r(z, s(s(s(elem!1))))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[585, 6982])).
% 1.87/2.11 tff(6984,plain,
% 1.87/2.11 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[5741, 6637, 564])).
% 1.87/2.11 tff(6985,plain,
% 1.87/2.11 (b(s(s(s(elem!1))), s(elem!1))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[664, 6984, 150])).
% 1.87/2.11 tff(6986,plain,
% 1.87/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))),
% 1.87/2.11 inference(rewrite,[status(thm)],[])).
% 1.87/2.11 tff(6987,plain,
% 1.87/2.11 (((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))),
% 1.87/2.11 inference(rewrite,[status(thm)],[])).
% 1.87/2.11 tff(6988,plain,
% 1.87/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1)))))),
% 1.87/2.11 inference(monotonicity,[status(thm)],[6987])).
% 1.87/2.11 tff(6989,plain,
% 1.87/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))),
% 1.87/2.11 inference(transitivity,[status(thm)],[6988, 6986])).
% 1.87/2.11 tff(6990,plain,
% 1.87/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~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))))))),
% 1.87/2.11 inference(quant_inst,[status(thm)],[])).
% 1.87/2.11 tff(6991,plain,
% 1.87/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1)))),
% 1.87/2.11 inference(modus_ponens,[status(thm)],[6990, 6989])).
% 1.87/2.11 tff(6992,plain,
% 1.87/2.11 ($false),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[6991, 306, 4012, 6985, 1663, 816, 815])).
% 1.87/2.11 tff(6993,plain,((~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.11 tff(6994,plain,
% 1.87/2.11 (~b(elem!1, s(s(s(elem!1))))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[6993, 6983, 816, 815, 150, 6971])).
% 1.87/2.11 tff(6995,plain,
% 1.87/2.11 (~r(s(s(elem!1)), z)),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[6643, 124, 6973, 244])).
% 1.87/2.11 tff(6996,plain,
% 1.87/2.11 (b(s(s(elem!1)), z)),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[476, 6995])).
% 1.87/2.11 tff(6997,plain,
% 1.87/2.11 (r(z, elem!1)),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[3976, 6996, 2170, 30, 6970])).
% 1.87/2.11 tff(6998,plain,
% 1.87/2.11 (~r(elem!1, s(s(s(elem!1))))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[573, 6997, 6983])).
% 1.87/2.11 tff(6999,plain,
% 1.87/2.11 ($false),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[3284, 6998, 6994, 1653])).
% 1.87/2.11 tff(7000,plain,((elem!1 = s(s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (s(s(s(elem!1))) = s(elem!1)) | (z = elem!1) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | b(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.87/2.11 tff(7001,plain,
% 1.87/2.11 (~b(s(s(elem!1)), elem!1)),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[7000, 6966, 6235, 144, 2170, 816, 601, 6963, 6952, 6949])).
% 1.87/2.11 tff(7002,plain,
% 1.87/2.11 (r(s(s(elem!1)), elem!1)),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[47, 7001, 91])).
% 1.87/2.11 tff(7003,plain,
% 1.87/2.11 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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)))),
% 1.87/2.11 inference(rewrite,[status(thm)],[])).
% 1.87/2.11 tff(7004,plain,
% 1.87/2.11 (((~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)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.87/2.11 inference(rewrite,[status(thm)],[])).
% 1.87/2.11 tff(7005,plain,
% 1.87/2.11 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))))),
% 1.87/2.11 inference(monotonicity,[status(thm)],[7004])).
% 1.87/2.11 tff(7006,plain,
% 1.87/2.11 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.87/2.11 inference(transitivity,[status(thm)],[7005, 7003])).
% 1.87/2.11 tff(7007,plain,
% 1.87/2.11 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.87/2.12 inference(quant_inst,[status(thm)],[])).
% 1.87/2.12 tff(7008,plain,
% 1.87/2.12 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))),
% 1.87/2.12 inference(modus_ponens,[status(thm)],[7007, 7006])).
% 1.87/2.12 tff(7009,plain,
% 1.87/2.12 ($false),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[7008, 124, 1730, 878, 1627])).
% 1.87/2.12 tff(7010,plain,((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.12 tff(7011,plain,
% 1.87/2.12 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[7010, 7002, 6964])).
% 1.87/2.12 tff(7012,plain,
% 1.87/2.12 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[891, 7011, 153])).
% 1.87/2.12 tff(7013,plain,
% 1.87/2.12 (~b(z, s(s(s(elem!1))))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[1598, 7012, 601, 6956])).
% 1.87/2.12 tff(7014,plain,
% 1.87/2.12 (r(z, s(s(s(elem!1))))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[585, 7013])).
% 1.87/2.12 tff(7015,plain,
% 1.87/2.12 (~r(z, elem!1)),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[573, 7014, 6950])).
% 1.87/2.12 tff(7016,plain,
% 1.87/2.12 (b(z, elem!1)),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[835, 7015, 2170])).
% 1.87/2.12 tff(7017,plain,
% 1.87/2.12 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[6115, 6965, 601])).
% 1.87/2.12 tff(7018,plain,
% 1.87/2.12 (~b(s(elem!1), z)),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[4020, 7016, 6235, 4012])).
% 1.87/2.12 tff(7019,plain,
% 1.87/2.12 (r(s(elem!1), z)),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[2380, 7018])).
% 1.87/2.12 tff(7020,plain,
% 1.87/2.12 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[6312, 7019, 7017, 7016, 4012, 816])).
% 1.87/2.12 tff(7021,plain,
% 1.87/2.12 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[4899, 7012, 6964, 6609, 6279, 601, 6278, 6966])).
% 1.87/2.12 tff(7022,plain,
% 1.87/2.12 (s(s(s(s(elem!1)))) = elem!1),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[1736, 7021, 7020])).
% 1.87/2.12 tff(7023,plain,
% 1.87/2.12 (~(elem!1 = s(z))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[6321, 7022])).
% 1.87/2.12 tff(7024,plain,
% 1.87/2.12 (~(s(z) = elem!1)),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[89, 7023])).
% 1.87/2.12 tff(7025,plain,
% 1.87/2.12 (~b(s(z), z)),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[6345, 306, 838, 4012, 2831])).
% 1.87/2.12 tff(7026,plain,
% 1.87/2.12 (r(s(z), z)),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[221, 7025])).
% 1.87/2.12 tff(7027,plain,
% 1.87/2.12 (~r(s(elem!1), s(z))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[2634, 7026, 466])).
% 1.87/2.12 tff(7028,plain,
% 1.87/2.12 (~b(s(elem!1), s(z))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[6354, 306, 838, 4012, 816, 2831])).
% 1.87/2.12 tff(7029,plain,
% 1.87/2.12 ($false),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[2612, 43, 7028, 7027, 2249])).
% 1.87/2.12 tff(7030,plain,((~b(s(z), elem!1)) | (s(elem!1) = s(z)) | (~r(s(elem!1), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.12 tff(7031,plain,
% 1.87/2.12 (~b(s(z), elem!1)),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[7030, 7019, 3099, 7016, 4012, 816])).
% 1.87/2.12 tff(7032,plain,
% 1.87/2.12 (r(s(z), elem!1)),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[1500, 43, 7031, 7024])).
% 1.87/2.12 tff(7033,plain,
% 1.87/2.12 (~r(s(z), s(s(s(elem!1))))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[3013, 124, 6964, 7032])).
% 1.87/2.12 tff(7034,plain,
% 1.87/2.12 (b(s(z), s(s(s(elem!1))))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[3017, 43, 645, 7033])).
% 1.87/2.12 tff(7035,plain,
% 1.87/2.12 (~r(s(z), s(s(elem!1)))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[6326, 124, 7002, 7032])).
% 1.87/2.12 tff(7036,plain,
% 1.87/2.12 (b(s(z), s(s(elem!1)))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[3997, 43, 79, 7035])).
% 1.87/2.12 tff(7037,plain,
% 1.87/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), 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(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), 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(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.87/2.12 inference(rewrite,[status(thm)],[])).
% 1.87/2.12 tff(7038,plain,
% 1.87/2.12 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(z), 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(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.87/2.12 inference(rewrite,[status(thm)],[])).
% 1.87/2.12 tff(7039,plain,
% 1.87/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), 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(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.87/2.12 inference(monotonicity,[status(thm)],[7038])).
% 1.87/2.12 tff(7040,plain,
% 1.87/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), 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(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.87/2.12 inference(transitivity,[status(thm)],[7039, 7037])).
% 1.87/2.12 tff(7041,plain,
% 1.87/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.87/2.12 inference(quant_inst,[status(thm)],[])).
% 1.87/2.12 tff(7042,plain,
% 1.87/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1)))))),
% 1.87/2.12 inference(modus_ponens,[status(thm)],[7041, 7040])).
% 1.87/2.12 tff(7043,plain,
% 1.87/2.12 ($false),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[7042, 306, 6609, 7012, 601, 7036, 7034])).
% 1.87/2.12 tff(7044,plain,((~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (z = elem!1) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.87/2.12 tff(7045,plain,
% 1.87/2.12 (~b(elem!1, z)),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[7044, 5619, 5620, 2170, 91])).
% 1.87/2.12 tff(7046,plain,
% 1.87/2.12 (r(elem!1, z)),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[174, 7045, 3103])).
% 1.87/2.12 tff(7047,plain,
% 1.87/2.12 (b(elem!1, s(elem!1))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[6234, 5620, 2170, 91, 5619])).
% 1.87/2.12 tff(7048,plain,
% 1.87/2.12 (b(s(s(s(elem!1))), s(elem!1))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[6608, 5619, 5620, 91, 2170])).
% 1.87/2.12 tff(7049,plain,
% 1.87/2.12 (~b(s(s(s(elem!1))), elem!1)),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[6962, 306, 7048, 5620, 7047])).
% 1.87/2.12 tff(7050,plain,
% 1.87/2.12 (~(s(s(s(elem!1))) = elem!1)),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[6947, 5620, 91, 2170, 5619])).
% 1.87/2.12 tff(7051,plain,
% 1.87/2.12 (r(s(s(s(elem!1))), elem!1)),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[1636, 7050, 7049])).
% 1.87/2.12 tff(7052,plain,
% 1.87/2.12 (~b(elem!1, s(s(s(elem!1))))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[6617, 7048, 5620, 7047])).
% 1.87/2.12 tff(7053,plain,
% 1.87/2.12 (~(elem!1 = s(s(s(elem!1))))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[1641, 7050])).
% 1.87/2.12 tff(7054,plain,
% 1.87/2.12 (r(elem!1, s(s(s(elem!1))))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[3284, 7053, 7052])).
% 1.87/2.12 tff(7055,plain,
% 1.87/2.12 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[7010, 1730, 1627])).
% 1.87/2.12 tff(7056,plain,
% 1.87/2.12 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[891, 7055, 157])).
% 1.87/2.12 tff(7057,plain,
% 1.87/2.12 (~b(z, s(s(elem!1)))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[5777, 1730, 601, 157, 565, 246])).
% 1.87/2.12 tff(7058,plain,
% 1.87/2.12 (r(z, s(s(elem!1)))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[460, 7057])).
% 1.87/2.12 tff(7059,plain,
% 1.87/2.12 (~r(elem!1, s(s(elem!1)))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[978, 7058, 246])).
% 1.87/2.12 tff(7060,plain,
% 1.87/2.12 (b(elem!1, s(s(elem!1)))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[516, 7059, 360])).
% 1.87/2.12 tff(7061,plain,
% 1.87/2.12 (~r(s(s(elem!1)), s(elem!1))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[799, 7058, 791])).
% 1.87/2.12 tff(7062,plain,
% 1.87/2.12 (b(s(s(elem!1)), s(elem!1))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[994, 7061, 403])).
% 1.87/2.12 tff(7063,plain,
% 1.87/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, 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(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.87/2.12 inference(rewrite,[status(thm)],[])).
% 1.87/2.12 tff(7064,plain,
% 1.87/2.12 (((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, 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(elem!1))))))),
% 1.87/2.12 inference(rewrite,[status(thm)],[])).
% 1.87/2.12 tff(7065,plain,
% 1.87/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, 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(elem!1)))))))),
% 1.87/2.12 inference(monotonicity,[status(thm)],[7064])).
% 1.87/2.12 tff(7066,plain,
% 1.87/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, 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(elem!1))))))),
% 1.87/2.12 inference(transitivity,[status(thm)],[7065, 7063])).
% 1.87/2.12 tff(7067,plain,
% 1.87/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.87/2.12 inference(quant_inst,[status(thm)],[])).
% 1.87/2.12 tff(7068,plain,
% 1.87/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.87/2.12 inference(modus_ponens,[status(thm)],[7067, 7066])).
% 1.87/2.12 tff(7069,plain,
% 1.87/2.12 ($false),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[7068, 306, 759, 7062, 7060, 7056, 816])).
% 1.87/2.12 tff(7070,plain,((~r(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (elem!1 = s(s(elem!1))) | (s(s(elem!1)) = s(elem!1)) | (~r(elem!1, z)) | (~r(z, s(elem!1))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.12 tff(7071,plain,
% 1.87/2.12 (~r(s(s(elem!1)), elem!1)),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[7070, 6683, 816, 187, 196, 246, 759, 153, 1627, 601, 565])).
% 1.87/2.12 tff(7072,plain,
% 1.87/2.12 (b(s(s(elem!1)), elem!1)),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[47, 7071, 91])).
% 1.87/2.12 tff(7073,plain,
% 1.87/2.12 (~r(elem!1, s(s(elem!1)))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[5088, 7072, 815, 601, 1627, 246])).
% 1.87/2.12 tff(7074,plain,
% 1.87/2.12 (b(elem!1, s(s(elem!1)))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[516, 7073, 187])).
% 1.87/2.12 tff(7075,plain,
% 1.87/2.12 (~r(s(s(elem!1)), s(elem!1))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[6693, 7074, 838, 816, 815])).
% 1.87/2.12 tff(7076,plain,
% 1.87/2.12 (~b(s(s(elem!1)), s(elem!1))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[1024, 7074, 816, 7072])).
% 1.87/2.12 tff(7077,plain,
% 1.87/2.12 ($false),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[994, 7076, 7075, 196])).
% 1.87/2.12 tff(7078,plain,((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (s(s(elem!1)) = elem!1) | (~b(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.12 tff(7079,plain,
% 1.87/2.12 (~b(z, elem!1)),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[7078, 5620, 7047, 5619, 7051, 7046, 91, 7048, 7054])).
% 1.87/2.12 tff(7080,plain,
% 1.87/2.12 (r(z, elem!1)),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[835, 7079, 2170])).
% 1.87/2.12 tff(7081,plain,
% 1.87/2.12 (~r(z, s(s(elem!1)))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[6466, 7080, 5620, 7047, 3099, 7050, 7046, 5619, 91])).
% 1.87/2.12 tff(7082,plain,
% 1.87/2.12 (b(z, s(s(elem!1)))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[460, 7081])).
% 1.87/2.12 tff(7083,plain,
% 1.87/2.12 (~r(s(s(elem!1)), elem!1)),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[5777, 7082, 5619, 153, 7054, 7046])).
% 1.87/2.12 tff(7084,plain,
% 1.87/2.12 (b(s(s(elem!1)), elem!1)),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[47, 7083, 91])).
% 1.87/2.12 tff(7085,plain,
% 1.87/2.12 (~r(elem!1, s(s(elem!1)))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[5088, 7084, 7047, 5619, 7051, 7046])).
% 1.87/2.12 tff(7086,plain,
% 1.87/2.12 (b(elem!1, s(s(elem!1)))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[516, 7085, 187])).
% 1.87/2.12 tff(7087,plain,
% 1.87/2.12 (~r(z, s(s(s(elem!1))))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[573, 7080, 7054])).
% 1.87/2.12 tff(7088,plain,
% 1.87/2.12 (b(z, s(s(s(elem!1))))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[585, 7087])).
% 1.87/2.12 tff(7089,plain,
% 1.87/2.12 ($false),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[5866, 306, 7084, 7088, 7082, 7086, 5619])).
% 1.87/2.12 tff(7090,plain,((s(s(elem!1)) = elem!1) | (z = elem!1) | r(s(s(s(elem!1))), s(s(elem!1))) | r(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.87/2.12 tff(7091,plain,
% 1.87/2.12 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[7090, 5618, 808, 2170])).
% 1.87/2.12 tff(7092,plain,
% 1.87/2.12 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[143, 5618])).
% 1.87/2.12 tff(7093,assumption,(~b(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 1.87/2.12 tff(7094,plain,
% 1.87/2.12 ((s(s(s(z))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 1.87/2.12 inference(commutativity,[status(thm)],[])).
% 1.87/2.12 tff(7095,plain,
% 1.87/2.12 ((s(s(elem!1)) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(elem!1)))),
% 1.87/2.12 inference(symmetry,[status(thm)],[7094])).
% 1.87/2.12 tff(7096,plain,
% 1.87/2.12 (r(s(elem!1), s(z))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[2964, 2609, 2249])).
% 1.87/2.12 tff(7097,plain,
% 1.87/2.12 (~r(elem!1, s(elem!1))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[287, 466, 2254])).
% 1.87/2.12 tff(7098,plain,
% 1.87/2.12 (b(s(elem!1), s(z)) <=> b(s(elem!1), elem!1)),
% 1.87/2.12 inference(monotonicity,[status(thm)],[85])).
% 1.87/2.12 tff(7099,plain,
% 1.87/2.12 ((~b(s(elem!1), s(z))) <=> (~b(s(elem!1), elem!1))),
% 1.87/2.12 inference(monotonicity,[status(thm)],[7098])).
% 1.87/2.12 tff(7100,plain,
% 1.87/2.12 (~b(s(elem!1), elem!1)),
% 1.87/2.12 inference(modus_ponens,[status(thm)],[2609, 7099])).
% 1.87/2.12 tff(7101,plain,
% 1.87/2.12 ((s(elem!1) = s(z)) <=> (s(elem!1) = elem!1)),
% 1.87/2.12 inference(monotonicity,[status(thm)],[85])).
% 1.87/2.12 tff(7102,plain,
% 1.87/2.12 ((~(s(elem!1) = s(z))) <=> (~(s(elem!1) = elem!1))),
% 1.87/2.12 inference(monotonicity,[status(thm)],[7101])).
% 1.87/2.12 tff(7103,plain,
% 1.87/2.12 (~(s(elem!1) = elem!1)),
% 1.87/2.12 inference(modus_ponens,[status(thm)],[2249, 7102])).
% 1.87/2.12 tff(7104,plain,
% 1.87/2.12 ($false),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[813, 7103, 7100, 808])).
% 1.87/2.12 tff(7105,plain,((~(s(z) = elem!1)) | r(s(elem!1), elem!1) | (s(elem!1) = s(z)) | b(s(elem!1), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.12 tff(7106,plain,
% 1.87/2.12 (~(s(z) = elem!1)),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[7105, 2609, 2249, 808])).
% 1.87/2.12 tff(7107,plain,
% 1.87/2.12 (r(s(z), elem!1)),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[1500, 43, 2715, 3094])).
% 1.87/2.12 tff(7108,plain,
% 1.87/2.12 (~r(z, s(z))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[6096, 7107, 374])).
% 1.87/2.12 tff(7109,plain,
% 1.87/2.12 (b(z, s(z))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[389, 43, 7108, 2260])).
% 1.87/2.12 tff(7110,plain,
% 1.87/2.12 (~r(s(s(elem!1)), z)),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[471, 244, 466])).
% 1.87/2.12 tff(7111,plain,
% 1.87/2.12 (b(s(s(elem!1)), z)),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[476, 7110])).
% 1.87/2.12 tff(7112,plain,
% 1.87/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), z)))),
% 1.87/2.12 inference(rewrite,[status(thm)],[])).
% 1.87/2.12 tff(7113,plain,
% 1.87/2.12 (((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), z)))),
% 1.87/2.12 inference(rewrite,[status(thm)],[])).
% 1.87/2.12 tff(7114,plain,
% 1.87/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), z))))),
% 1.87/2.12 inference(monotonicity,[status(thm)],[7113])).
% 1.87/2.12 tff(7115,plain,
% 1.87/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), z)))),
% 1.87/2.12 inference(transitivity,[status(thm)],[7114, 7112])).
% 1.87/2.12 tff(7116,plain,
% 1.87/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))),
% 1.87/2.12 inference(quant_inst,[status(thm)],[])).
% 1.87/2.12 tff(7117,plain,
% 1.87/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), z))),
% 1.87/2.12 inference(modus_ponens,[status(thm)],[7116, 7115])).
% 1.87/2.12 tff(7118,plain,
% 1.87/2.12 (~b(s(s(elem!1)), s(z))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[7117, 306, 7111, 247, 485])).
% 1.87/2.12 tff(7119,plain,
% 1.87/2.12 (r(s(s(elem!1)), s(z))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[3989, 7118])).
% 1.87/2.12 tff(7120,plain,
% 1.87/2.12 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(z))))),
% 1.87/2.12 inference(rewrite,[status(thm)],[])).
% 1.87/2.12 tff(7121,plain,
% 1.87/2.12 (((~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(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(z))))),
% 1.87/2.12 inference(rewrite,[status(thm)],[])).
% 1.87/2.12 tff(7122,plain,
% 1.87/2.12 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(z)))))),
% 1.87/2.12 inference(monotonicity,[status(thm)],[7121])).
% 1.87/2.12 tff(7123,plain,
% 1.87/2.12 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(z))))),
% 1.87/2.12 inference(transitivity,[status(thm)],[7122, 7120])).
% 1.87/2.12 tff(7124,plain,
% 1.87/2.12 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.87/2.12 inference(quant_inst,[status(thm)],[])).
% 1.87/2.12 tff(7125,plain,
% 1.87/2.12 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(z)))),
% 1.87/2.12 inference(modus_ponens,[status(thm)],[7124, 7123])).
% 1.87/2.12 tff(7126,plain,
% 1.87/2.12 ($false),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[7125, 124, 244, 2626, 7119])).
% 1.87/2.12 tff(7127,plain,((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.12 tff(7128,plain,
% 1.87/2.12 (~r(s(s(elem!1)), s(elem!1))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[7127, 7109, 247, 7096, 466])).
% 1.87/2.12 tff(7129,plain,
% 1.87/2.12 (s(s(elem!1)) = s(elem!1)),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[994, 7128, 7093])).
% 1.87/2.12 tff(7130,plain,
% 1.87/2.12 (s(elem!1) = elem!1),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[195, 7129])).
% 1.87/2.12 tff(7131,plain,
% 1.87/2.12 (elem!1 = s(elem!1)),
% 1.87/2.12 inference(symmetry,[status(thm)],[7130])).
% 1.87/2.12 tff(7132,plain,
% 1.87/2.12 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(elem!1))),
% 1.87/2.12 inference(monotonicity,[status(thm)],[7131])).
% 1.87/2.12 tff(7133,plain,
% 1.87/2.12 (s(s(s(elem!1))) = elem!1),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[1564, 7129])).
% 1.87/2.12 tff(7134,plain,
% 1.87/2.12 (~(s(s(s(z))) = elem!1)),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[4105, 7133, 2249])).
% 1.87/2.12 tff(7135,plain,
% 1.87/2.12 (~r(s(s(s(z))), z)),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[6831, 2859, 374])).
% 1.87/2.12 tff(7136,plain,
% 1.87/2.12 (b(s(s(s(z))), z)),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[2197, 7135])).
% 1.87/2.12 tff(7137,plain,
% 1.87/2.12 (~r(s(s(s(z))), s(z))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[6816, 2859, 4])).
% 1.87/2.12 tff(7138,plain,
% 1.87/2.12 (b(s(s(s(z))), s(z))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[113, 7137])).
% 1.87/2.12 tff(7139,plain,
% 1.87/2.12 ($false),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[2290, 306, 7138, 8, 7136, 6809])).
% 1.87/2.12 tff(7140,plain,((~r(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.12 tff(7141,plain,
% 1.87/2.12 (~r(s(s(s(z))), elem!1)),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[7140, 8, 4, 374])).
% 1.87/2.12 tff(7142,plain,
% 1.87/2.12 (s(s(s(z))) = elem!1),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[1489, 7141, 1])).
% 1.87/2.12 tff(7143,plain,
% 1.87/2.12 (b(s(z), s(s(s(z)))) <=> b(s(z), elem!1)),
% 1.87/2.12 inference(monotonicity,[status(thm)],[7142])).
% 1.87/2.12 tff(7144,plain,
% 1.87/2.12 (b(s(z), elem!1) <=> b(s(z), s(s(s(z))))),
% 1.87/2.12 inference(symmetry,[status(thm)],[7143])).
% 1.87/2.12 tff(7145,plain,
% 1.87/2.12 ((~b(s(z), elem!1)) <=> (~b(s(z), s(s(s(z)))))),
% 1.87/2.12 inference(monotonicity,[status(thm)],[7144])).
% 1.87/2.12 tff(7146,plain,
% 1.87/2.12 (~b(s(z), s(s(s(z))))),
% 1.87/2.12 inference(modus_ponens,[status(thm)],[2715, 7145])).
% 1.87/2.12 tff(7147,plain,
% 1.87/2.12 ($false),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[8, 7146])).
% 1.87/2.12 tff(7148,plain,((~b(s(z), s(s(s(z))))) | b(s(z), elem!1) | b(s(s(s(z))), elem!1) | (~r(s(z), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.12 tff(7149,plain,
% 1.87/2.12 (~b(s(z), s(s(s(z))))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[7148, 1, 2715, 4, 374])).
% 1.87/2.12 tff(7150,plain,
% 1.87/2.12 (r(s(z), s(s(s(z))))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[3302, 7149])).
% 1.87/2.12 tff(7151,plain,
% 1.87/2.12 ($false),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[3790, 7150, 4200, 4])).
% 1.87/2.12 tff(7152,plain,(b(s(s(s(z))), elem!1) | (~r(s(z), elem!1)) | (s(s(s(z))) = elem!1) | b(s(z), elem!1) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.12 tff(7153,plain,
% 1.87/2.12 (b(s(s(s(z))), elem!1)),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[7152, 7107, 7134, 2715, 374])).
% 1.87/2.12 tff(7154,plain,
% 1.87/2.12 (b(s(s(s(z))), s(elem!1))),
% 1.87/2.12 inference(modus_ponens,[status(thm)],[7153, 7132])).
% 1.87/2.12 tff(7155,plain,
% 1.87/2.12 (r(z, elem!1) <=> r(z, s(elem!1))),
% 1.87/2.12 inference(monotonicity,[status(thm)],[7131])).
% 1.87/2.12 tff(7156,plain,
% 1.87/2.12 (r(z, s(elem!1))),
% 1.87/2.12 inference(modus_ponens,[status(thm)],[374, 7155])).
% 1.97/2.13 tff(7157,plain,
% 1.97/2.13 (r(elem!1, s(z)) <=> r(s(elem!1), s(z))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[7131])).
% 1.97/2.13 tff(7158,plain,
% 1.97/2.13 (r(s(elem!1), s(z)) <=> r(elem!1, s(z))),
% 1.97/2.13 inference(symmetry,[status(thm)],[7157])).
% 1.97/2.13 tff(7159,plain,
% 1.97/2.13 (r(elem!1, s(z))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[7096, 7158])).
% 1.97/2.13 tff(7160,plain,
% 1.97/2.13 (b(elem!1, s(z)) <=> b(s(elem!1), s(z))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[7131])).
% 1.97/2.13 tff(7161,plain,
% 1.97/2.13 (b(s(elem!1), s(z)) <=> b(elem!1, s(z))),
% 1.97/2.13 inference(symmetry,[status(thm)],[7160])).
% 1.97/2.13 tff(7162,plain,
% 1.97/2.13 ((~b(s(elem!1), s(z))) <=> (~b(elem!1, s(z)))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[7161])).
% 1.97/2.13 tff(7163,plain,
% 1.97/2.13 (~b(elem!1, s(z))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[2609, 7162])).
% 1.97/2.13 tff(7164,plain,
% 1.97/2.13 (~(s(s(z)) = elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[2398, 7130, 5331])).
% 1.97/2.13 tff(7165,plain,
% 1.97/2.13 ((s(s(elem!1)) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[7129])).
% 1.97/2.13 tff(7166,plain,
% 1.97/2.13 ((s(elem!1) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 1.97/2.13 inference(symmetry,[status(thm)],[7165])).
% 1.97/2.13 tff(7167,plain,
% 1.97/2.13 ((~(s(elem!1) = s(s(s(z))))) <=> (~(s(s(elem!1)) = s(s(s(z)))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[7166])).
% 1.97/2.13 tff(7168,plain,
% 1.97/2.13 (s(s(s(elem!1))) = s(elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[1181, 7129])).
% 1.97/2.13 tff(7169,plain,
% 1.97/2.13 (s(s(elem!1)) = elem!1),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[143, 7168])).
% 1.97/2.13 tff(7170,plain,
% 1.97/2.13 (~(s(elem!1) = s(s(s(z))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[2356, 7169])).
% 1.97/2.13 tff(7171,plain,
% 1.97/2.13 (~(s(s(elem!1)) = s(s(s(z))))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[7170, 7167])).
% 1.97/2.13 tff(7172,plain,
% 1.97/2.13 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(7173,plain,
% 1.97/2.13 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 1.97/2.13 inference(quant_inst,[status(thm)],[])).
% 1.97/2.13 tff(7174,plain,
% 1.97/2.13 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(z)))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[7173, 7172])).
% 1.97/2.13 tff(7175,plain,
% 1.97/2.13 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7174, 124, 4, 2858])).
% 1.97/2.13 tff(7176,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(7177,plain,
% 1.97/2.13 (((~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(7178,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z)))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[7177])).
% 1.97/2.13 tff(7179,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.97/2.13 inference(transitivity,[status(thm)],[7178, 7176])).
% 1.97/2.13 tff(7180,plain,
% 1.97/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 1.97/2.13 inference(quant_inst,[status(thm)],[])).
% 1.97/2.13 tff(7181,plain,
% 1.97/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[7180, 7179])).
% 1.97/2.13 tff(7182,plain,
% 1.97/2.13 ($false),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7181, 306, 247, 954, 485, 4247])).
% 1.97/2.13 tff(7183,plain,((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.13 tff(7184,plain,
% 1.97/2.13 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7183, 5454, 247, 6809])).
% 1.97/2.13 tff(7185,plain,
% 1.97/2.13 ($false),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[651, 43, 2844, 7184, 7175])).
% 1.97/2.13 tff(7186,plain,((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(z), elem!1)) | (~b(s(z), z)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.13 tff(7187,plain,
% 1.97/2.13 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7186, 7107, 247, 374])).
% 1.97/2.13 tff(7188,plain,
% 1.97/2.13 ((s(s(s(s(s(s(z)))))) = elem!1) <=> (s(s(s(s(s(s(z)))))) = s(elem!1))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[7131])).
% 1.97/2.13 tff(7189,plain,
% 1.97/2.13 ((s(s(s(s(s(s(z)))))) = s(elem!1)) <=> (s(s(s(s(s(s(z)))))) = elem!1)),
% 1.97/2.13 inference(symmetry,[status(thm)],[7188])).
% 1.97/2.13 tff(7190,plain,
% 1.97/2.13 ((~(s(s(s(s(s(s(z)))))) = s(elem!1))) <=> (~(s(s(s(s(s(s(z)))))) = elem!1))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[7189])).
% 1.97/2.13 tff(7191,plain,
% 1.97/2.13 ((s(s(s(s(s(s(z)))))) = s(s(elem!1))) <=> (s(s(s(s(s(s(z)))))) = s(elem!1))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[7129])).
% 1.97/2.13 tff(7192,plain,
% 1.97/2.13 ((~(s(s(s(s(s(s(z)))))) = s(s(elem!1)))) <=> (~(s(s(s(s(s(s(z)))))) = s(elem!1)))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[7191])).
% 1.97/2.13 tff(7193,assumption,(s(s(s(s(s(s(z)))))) = s(s(elem!1))), introduced(assumption)).
% 1.97/2.13 tff(7194,plain,
% 1.97/2.13 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(elem!1)))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[7193])).
% 1.97/2.13 tff(7195,plain,
% 1.97/2.13 (s(s(s(s(s(z))))) = s(elem!1)),
% 1.97/2.13 inference(transitivity,[status(thm)],[2823, 7194, 66])).
% 1.97/2.13 tff(7196,plain,
% 1.97/2.13 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(elem!1))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[7195])).
% 1.97/2.13 tff(7197,plain,
% 1.97/2.13 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.97/2.13 inference(transitivity,[status(thm)],[497, 7196, 135, 4097])).
% 1.97/2.13 tff(7198,plain,
% 1.97/2.13 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(elem!1))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[7197])).
% 1.97/2.13 tff(7199,plain,
% 1.97/2.13 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(z)))))),
% 1.97/2.13 inference(symmetry,[status(thm)],[7198])).
% 1.97/2.13 tff(7200,plain,
% 1.97/2.13 (s(s(elem!1)) = s(s(s(z)))),
% 1.97/2.13 inference(transitivity,[status(thm)],[140, 7199, 320])).
% 1.97/2.13 tff(7201,plain,
% 1.97/2.13 ((s(s(s(z))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(z))) = s(s(elem!1)))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[7193])).
% 1.97/2.13 tff(7202,plain,
% 1.97/2.13 ((s(s(s(z))) = s(s(s(s(s(s(z))))))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 1.97/2.13 inference(transitivity,[status(thm)],[7201, 7094])).
% 1.97/2.13 tff(7203,plain,
% 1.97/2.13 ((~(s(s(s(z))) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(elem!1)) = s(s(s(z)))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[7202])).
% 1.97/2.13 tff(7204,plain,
% 1.97/2.13 (~(s(s(elem!1)) = s(s(s(z))))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[556, 7203])).
% 1.97/2.13 tff(7205,plain,
% 1.97/2.13 ($false),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7204, 7200])).
% 1.97/2.13 tff(7206,plain,((~(s(s(s(s(s(s(z)))))) = s(s(elem!1)))) | (~(s(s(s(elem!1))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.13 tff(7207,plain,
% 1.97/2.13 (~(s(s(s(s(s(s(z)))))) = s(s(elem!1)))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7206, 7133])).
% 1.97/2.13 tff(7208,plain,
% 1.97/2.13 (~(s(s(s(s(s(s(z)))))) = s(elem!1))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[7207, 7192])).
% 1.97/2.13 tff(7209,plain,
% 1.97/2.13 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[7208, 7190])).
% 1.97/2.13 tff(7210,plain,
% 1.97/2.13 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[1144, 7209, 7187])).
% 1.97/2.13 tff(7211,plain,
% 1.97/2.13 ((s(s(s(z))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = s(s(s(z))))),
% 1.97/2.13 inference(symmetry,[status(thm)],[1122])).
% 1.97/2.13 tff(7212,plain,
% 1.97/2.13 ((~(s(s(s(z))) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(s(s(s(s(z)))))) = s(s(s(z)))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[7211])).
% 1.97/2.13 tff(7213,plain,
% 1.97/2.13 (~(s(s(s(s(s(s(z)))))) = s(s(s(z))))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[556, 7212])).
% 1.97/2.13 tff(7214,plain,
% 1.97/2.13 (b(s(s(s(s(s(s(z)))))), s(elem!1)) <=> b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.97/2.13 inference(monotonicity,[status(thm)],[176])).
% 1.97/2.13 tff(7215,plain,
% 1.97/2.13 (b(s(s(s(s(s(s(z)))))), elem!1) <=> b(s(s(s(s(s(s(z)))))), s(elem!1))),
% 1.97/2.13 inference(symmetry,[status(thm)],[7214])).
% 1.97/2.13 tff(7216,plain,
% 1.97/2.13 (b(s(s(s(s(s(s(z)))))), s(elem!1))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[2812, 7215])).
% 1.97/2.13 tff(7217,plain,
% 1.97/2.13 (~r(s(s(z)), s(z))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[2484, 2478, 359])).
% 1.97/2.13 tff(7218,plain,
% 1.97/2.13 (b(s(s(z)), s(z))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[2476, 7217])).
% 1.97/2.13 tff(7219,plain,
% 1.97/2.13 (r(s(s(z)), s(elem!1))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[2478, 2451])).
% 1.97/2.13 tff(7220,plain,
% 1.97/2.13 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(elem!1))))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(7221,plain,
% 1.97/2.13 (((~r(z, s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), z))) <=> ((~r(z, s(elem!1))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(elem!1))))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(7222,plain,
% 1.97/2.13 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(elem!1)))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[7221])).
% 1.97/2.13 tff(7223,plain,
% 1.97/2.13 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(elem!1))))),
% 1.97/2.13 inference(transitivity,[status(thm)],[7222, 7220])).
% 1.97/2.13 tff(7224,plain,
% 1.97/2.13 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), z)))),
% 1.97/2.13 inference(quant_inst,[status(thm)],[])).
% 1.97/2.13 tff(7225,plain,
% 1.97/2.13 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(elem!1)))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[7224, 7223])).
% 1.97/2.13 tff(7226,plain,
% 1.97/2.13 (~r(s(s(z)), z)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7225, 124, 791, 7219])).
% 1.97/2.13 tff(7227,plain,
% 1.97/2.13 (b(s(s(z)), z)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[2531, 7226])).
% 1.97/2.13 tff(7228,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(7229,plain,
% 1.97/2.13 (((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(7230,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z)))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[7229])).
% 1.97/2.13 tff(7231,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))))),
% 1.97/2.13 inference(transitivity,[status(thm)],[7230, 7228])).
% 1.97/2.13 tff(7232,plain,
% 1.97/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 1.97/2.13 inference(quant_inst,[status(thm)],[])).
% 1.97/2.13 tff(7233,plain,
% 1.97/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z)))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[7232, 7231])).
% 1.97/2.13 tff(7234,plain,
% 1.97/2.13 ($false),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7233, 306, 8, 7227, 247, 7218, 485])).
% 1.97/2.13 tff(7235,plain,((~r(s(s(z)), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(z, s(elem!1))) | (~(s(elem!1) = elem!1)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.13 tff(7236,plain,
% 1.97/2.13 (~r(s(s(z)), elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7235, 8, 247, 485, 791, 176, 359])).
% 1.97/2.13 tff(7237,plain,
% 1.97/2.13 (b(s(s(z)), elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[5555, 7236, 176, 2448])).
% 1.97/2.13 tff(7238,plain,
% 1.97/2.13 (~b(s(s(s(z))), z)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[4569, 859, 8, 247])).
% 1.97/2.13 tff(7239,plain,
% 1.97/2.13 (r(s(s(s(z))), z)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[2197, 7238])).
% 1.97/2.13 tff(7240,plain,
% 1.97/2.13 (~r(elem!1, s(s(s(z))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[2312, 7239, 246])).
% 1.97/2.13 tff(7241,plain,
% 1.97/2.13 ((s(elem!1) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[2580])).
% 1.97/2.13 tff(7242,plain,
% 1.97/2.13 ((s(s(elem!1)) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 1.97/2.13 inference(symmetry,[status(thm)],[7241])).
% 1.97/2.13 tff(7243,plain,
% 1.97/2.13 ((~(s(s(elem!1)) = s(s(s(z))))) <=> (~(s(elem!1) = s(s(s(z)))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[7242])).
% 1.97/2.13 tff(7244,plain,
% 1.97/2.13 (~(s(elem!1) = s(s(s(z))))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[16, 7243])).
% 1.97/2.13 tff(7245,plain,
% 1.97/2.13 (r(s(elem!1), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[362])).
% 1.97/2.13 tff(7246,plain,
% 1.97/2.13 (r(elem!1, s(s(s(z)))) <=> r(s(elem!1), s(s(s(z))))),
% 1.97/2.13 inference(symmetry,[status(thm)],[7245])).
% 1.97/2.13 tff(7247,plain,
% 1.97/2.13 ((~r(elem!1, s(s(s(z))))) <=> (~r(s(elem!1), s(s(s(z)))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[7246])).
% 1.97/2.13 tff(7248,plain,
% 1.97/2.13 (~r(s(elem!1), s(s(s(z))))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[2302, 7247])).
% 1.97/2.13 tff(7249,plain,
% 1.97/2.13 ((s(elem!1) = s(s(s(z)))) | r(s(elem!1), s(s(s(z))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[2367, 43, 2420])).
% 1.97/2.13 tff(7250,plain,
% 1.97/2.13 ($false),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7249, 7248, 7244])).
% 1.97/2.13 tff(7251,plain,(r(elem!1, s(s(s(z)))) | b(s(elem!1), s(s(s(z)))) | (~(elem!1 = s(elem!1))) | (s(s(elem!1)) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.13 tff(7252,plain,
% 1.97/2.13 (b(s(elem!1), s(s(s(z))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7251, 7240, 361, 16])).
% 1.97/2.13 tff(7253,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(7254,plain,
% 1.97/2.13 (((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(7255,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1)))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[7254])).
% 1.97/2.13 tff(7256,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))))),
% 1.97/2.13 inference(transitivity,[status(thm)],[7255, 7253])).
% 1.97/2.13 tff(7257,plain,
% 1.97/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))))),
% 1.97/2.13 inference(quant_inst,[status(thm)],[])).
% 1.97/2.13 tff(7258,plain,
% 1.97/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1)))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[7257, 7256])).
% 1.97/2.13 tff(7259,plain,
% 1.97/2.13 ($false),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7258, 306, 8, 7252, 859, 485, 2453])).
% 1.97/2.13 tff(7260,plain,((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~(elem!1 = s(elem!1))) | (s(s(elem!1)) = s(s(s(z)))) | (~r(elem!1, z)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.13 tff(7261,plain,
% 1.97/2.13 (~b(z, s(s(s(z))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7260, 8, 485, 2453, 2569, 16, 246, 247])).
% 1.97/2.13 tff(7262,plain,
% 1.97/2.13 ((z = s(s(s(z)))) | r(z, s(s(s(z))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[2415, 43, 7261])).
% 1.97/2.13 tff(7263,plain,
% 1.97/2.13 (r(z, s(s(s(z))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7262, 3385])).
% 1.97/2.13 tff(7264,plain,
% 1.97/2.13 (~r(elem!1, s(s(s(z))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[3392, 7263, 246])).
% 1.97/2.13 tff(7265,plain,
% 1.97/2.13 (b(s(elem!1), s(s(s(z))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7251, 7264, 2569, 16])).
% 1.97/2.13 tff(7266,plain,
% 1.97/2.13 (b(s(s(z)), s(elem!1))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[2811, 5549])).
% 1.97/2.13 tff(7267,assumption,(b(s(s(z)), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.97/2.13 tff(7268,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(elem!1))))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(7269,plain,
% 1.97/2.13 (((~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))) <=> ((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(elem!1))))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(7270,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(elem!1)))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[7269])).
% 1.97/2.13 tff(7271,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(elem!1))))),
% 1.97/2.13 inference(transitivity,[status(thm)],[7270, 7268])).
% 1.97/2.13 tff(7272,plain,
% 1.97/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.97/2.13 inference(quant_inst,[status(thm)],[])).
% 1.97/2.13 tff(7273,plain,
% 1.97/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(elem!1)))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[7272, 7271])).
% 1.97/2.13 tff(7274,plain,
% 1.97/2.13 (~b(s(s(z)), s(elem!1))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7273, 306, 2455, 2453, 3875, 7267])).
% 1.97/2.13 tff(7275,plain,
% 1.97/2.13 ($false),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7274, 7266])).
% 1.97/2.13 tff(7276,plain,((~b(s(s(z)), elem!1)) | (~(s(elem!1) = elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.13 tff(7277,plain,
% 1.97/2.13 (~b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7276, 7265, 7237, 2453, 7216, 176])).
% 1.97/2.13 tff(7278,plain,
% 1.97/2.13 (r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[2829, 43, 2826, 7277])).
% 1.97/2.13 tff(7279,plain,
% 1.97/2.13 (~b(s(s(z)), s(s(s(z))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[2499, 7265, 2448, 359, 176, 2453, 8])).
% 1.97/2.13 tff(7280,plain,
% 1.97/2.13 (r(s(s(z)), s(s(s(z))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[2514, 7279])).
% 1.97/2.13 tff(7281,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(7282,plain,
% 1.97/2.14 (((~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(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(s(z))))))))) <=> ((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(7283,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(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(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1)))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[7282])).
% 1.97/2.14 tff(7284,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(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(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 1.97/2.14 inference(transitivity,[status(thm)],[7283, 7281])).
% 1.97/2.14 tff(7285,plain,
% 1.97/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(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(s(z)))))))))),
% 1.97/2.14 inference(quant_inst,[status(thm)],[])).
% 1.97/2.14 tff(7286,plain,
% 1.97/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1)))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[7285, 7284])).
% 1.97/2.14 tff(7287,plain,
% 1.97/2.14 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[7286, 306, 7265, 2453, 7216])).
% 1.97/2.14 tff(7288,plain,
% 1.97/2.14 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[3207, 7287])).
% 1.97/2.14 tff(7289,plain,
% 1.97/2.14 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(7290,plain,
% 1.97/2.14 (((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(7291,plain,
% 1.97/2.14 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[7290])).
% 1.97/2.14 tff(7292,plain,
% 1.97/2.14 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.97/2.14 inference(transitivity,[status(thm)],[7291, 7289])).
% 1.97/2.14 tff(7293,plain,
% 1.97/2.14 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.97/2.14 inference(quant_inst,[status(thm)],[])).
% 1.97/2.14 tff(7294,plain,
% 1.97/2.14 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[7293, 7292])).
% 1.97/2.14 tff(7295,plain,
% 1.97/2.14 ($false),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[7294, 124, 7288, 7280, 7278])).
% 1.97/2.14 tff(7296,plain,((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~(s(elem!1) = elem!1)) | (s(s(z)) = elem!1) | (~r(elem!1, s(z))) | (s(s(elem!1)) = s(s(s(z)))) | (~r(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.14 tff(7297,plain,
% 1.97/2.14 (~b(s(z), s(s(s(z))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[7296, 2453, 176, 2448, 359, 16, 246, 485, 247, 2812, 791])).
% 1.97/2.14 tff(7298,plain,
% 1.97/2.14 (r(s(z), s(s(s(z))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[3302, 7297])).
% 1.97/2.14 tff(7299,plain,
% 1.97/2.14 (~r(elem!1, s(s(s(z))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[3347, 7298, 4])).
% 1.97/2.14 tff(7300,plain,
% 1.97/2.14 (b(s(elem!1), s(s(s(z))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[7251, 7299, 2569, 16])).
% 1.97/2.14 tff(7301,plain,
% 1.97/2.14 (b(elem!1, s(s(s(z))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[1455, 9, 6, 2, 5])).
% 1.97/2.14 tff(7302,plain,
% 1.97/2.14 (~r(s(s(s(z))), elem!1)),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[6816, 114, 4])).
% 1.97/2.14 tff(7303,plain,
% 1.97/2.14 (b(s(s(s(z))), elem!1)),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[1489, 7302, 1483])).
% 1.97/2.14 tff(7304,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(7305,plain,
% 1.97/2.14 (((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))) <=> ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(7306,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~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(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), elem!1))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[7305])).
% 1.97/2.14 tff(7307,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~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(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.97/2.14 inference(transitivity,[status(thm)],[7306, 7304])).
% 1.97/2.14 tff(7308,plain,
% 1.97/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.97/2.14 inference(quant_inst,[status(thm)],[])).
% 1.97/2.14 tff(7309,plain,
% 1.97/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), elem!1))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[7308, 7307])).
% 1.97/2.14 tff(7310,plain,
% 1.97/2.14 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[7309, 306, 7303, 2812, 7301])).
% 1.97/2.14 tff(7311,plain,
% 1.97/2.14 ((s(s(s(s(s(s(z)))))) = s(s(s(z)))) | r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[4603, 43, 7310])).
% 1.97/2.14 tff(7312,plain,
% 1.97/2.14 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[7311, 7213])).
% 1.97/2.14 tff(7313,plain,
% 1.97/2.14 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[870, 124, 114, 4268])).
% 1.97/2.14 tff(7314,plain,
% 1.97/2.14 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[3207, 7313])).
% 1.97/2.14 tff(7315,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(7316,plain,
% 1.97/2.14 (((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(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(s(z))))))))) <=> ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(7317,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(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(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~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(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[7316])).
% 1.97/2.14 tff(7318,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(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(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~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(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.97/2.14 inference(transitivity,[status(thm)],[7317, 7315])).
% 1.97/2.14 tff(7319,plain,
% 1.97/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(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(s(z)))))))))),
% 1.97/2.14 inference(quant_inst,[status(thm)],[])).
% 1.97/2.14 tff(7320,plain,
% 1.97/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[7319, 7318])).
% 1.97/2.14 tff(7321,plain,
% 1.97/2.14 ($false),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[7320, 306, 7303, 2812, 7301, 7314])).
% 1.97/2.14 tff(7322,plain,(b(s(s(s(z))), s(z)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (s(s(s(z))) = elem!1) | (~r(s(z), elem!1)) | r(s(s(elem!1)), elem!1) | b(elem!1, z) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.14 tff(7323,plain,
% 1.97/2.14 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[7322, 2812, 5, 1483, 4, 6, 2, 9])).
% 1.97/2.14 tff(7324,plain,
% 1.97/2.14 (b(s(s(s(s(s(s(z)))))), s(z))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[651, 43, 2844, 7323])).
% 1.97/2.14 tff(7325,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(7326,plain,
% 1.97/2.14 (((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(s(z))))))))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(7327,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z))))))))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[7326])).
% 1.97/2.14 tff(7328,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 1.97/2.14 inference(transitivity,[status(thm)],[7327, 7325])).
% 1.97/2.14 tff(7329,plain,
% 1.97/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 1.97/2.14 inference(quant_inst,[status(thm)],[])).
% 1.97/2.14 tff(7330,plain,
% 1.97/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z))))))))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[7329, 7328])).
% 1.97/2.14 tff(7331,plain,
% 1.97/2.14 (~b(z, s(s(s(s(s(s(z)))))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[7330, 306, 247, 485, 7324])).
% 1.97/2.14 tff(7332,plain,
% 1.97/2.14 ((z = s(s(s(s(s(s(z))))))) | r(z, s(s(s(s(s(s(z)))))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[5445, 43, 7331])).
% 1.97/2.14 tff(7333,plain,
% 1.97/2.14 (r(z, s(s(s(s(s(s(z)))))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[7332, 5435])).
% 1.97/2.14 tff(7334,plain,
% 1.97/2.14 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[7320, 306, 7303, 2812, 7301])).
% 1.97/2.14 tff(7335,plain,
% 1.97/2.14 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[3207, 7334])).
% 1.97/2.14 tff(7336,plain,
% 1.97/2.14 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(7337,plain,
% 1.97/2.14 (((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(7338,plain,
% 1.97/2.14 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[7337])).
% 1.97/2.14 tff(7339,plain,
% 1.97/2.14 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.97/2.14 inference(transitivity,[status(thm)],[7338, 7336])).
% 1.97/2.14 tff(7340,plain,
% 1.97/2.14 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(z))))))),
% 1.97/2.14 inference(quant_inst,[status(thm)],[])).
% 1.97/2.14 tff(7341,plain,
% 1.97/2.14 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[7340, 7339])).
% 1.97/2.14 tff(7342,plain,
% 1.97/2.14 (~r(z, s(s(s(z))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[7341, 124, 7335, 7333])).
% 1.97/2.14 tff(7343,plain,
% 1.97/2.14 ((z = s(s(s(z)))) | b(z, s(s(s(z))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[2415, 43, 7342])).
% 1.97/2.14 tff(7344,plain,
% 1.97/2.14 (b(z, s(s(s(z))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[7343, 3385])).
% 1.97/2.14 tff(7345,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(7346,plain,
% 1.97/2.14 (((~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))) <=> ((~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(7347,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[7346])).
% 1.97/2.15 tff(7348,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.97/2.15 inference(transitivity,[status(thm)],[7347, 7345])).
% 1.97/2.15 tff(7349,plain,
% 1.97/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.97/2.15 inference(quant_inst,[status(thm)],[])).
% 1.97/2.15 tff(7350,plain,
% 1.97/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[7349, 7348])).
% 1.97/2.15 tff(7351,plain,
% 1.97/2.15 ($false),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[7350, 306, 859, 247, 5493, 4247, 5491])).
% 1.97/2.15 tff(7352,plain,((~r(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.15 tff(7353,plain,
% 1.97/2.15 (~r(s(s(z)), s(s(s(z))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[7352, 7344, 247, 7324, 7312, 1034])).
% 1.97/2.15 tff(7354,plain,
% 1.97/2.15 (b(s(s(z)), s(s(s(z))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[2512, 43, 2508, 7353])).
% 1.97/2.15 tff(7355,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(7356,plain,
% 1.97/2.15 (((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1))) <=> ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(7357,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1))))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[7356])).
% 1.97/2.15 tff(7358,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 1.97/2.15 inference(transitivity,[status(thm)],[7357, 7355])).
% 1.97/2.15 tff(7359,plain,
% 1.97/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 1.97/2.15 inference(quant_inst,[status(thm)],[])).
% 1.97/2.15 tff(7360,plain,
% 1.97/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[7359, 7358])).
% 1.97/2.15 tff(7361,plain,
% 1.97/2.15 (~b(s(s(z)), elem!1)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[7360, 306, 7303, 7301, 7354])).
% 1.97/2.15 tff(7362,plain,
% 1.97/2.15 (r(s(s(z)), elem!1)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[2544, 43, 7361, 2448])).
% 1.97/2.15 tff(7363,plain,
% 1.97/2.15 (~b(s(s(z)), s(s(s(z))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[5582, 2061, 1967, 859, 1470])).
% 1.97/2.15 tff(7364,plain,
% 1.97/2.15 (r(s(s(z)), s(s(s(z))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[2512, 43, 7363, 2508])).
% 1.97/2.15 tff(7365,plain,
% 1.97/2.15 (~r(s(s(z)), s(z))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[3833, 7364, 1034])).
% 1.97/2.15 tff(7366,plain,
% 1.97/2.15 (b(s(s(z)), s(z))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[2476, 7365])).
% 1.97/2.15 tff(7367,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(7368,plain,
% 1.97/2.15 (((~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))) <=> ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(7369,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z)))))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[7368])).
% 1.97/2.15 tff(7370,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))))),
% 1.97/2.15 inference(transitivity,[status(thm)],[7369, 7367])).
% 1.97/2.15 tff(7371,plain,
% 1.97/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 1.97/2.15 inference(quant_inst,[status(thm)],[])).
% 1.97/2.15 tff(7372,plain,
% 1.97/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z)))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[7371, 7370])).
% 1.97/2.15 tff(7373,plain,
% 1.97/2.15 ($false),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[7372, 306, 2061, 859, 247, 7366, 485])).
% 1.97/2.15 tff(7374,plain,((~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.15 tff(7375,plain,
% 1.97/2.15 (~b(s(s(z)), z)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[7374, 7344, 247, 485, 1034, 7303, 7301])).
% 1.97/2.15 tff(7376,plain,
% 1.97/2.15 (r(s(s(z)), z)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[2531, 7375])).
% 1.97/2.15 tff(7377,plain,
% 1.97/2.15 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(7378,plain,
% 1.97/2.15 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)))),
% 1.97/2.15 inference(quant_inst,[status(thm)],[])).
% 1.97/2.15 tff(7379,plain,
% 1.97/2.15 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[7378, 7377])).
% 1.97/2.15 tff(7380,plain,
% 1.97/2.15 ($false),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[7379, 124, 246, 7376, 7362])).
% 1.97/2.15 tff(7381,plain,((~b(s(s(s(s(s(s(z)))))), elem!1)) | (~r(elem!1, z)) | (s(s(z)) = elem!1) | (~b(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~b(z, s(z))) | b(elem!1, s(z)) | (s(s(s(z))) = elem!1) | (~r(s(z), elem!1)) | r(s(s(elem!1)), elem!1) | b(elem!1, z) | b(s(s(s(z))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.15 tff(7382,plain,
% 1.97/2.15 (b(s(s(s(z))), s(z))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[7381, 7298, 1483, 247, 246, 485, 2448, 5, 4, 6, 2, 2812])).
% 1.97/2.15 tff(7383,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(7384,plain,
% 1.97/2.15 (((~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(7385,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1)))))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[7384])).
% 1.97/2.15 tff(7386,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 1.97/2.15 inference(transitivity,[status(thm)],[7385, 7383])).
% 1.97/2.15 tff(7387,plain,
% 1.97/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.97/2.15 inference(quant_inst,[status(thm)],[])).
% 1.97/2.15 tff(7388,plain,
% 1.97/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1)))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[7387, 7386])).
% 1.97/2.15 tff(7389,plain,
% 1.97/2.15 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[7388, 306, 7382, 7300, 2453, 7216])).
% 1.97/2.15 tff(7390,plain,
% 1.97/2.15 ((s(s(s(s(s(s(z)))))) = s(s(s(z)))) | r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[4603, 43, 7389])).
% 1.97/2.15 tff(7391,plain,
% 1.97/2.15 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[7390, 7213])).
% 1.97/2.15 tff(7392,plain,
% 1.97/2.15 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[5339, 124, 7298, 7391])).
% 1.97/2.15 tff(7393,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(z), z)))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(7394,plain,
% 1.97/2.15 (((~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(z), z)))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(7395,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(z), z))))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[7394])).
% 1.97/2.15 tff(7396,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(z), z)))),
% 1.97/2.15 inference(transitivity,[status(thm)],[7395, 7393])).
% 1.97/2.15 tff(7397,plain,
% 1.97/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 1.97/2.15 inference(quant_inst,[status(thm)],[])).
% 1.97/2.15 tff(7398,plain,
% 1.97/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(z), z))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[7397, 7396])).
% 1.97/2.15 tff(7399,plain,
% 1.97/2.15 (~b(s(s(s(z))), z)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[7398, 306, 7382, 247, 485])).
% 1.97/2.15 tff(7400,plain,
% 1.97/2.15 (r(s(s(s(z))), z)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[2197, 7399])).
% 1.97/2.15 tff(7401,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(7402,plain,
% 1.97/2.15 (((~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(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(s(z))))))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(7403,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(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(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1)))))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[7402])).
% 1.97/2.15 tff(7404,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(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(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 1.97/2.15 inference(transitivity,[status(thm)],[7403, 7401])).
% 1.97/2.15 tff(7405,plain,
% 1.97/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(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(s(z)))))))))),
% 1.97/2.15 inference(quant_inst,[status(thm)],[])).
% 1.97/2.15 tff(7406,plain,
% 1.97/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1)))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[7405, 7404])).
% 1.97/2.15 tff(7407,plain,
% 1.97/2.15 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[7406, 306, 7382, 7300, 2453, 7216])).
% 1.97/2.15 tff(7408,plain,
% 1.97/2.15 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[3207, 7407])).
% 1.97/2.15 tff(7409,plain,
% 1.97/2.15 (~r(s(s(s(s(s(s(z)))))), z)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[3203, 7408, 7400])).
% 1.97/2.15 tff(7410,plain,
% 1.97/2.15 (b(s(s(s(s(s(s(z)))))), z)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[4232, 7409])).
% 1.97/2.15 tff(7411,plain,
% 1.97/2.15 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[7183, 7410, 247, 485])).
% 1.97/2.15 tff(7412,plain,
% 1.97/2.15 ($false),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[651, 43, 2844, 7411, 7392])).
% 1.97/2.15 tff(7413,plain,((~b(s(s(s(z))), s(elem!1))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~(s(elem!1) = elem!1)) | (s(s(elem!1)) = s(s(s(z)))) | (s(s(s(z))) = elem!1) | (~r(elem!1, z)) | (s(s(z)) = elem!1) | b(elem!1, s(z)) | (~r(s(z), elem!1)) | r(s(s(elem!1)), elem!1) | b(elem!1, z) | (~r(elem!1, s(z))) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.15 tff(7414,plain,
% 1.97/2.15 (~b(s(s(s(z))), s(elem!1))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[7413, 7109, 247, 7210, 7130, 7171, 7134, 2254, 7164, 7163, 7107, 6, 2, 7159, 7156])).
% 1.97/2.15 tff(7415,plain,
% 1.97/2.15 ($false),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[7414, 7154])).
% 1.97/2.15 tff(7416,plain,(b(s(z), elem!1) | (~b(s(z), z)) | r(s(s(elem!1)), elem!1) | b(elem!1, z) | (~r(z, elem!1)) | b(s(elem!1), s(z)) | (s(elem!1) = s(z)) | b(s(s(elem!1)), s(elem!1)) | (~r(s(elem!1), z)) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.15 tff(7417,plain,
% 1.97/2.15 (b(s(z), elem!1)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[7416, 466, 6, 2, 374, 2609, 2249, 7093, 247, 7106])).
% 1.97/2.15 tff(7418,plain,
% 1.97/2.15 (~(s(z) = s(elem!1))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[2249, 4039])).
% 1.97/2.16 tff(7419,plain,
% 1.97/2.16 (b(elem!1, s(elem!1))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[372, 365, 345])).
% 1.97/2.16 tff(7420,plain,
% 1.97/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(7421,plain,
% 1.97/2.16 (((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1)))) <=> ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(7422,plain,
% 1.97/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1)))))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[7421])).
% 1.97/2.16 tff(7423,plain,
% 1.97/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))))),
% 1.97/2.16 inference(transitivity,[status(thm)],[7422, 7420])).
% 1.97/2.16 tff(7424,plain,
% 1.97/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))),
% 1.97/2.16 inference(quant_inst,[status(thm)],[])).
% 1.97/2.16 tff(7425,plain,
% 1.97/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1)))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[7424, 7423])).
% 1.97/2.16 tff(7426,plain,
% 1.97/2.16 (~b(s(z), s(elem!1))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[7425, 306, 2323, 7419, 2831])).
% 1.97/2.16 tff(7427,plain,
% 1.97/2.16 ((s(z) = s(elem!1)) | r(s(z), s(elem!1))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[4047, 43, 7426])).
% 1.97/2.16 tff(7428,plain,
% 1.97/2.16 (r(s(z), s(elem!1))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[7427, 7418])).
% 1.97/2.16 tff(7429,plain,
% 1.97/2.16 (r(s(s(elem!1)), s(elem!1))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[994, 392, 7093])).
% 1.97/2.16 tff(7430,plain,
% 1.97/2.16 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(z))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(7431,plain,
% 1.97/2.16 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(z))))),
% 1.97/2.16 inference(quant_inst,[status(thm)],[])).
% 1.97/2.16 tff(7432,plain,
% 1.97/2.16 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(z)))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[7431, 7430])).
% 1.97/2.16 tff(7433,plain,
% 1.97/2.16 (~r(s(s(elem!1)), s(z))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[7432, 124, 7429, 7428])).
% 1.97/2.16 tff(7434,plain,
% 1.97/2.16 (b(s(s(elem!1)), s(z))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[3989, 7433])).
% 1.97/2.16 tff(7435,plain,
% 1.97/2.16 (b(s(s(elem!1)), s(elem!1)) <=> b(elem!1, s(elem!1))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[1171])).
% 1.97/2.16 tff(7436,plain,
% 1.97/2.16 (b(elem!1, s(elem!1)) <=> b(s(s(elem!1)), s(elem!1))),
% 1.97/2.16 inference(symmetry,[status(thm)],[7435])).
% 1.97/2.16 tff(7437,plain,
% 1.97/2.16 (b(s(s(elem!1)), s(elem!1))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[815, 7436])).
% 1.97/2.16 tff(7438,plain,
% 1.97/2.16 ($false),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[7093, 7437])).
% 1.97/2.16 tff(7439,plain,((~(s(s(elem!1)) = elem!1)) | b(s(s(elem!1)), s(elem!1)) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.16 tff(7440,plain,
% 1.97/2.16 (~(s(s(elem!1)) = elem!1)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[7439, 7419, 7093])).
% 1.97/2.16 tff(7441,plain,
% 1.97/2.16 (b(s(s(elem!1)), elem!1)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[47, 7440, 6])).
% 1.97/2.16 tff(7442,plain,
% 1.97/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(z))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(7443,plain,
% 1.97/2.16 (((~b(s(elem!1), elem!1)) | (~b(elem!1, 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)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(z))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(7444,plain,
% 1.97/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(z)))))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[7443])).
% 1.97/2.16 tff(7445,plain,
% 1.97/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(z))))),
% 1.97/2.16 inference(transitivity,[status(thm)],[7444, 7442])).
% 1.97/2.16 tff(7446,plain,
% 1.97/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))),
% 1.97/2.16 inference(quant_inst,[status(thm)],[])).
% 1.97/2.16 tff(7447,plain,
% 1.97/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(z)))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[7446, 7445])).
% 1.97/2.16 tff(7448,plain,
% 1.97/2.16 ($false),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[7447, 306, 7441, 2323, 7419, 2831, 7434])).
% 1.97/2.16 tff(7449,plain,((s(elem!1) = elem!1) | (~b(s(z), elem!1)) | r(s(s(elem!1)), elem!1) | b(s(s(elem!1)), s(elem!1)) | (s(elem!1) = s(z)) | r(elem!1, s(elem!1)) | r(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.16 tff(7450,plain,
% 1.97/2.16 (s(elem!1) = elem!1),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[7449, 7417, 6, 7093, 2249, 7097, 808])).
% 1.97/2.16 tff(7451,plain,
% 1.97/2.16 (s(s(elem!1)) = elem!1),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[180, 7450])).
% 1.97/2.16 tff(7452,plain,
% 1.97/2.16 (~b(elem!1, s(elem!1))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[7439, 7451, 7093])).
% 1.97/2.16 tff(7453,plain,
% 1.97/2.16 (elem!1 = s(elem!1)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[372, 7452, 7097])).
% 1.97/2.16 tff(7454,plain,
% 1.97/2.16 (r(elem!1, s(z))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[2615, 7453, 2609])).
% 1.97/2.16 tff(7455,plain,
% 1.97/2.16 (~r(z, s(z))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[385, 7454, 374])).
% 1.97/2.16 tff(7456,plain,
% 1.97/2.16 (b(z, s(z))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[389, 43, 7455, 2260])).
% 1.97/2.16 tff(7457,plain,
% 1.97/2.16 (b(s(elem!1), s(z)) <=> b(elem!1, s(z))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[7450])).
% 1.97/2.16 tff(7458,plain,
% 1.97/2.16 ((~b(s(elem!1), s(z))) <=> (~b(elem!1, s(z)))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[7457])).
% 1.97/2.16 tff(7459,plain,
% 1.97/2.16 (~b(elem!1, s(z))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[2609, 7458])).
% 1.97/2.16 tff(7460,plain,
% 1.97/2.16 ((s(elem!1) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[7450])).
% 1.97/2.16 tff(7461,plain,
% 1.97/2.16 ((s(elem!1) = s(s(s(z)))) <=> (s(s(s(z))) = elem!1)),
% 1.97/2.16 inference(transitivity,[status(thm)],[7460, 1414])).
% 1.97/2.16 tff(7462,plain,
% 1.97/2.16 ((~(s(elem!1) = s(s(s(z))))) <=> (~(s(s(s(z))) = elem!1))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[7461])).
% 1.97/2.16 tff(7463,plain,
% 1.97/2.16 (~(s(elem!1) = s(s(s(z))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[2356, 7451])).
% 1.97/2.16 tff(7464,plain,
% 1.97/2.16 (~(s(s(s(z))) = elem!1)),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[7463, 7462])).
% 1.97/2.16 tff(7465,plain,
% 1.97/2.16 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[7451])).
% 1.97/2.16 tff(7466,plain,
% 1.97/2.16 ((elem!1 = s(s(s(elem!1)))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 1.97/2.16 inference(symmetry,[status(thm)],[7465])).
% 1.97/2.16 tff(7467,plain,
% 1.97/2.16 ((elem!1 = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 1.97/2.16 inference(transitivity,[status(thm)],[7466, 2425])).
% 1.97/2.16 tff(7468,plain,
% 1.97/2.16 (elem!1 = s(s(elem!1))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[1174, 7451])).
% 1.97/2.16 tff(7469,plain,
% 1.97/2.16 (s(s(s(elem!1))) = s(elem!1)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[1168, 7468])).
% 1.97/2.16 tff(7470,plain,
% 1.97/2.16 (s(elem!1) = s(s(s(elem!1)))),
% 1.97/2.16 inference(symmetry,[status(thm)],[7469])).
% 1.97/2.16 tff(7471,plain,
% 1.97/2.16 (elem!1 = s(elem!1)),
% 1.97/2.16 inference(symmetry,[status(thm)],[7450])).
% 1.97/2.16 tff(7472,plain,
% 1.97/2.16 (elem!1 = s(s(s(elem!1)))),
% 1.97/2.16 inference(transitivity,[status(thm)],[7471, 7470])).
% 1.97/2.16 tff(7473,plain,
% 1.97/2.16 (s(s(s(elem!1))) = s(s(elem!1))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[7472, 7467])).
% 1.97/2.16 tff(7474,plain,
% 1.97/2.16 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[5403, 7473])).
% 1.97/2.16 tff(7475,plain,
% 1.97/2.16 (~r(z, s(z))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[385, 359, 374])).
% 1.97/2.16 tff(7476,plain,
% 1.97/2.16 (b(z, s(z))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[389, 43, 7475, 2260])).
% 1.97/2.16 tff(7477,plain,
% 1.97/2.16 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[7183, 5454, 247, 7476])).
% 1.97/2.16 tff(7478,plain,
% 1.97/2.16 (r(s(s(s(s(s(s(z)))))), s(z))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[651, 43, 2844, 7477])).
% 1.97/2.16 tff(7479,plain,
% 1.97/2.16 ($false),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[2904, 124, 359, 2858, 7478])).
% 1.97/2.16 tff(7480,plain,((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(elem!1, s(z))) | (~b(s(z), z)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.16 tff(7481,plain,
% 1.97/2.16 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[7480, 7454, 247, 374])).
% 1.97/2.16 tff(7482,plain,
% 1.97/2.16 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[1144, 7481, 7474])).
% 1.97/2.16 tff(7483,plain,
% 1.97/2.16 (~r(s(s(s(z))), s(z))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[1481, 2859, 359])).
% 1.97/2.16 tff(7484,plain,
% 1.97/2.16 (b(s(s(s(z))), s(z))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[113, 7483])).
% 1.97/2.16 tff(7485,plain,
% 1.97/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(7486,plain,
% 1.97/2.16 (((~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(7487,plain,
% 1.97/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z)))))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[7486])).
% 1.97/2.16 tff(7488,plain,
% 1.97/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))))),
% 1.97/2.16 inference(transitivity,[status(thm)],[7487, 7485])).
% 1.97/2.16 tff(7489,plain,
% 1.97/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 1.97/2.16 inference(quant_inst,[status(thm)],[])).
% 1.97/2.16 tff(7490,plain,
% 1.97/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z)))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[7489, 7488])).
% 1.97/2.16 tff(7491,plain,
% 1.97/2.16 ($false),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[7490, 306, 7484, 2831, 7136, 1470, 7476])).
% 1.97/2.16 tff(7492,plain,((~r(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~r(elem!1, s(z))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.16 tff(7493,plain,
% 1.97/2.16 (~r(s(s(s(z))), elem!1)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[7492, 1470, 2831, 359, 374])).
% 1.97/2.16 tff(7494,plain,
% 1.97/2.16 (b(s(s(s(z))), elem!1)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[1489, 7493, 1483])).
% 1.97/2.16 tff(7495,plain,
% 1.97/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(7496,plain,
% 1.97/2.16 (((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(z))))))))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(7497,plain,
% 1.97/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1))))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[7496])).
% 1.97/2.16 tff(7498,plain,
% 1.97/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.97/2.16 inference(transitivity,[status(thm)],[7497, 7495])).
% 1.97/2.16 tff(7499,plain,
% 1.97/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 1.97/2.16 inference(quant_inst,[status(thm)],[])).
% 1.97/2.16 tff(7500,plain,
% 1.97/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[7499, 7498])).
% 1.97/2.16 tff(7501,plain,
% 1.97/2.16 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[7500, 306, 2831, 7494, 2812, 1470])).
% 1.97/2.16 tff(7502,plain,
% 1.97/2.16 (r(s(z), s(s(s(s(s(s(z)))))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[5358, 43, 5355, 7501])).
% 1.97/2.16 tff(7503,plain,
% 1.97/2.16 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[7320, 306, 7494, 2812, 1470])).
% 1.97/2.16 tff(7504,plain,
% 1.97/2.16 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[3207, 7503])).
% 1.97/2.16 tff(7505,plain,
% 1.97/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(7506,plain,
% 1.97/2.16 (((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(7507,plain,
% 1.97/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[7506])).
% 1.97/2.16 tff(7508,plain,
% 1.97/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.97/2.16 inference(transitivity,[status(thm)],[7507, 7505])).
% 1.97/2.16 tff(7509,plain,
% 1.97/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 1.97/2.16 inference(quant_inst,[status(thm)],[])).
% 1.97/2.16 tff(7510,plain,
% 1.97/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[7509, 7508])).
% 1.97/2.16 tff(7511,plain,
% 1.97/2.16 (~b(s(s(s(z))), s(z))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[7510, 306, 2831, 7494, 1470])).
% 1.97/2.16 tff(7512,plain,
% 1.97/2.16 (r(s(s(s(z))), s(z))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[113, 7511])).
% 1.97/2.16 tff(7513,plain,
% 1.97/2.16 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(7514,plain,
% 1.97/2.16 (((~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(7515,plain,
% 1.97/2.16 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[7514])).
% 1.97/2.16 tff(7516,plain,
% 1.97/2.16 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.97/2.16 inference(transitivity,[status(thm)],[7515, 7513])).
% 1.97/2.16 tff(7517,plain,
% 1.97/2.16 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(z))))),
% 1.97/2.16 inference(quant_inst,[status(thm)],[])).
% 1.97/2.16 tff(7518,plain,
% 1.97/2.16 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[7517, 7516])).
% 1.97/2.16 tff(7519,plain,
% 1.97/2.16 ($false),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[7518, 124, 7512, 7504, 7502])).
% 1.97/2.16 tff(7520,plain,((~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (s(s(s(z))) = elem!1) | (~r(elem!1, s(z))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.17 tff(7521,plain,
% 1.97/2.17 (~b(elem!1, s(s(s(z))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7520, 7417, 7482, 7464, 7454, 374])).
% 1.97/2.17 tff(7522,plain,
% 1.97/2.17 (b(s(s(s(z))), s(z))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[1455, 7521, 6, 2, 7459])).
% 1.97/2.17 tff(7523,plain,
% 1.97/2.17 (~b(s(s(s(z))), z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7398, 306, 7522, 247, 7456])).
% 1.97/2.17 tff(7524,plain,
% 1.97/2.17 ((s(elem!1) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 1.97/2.17 inference(transitivity,[status(thm)],[7461, 6881])).
% 1.97/2.17 tff(7525,plain,
% 1.97/2.17 ((~(s(elem!1) = s(s(s(z))))) <=> (~(elem!1 = s(s(s(z)))))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[7524])).
% 1.97/2.17 tff(7526,plain,
% 1.97/2.17 (~(elem!1 = s(s(s(z))))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[7463, 7525])).
% 1.97/2.17 tff(7527,plain,
% 1.97/2.17 (r(elem!1, s(s(s(z))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[131, 43, 7521, 7526])).
% 1.97/2.17 tff(7528,plain,
% 1.97/2.17 (~r(s(s(s(z))), z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[2312, 7527, 2254])).
% 1.97/2.17 tff(7529,plain,
% 1.97/2.17 ($false),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[2197, 7528, 7523])).
% 1.97/2.17 tff(7530,plain,((~r(s(elem!1), z)) | (~b(s(z), z)) | r(s(s(elem!1)), elem!1) | b(elem!1, z) | (~r(z, elem!1)) | b(s(elem!1), s(z)) | b(s(s(elem!1)), s(elem!1)) | (s(elem!1) = s(z)) | r(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.17 tff(7531,plain,
% 1.97/2.17 (~r(s(elem!1), z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7530, 247, 6, 2, 374, 2609, 7093, 2249, 808])).
% 1.97/2.17 tff(7532,plain,
% 1.97/2.17 (b(s(elem!1), z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[2380, 7531])).
% 1.97/2.17 tff(7533,plain,
% 1.97/2.17 (~(elem!1 = s(z))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[3096, 7106])).
% 1.97/2.17 tff(7534,plain,
% 1.97/2.17 (b(elem!1, s(z))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[96, 43, 2607, 7533])).
% 1.97/2.17 tff(7535,plain,
% 1.97/2.17 (~(elem!1 = s(elem!1))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[2615, 2607, 2609])).
% 1.97/2.17 tff(7536,plain,
% 1.97/2.17 (~(s(elem!1) = elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[2571, 7535])).
% 1.97/2.17 tff(7537,plain,
% 1.97/2.17 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(7538,plain,
% 1.97/2.17 (((~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1)))) <=> ((~r(z, s(elem!1))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(7539,plain,
% 1.97/2.17 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(z, s(z))) | (~r(s(elem!1), s(z)))))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[7538])).
% 1.97/2.17 tff(7540,plain,
% 1.97/2.17 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))))),
% 1.97/2.17 inference(transitivity,[status(thm)],[7539, 7537])).
% 1.97/2.17 tff(7541,plain,
% 1.97/2.17 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))))),
% 1.97/2.17 inference(quant_inst,[status(thm)],[])).
% 1.97/2.17 tff(7542,plain,
% 1.97/2.17 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(z, s(z))) | (~r(s(elem!1), s(z)))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[7541, 7540])).
% 1.97/2.17 tff(7543,plain,
% 1.97/2.17 (~r(z, s(elem!1))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7542, 124, 2265, 2626])).
% 1.97/2.17 tff(7544,plain,
% 1.97/2.17 (b(z, s(elem!1))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[275, 7543])).
% 1.97/2.17 tff(7545,plain,
% 1.97/2.17 (~b(s(z), s(elem!1))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[6801, 306, 1199, 7544, 247])).
% 1.97/2.17 tff(7546,plain,
% 1.97/2.17 ((s(z) = s(elem!1)) | r(s(z), s(elem!1))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[4047, 43, 7545])).
% 1.97/2.17 tff(7547,plain,
% 1.97/2.17 (r(s(z), s(elem!1))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7546, 7418])).
% 1.97/2.17 tff(7548,plain,
% 1.97/2.17 (~r(s(z), elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[6096, 2265, 374])).
% 1.97/2.17 tff(7549,plain,
% 1.97/2.17 (b(s(z), elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[1500, 43, 7548, 3094])).
% 1.97/2.17 tff(7550,plain,
% 1.97/2.17 (~r(elem!1, s(z))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[385, 2265, 374])).
% 1.97/2.17 tff(7551,plain,
% 1.97/2.17 (b(elem!1, s(z))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[96, 43, 7550, 5331])).
% 1.97/2.17 tff(7552,plain,
% 1.97/2.17 ((s(s(s(z))) = s(elem!1)) <=> (s(elem!1) = s(s(s(z))))),
% 1.97/2.17 inference(commutativity,[status(thm)],[])).
% 1.97/2.17 tff(7553,plain,
% 1.97/2.17 (s(elem!1) = s(s(s(z)))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[4121, 7552])).
% 1.97/2.17 tff(7554,assumption,(~(s(elem!1) = s(s(s(z))))), introduced(assumption)).
% 1.97/2.17 tff(7555,plain,
% 1.97/2.17 ($false),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7554, 7553])).
% 1.97/2.17 tff(7556,plain,((~(s(s(s(z))) = s(elem!1))) | (s(elem!1) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.17 tff(7557,plain,
% 1.97/2.17 (~(s(s(s(z))) = s(elem!1))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7556, 4282])).
% 1.97/2.17 tff(7558,plain,
% 1.97/2.17 (~b(s(s(s(z))), z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[6790, 7557, 247, 1199, 7544, 2626])).
% 1.97/2.17 tff(7559,plain,
% 1.97/2.17 (r(s(s(s(z))), z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[2197, 7558])).
% 1.97/2.17 tff(7560,plain,
% 1.97/2.17 (~r(s(s(s(z))), elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[6831, 7559, 374])).
% 1.97/2.17 tff(7561,plain,
% 1.97/2.17 (b(s(s(s(z))), elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[1489, 7560, 1444])).
% 1.97/2.17 tff(7562,plain,
% 1.97/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(7563,plain,
% 1.97/2.17 (((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(7564,plain,
% 1.97/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1))))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[7563])).
% 1.97/2.17 tff(7565,plain,
% 1.97/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.97/2.17 inference(transitivity,[status(thm)],[7564, 7562])).
% 1.97/2.17 tff(7566,plain,
% 1.97/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 1.97/2.17 inference(quant_inst,[status(thm)],[])).
% 1.97/2.17 tff(7567,plain,
% 1.97/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[7566, 7565])).
% 1.97/2.17 tff(7568,plain,
% 1.97/2.17 (~b(s(s(s(z))), s(z))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7567, 306, 2831, 7561, 4346])).
% 1.97/2.17 tff(7569,plain,
% 1.97/2.17 (r(s(s(s(z))), s(z))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[113, 7568])).
% 1.97/2.17 tff(7570,plain,
% 1.97/2.17 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(7571,plain,
% 1.97/2.17 (((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z))) <=> ((~r(s(s(s(z))), z)) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(7572,plain,
% 1.97/2.17 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z)))))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[7571])).
% 1.97/2.17 tff(7573,plain,
% 1.97/2.17 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))))),
% 1.97/2.17 inference(transitivity,[status(thm)],[7572, 7570])).
% 1.97/2.17 tff(7574,plain,
% 1.97/2.17 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))),
% 1.97/2.17 inference(quant_inst,[status(thm)],[])).
% 1.97/2.17 tff(7575,plain,
% 1.97/2.17 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z)))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[7574, 7573])).
% 1.97/2.17 tff(7576,plain,
% 1.97/2.17 ($false),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7575, 124, 7569, 2265, 7559])).
% 1.97/2.17 tff(7577,plain,((~(s(s(elem!1)) = elem!1)) | (~r(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~r(z, elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~r(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.17 tff(7578,plain,
% 1.97/2.17 (~(s(s(elem!1)) = elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7577, 2265, 7549, 7551, 374, 247, 1199, 2626])).
% 1.97/2.17 tff(7579,plain,
% 1.97/2.17 (b(s(s(elem!1)), elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[47, 7578, 6])).
% 1.97/2.17 tff(7580,plain,
% 1.97/2.17 (~b(s(s(elem!1)), s(z))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[4380, 7579, 7551, 7549])).
% 1.97/2.17 tff(7581,plain,
% 1.97/2.17 (r(s(s(elem!1)), s(z))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[3989, 7580])).
% 1.97/2.17 tff(7582,plain,
% 1.97/2.17 (~(s(elem!1) = elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[180, 7578])).
% 1.97/2.17 tff(7583,plain,
% 1.97/2.17 (~(s(s(elem!1)) = s(elem!1))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[195, 7582])).
% 1.97/2.17 tff(7584,plain,
% 1.97/2.17 (r(s(s(elem!1)), s(elem!1))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[994, 7583, 7093])).
% 1.97/2.17 tff(7585,plain,
% 1.97/2.17 ($false),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7432, 124, 7584, 7581, 7547])).
% 1.97/2.17 tff(7586,plain,((~r(z, s(z))) | b(s(s(elem!1)), s(elem!1)) | r(s(s(elem!1)), elem!1) | (~r(z, elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~r(s(elem!1), s(z))) | (s(elem!1) = s(z)) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.17 tff(7587,plain,
% 1.97/2.17 (~r(z, s(z))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7586, 247, 6, 374, 7093, 1199, 7096, 2249, 7106])).
% 1.97/2.17 tff(7588,plain,
% 1.97/2.17 (b(z, s(z))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[2263, 7587])).
% 1.97/2.17 tff(7589,plain,
% 1.97/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(7590,plain,
% 1.97/2.17 (((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1)))) <=> ((~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(7591,plain,
% 1.97/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(elem!1)))))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[7590])).
% 1.97/2.17 tff(7592,plain,
% 1.97/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))),
% 1.97/2.17 inference(transitivity,[status(thm)],[7591, 7589])).
% 1.97/2.17 tff(7593,plain,
% 1.97/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))),
% 1.97/2.17 inference(quant_inst,[status(thm)],[])).
% 1.97/2.17 tff(7594,plain,
% 1.97/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(elem!1)))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[7593, 7592])).
% 1.97/2.17 tff(7595,plain,
% 1.97/2.17 (~b(s(z), s(elem!1))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7594, 306, 1199, 247, 7588])).
% 1.97/2.17 tff(7596,plain,
% 1.97/2.17 ((s(z) = s(elem!1)) | r(s(z), s(elem!1))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[4047, 43, 7595])).
% 1.97/2.17 tff(7597,plain,
% 1.97/2.17 (r(s(z), s(elem!1))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7596, 7418])).
% 1.97/2.17 tff(7598,plain,
% 1.97/2.17 (~(s(s(elem!1)) = s(elem!1))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[195, 7536])).
% 1.97/2.17 tff(7599,plain,
% 1.97/2.17 (r(s(s(elem!1)), s(elem!1))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[994, 7598, 7093])).
% 1.97/2.17 tff(7600,assumption,(r(s(z), s(elem!1))), introduced(assumption)).
% 1.97/2.17 tff(7601,plain,
% 1.97/2.17 (~r(s(s(elem!1)), s(z))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7432, 124, 244, 7600])).
% 1.97/2.17 tff(7602,plain,
% 1.97/2.17 (b(s(s(elem!1)), s(z))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[3989, 7601])).
% 1.97/2.17 tff(7603,plain,
% 1.97/2.17 (~r(s(z), s(s(elem!1)))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[6725, 124, 244, 7600])).
% 1.97/2.17 tff(7604,plain,
% 1.97/2.17 (b(s(z), s(s(elem!1)))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[3997, 43, 79, 7603])).
% 1.97/2.17 tff(7605,plain,
% 1.97/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(7606,plain,
% 1.97/2.17 (((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(7607,plain,
% 1.97/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z)))))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[7606])).
% 1.97/2.17 tff(7608,plain,
% 1.97/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))))),
% 1.97/2.17 inference(transitivity,[status(thm)],[7607, 7605])).
% 1.97/2.17 tff(7609,plain,
% 1.97/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))),
% 1.97/2.17 inference(quant_inst,[status(thm)],[])).
% 1.97/2.17 tff(7610,plain,
% 1.97/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z)))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[7609, 7608])).
% 1.97/2.17 tff(7611,plain,
% 1.97/2.17 (~b(s(s(elem!1)), elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7610, 306, 7604, 4346, 7602])).
% 1.97/2.17 tff(7612,plain,
% 1.97/2.17 (s(s(elem!1)) = elem!1),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[47, 7611, 6])).
% 1.97/2.17 tff(7613,plain,
% 1.97/2.17 (b(s(z), s(s(elem!1))) <=> b(s(z), elem!1)),
% 1.97/2.17 inference(monotonicity,[status(thm)],[7612])).
% 1.97/2.17 tff(7614,plain,
% 1.97/2.17 (b(s(z), elem!1) <=> b(s(z), s(s(elem!1)))),
% 1.97/2.17 inference(symmetry,[status(thm)],[7613])).
% 1.97/2.17 tff(7615,plain,
% 1.97/2.17 ((~b(s(z), elem!1)) <=> (~b(s(z), s(s(elem!1))))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[7614])).
% 1.97/2.17 tff(7616,plain,
% 1.97/2.17 (~b(s(z), s(s(elem!1)))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[2715, 7615])).
% 1.97/2.17 tff(7617,plain,
% 1.97/2.17 ($false),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7604, 7616])).
% 1.97/2.17 tff(7618,plain,((~r(s(s(elem!1)), s(elem!1))) | b(s(z), elem!1) | r(s(s(elem!1)), elem!1) | (~b(elem!1, s(z))) | (~r(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.17 tff(7619,plain,
% 1.97/2.17 (b(s(z), elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7618, 7599, 6, 7534, 7597])).
% 1.97/2.17 tff(7620,plain,
% 1.97/2.17 (r(elem!1, s(elem!1))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7449, 7619, 6, 7093, 2249, 7536, 808])).
% 1.97/2.17 tff(7621,plain,
% 1.97/2.17 (~r(z, s(elem!1))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[5668, 7620, 374])).
% 1.97/2.17 tff(7622,plain,
% 1.97/2.17 (b(z, s(elem!1))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[275, 7621])).
% 1.97/2.17 tff(7623,plain,
% 1.97/2.17 (~r(s(s(elem!1)), s(z))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7432, 124, 7599, 7597])).
% 1.97/2.17 tff(7624,plain,
% 1.97/2.17 (b(s(s(elem!1)), s(z))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[3989, 7623])).
% 1.97/2.17 tff(7625,plain,
% 1.97/2.17 (~b(s(s(elem!1)), elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[4380, 7624, 7534, 7619])).
% 1.97/2.17 tff(7626,plain,
% 1.97/2.17 (s(s(elem!1)) = elem!1),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[47, 7625, 6])).
% 1.97/2.17 tff(7627,plain,
% 1.97/2.17 (~(s(elem!1) = s(s(s(z))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[2356, 7626])).
% 1.97/2.17 tff(7628,plain,
% 1.97/2.17 (~(s(s(s(z))) = s(elem!1))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7556, 7627])).
% 1.97/2.17 tff(7629,plain,
% 1.97/2.17 (~b(s(s(s(z))), z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[6790, 7628, 247, 1199, 7622, 7096])).
% 1.97/2.17 tff(7630,plain,
% 1.97/2.17 (r(s(s(s(z))), z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[2197, 7629])).
% 1.97/2.17 tff(7631,plain,
% 1.97/2.17 (~r(s(s(s(z))), elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[6831, 7630, 374])).
% 1.97/2.17 tff(7632,plain,
% 1.97/2.17 (elem!1 = s(s(elem!1))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[1174, 7626])).
% 1.97/2.17 tff(7633,plain,
% 1.97/2.17 (s(s(s(elem!1))) = s(elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[1168, 7632])).
% 1.97/2.17 tff(7634,plain,
% 1.97/2.17 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[7633])).
% 1.97/2.17 tff(7635,plain,
% 1.97/2.17 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 1.97/2.17 inference(symmetry,[status(thm)],[7634])).
% 1.97/2.17 tff(7636,plain,
% 1.97/2.17 (elem!1 = s(s(elem!1))),
% 1.97/2.17 inference(symmetry,[status(thm)],[7626])).
% 1.97/2.17 tff(7637,plain,
% 1.97/2.17 (elem!1 = s(s(s(s(elem!1))))),
% 1.97/2.17 inference(transitivity,[status(thm)],[7636, 7635])).
% 1.97/2.17 tff(7638,plain,
% 1.97/2.17 (~(s(s(s(z))) = elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[1443, 7637])).
% 1.97/2.17 tff(7639,plain,
% 1.97/2.17 (b(s(s(s(z))), elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[1489, 7638, 7631])).
% 1.97/2.17 tff(7640,plain,
% 1.97/2.17 (b(s(elem!1), elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[813, 7536, 808])).
% 1.97/2.17 tff(7641,plain,
% 1.97/2.17 (~b(s(s(s(z))), s(elem!1))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[5607, 306, 7640, 7619, 7639, 7534])).
% 1.97/2.17 tff(7642,plain,
% 1.97/2.17 (r(s(s(s(z))), s(elem!1))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[4132, 43, 7628, 7641])).
% 1.97/2.17 tff(7643,plain,
% 1.97/2.17 (~b(s(s(s(z))), s(z))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7567, 306, 7619, 7639, 7534])).
% 1.97/2.17 tff(7644,plain,
% 1.97/2.17 (r(s(s(s(z))), s(z))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[113, 7643])).
% 1.97/2.17 tff(7645,plain,
% 1.97/2.17 ($false),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[5600, 124, 7644, 7096, 7642])).
% 1.97/2.17 tff(7646,plain,(r(elem!1, s(z)) | (~r(z, elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | r(s(s(elem!1)), elem!1) | b(s(s(elem!1)), s(elem!1)) | (s(elem!1) = s(z)) | r(s(elem!1), elem!1) | b(s(elem!1), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.17 tff(7647,plain,
% 1.97/2.17 (r(elem!1, s(z))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7646, 247, 374, 7532, 6, 7093, 2249, 808, 2609])).
% 1.97/2.17 tff(7648,plain,
% 1.97/2.17 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(7649,plain,
% 1.97/2.17 (((~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(7650,plain,
% 1.97/2.17 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z)))))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[7649])).
% 1.97/2.17 tff(7651,plain,
% 1.97/2.17 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))))),
% 1.97/2.17 inference(transitivity,[status(thm)],[7650, 7648])).
% 1.97/2.17 tff(7652,plain,
% 1.97/2.17 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1))))),
% 1.97/2.17 inference(quant_inst,[status(thm)],[])).
% 1.97/2.17 tff(7653,plain,
% 1.97/2.17 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z)))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[7652, 7651])).
% 1.97/2.17 tff(7654,plain,
% 1.97/2.17 (~r(elem!1, s(elem!1))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7653, 124, 7647, 7096])).
% 1.97/2.17 tff(7655,plain,
% 1.97/2.17 (~r(z, s(z))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7586, 247, 6, 374, 7093, 7532, 7096, 2249, 7106])).
% 1.97/2.17 tff(7656,plain,
% 1.97/2.17 (b(z, s(z))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[2263, 7655])).
% 1.97/2.17 tff(7657,plain,
% 1.97/2.17 (~b(s(z), s(elem!1))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7594, 306, 7532, 247, 7656])).
% 1.97/2.17 tff(7658,plain,
% 1.97/2.17 ((s(z) = s(elem!1)) | r(s(z), s(elem!1))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[4047, 43, 7657])).
% 1.97/2.17 tff(7659,plain,
% 1.97/2.17 (r(s(z), s(elem!1))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7658, 7418])).
% 1.97/2.17 tff(7660,plain,
% 1.97/2.17 (~r(s(s(elem!1)), s(z))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7432, 124, 7429, 7600])).
% 1.97/2.17 tff(7661,plain,
% 1.97/2.17 (b(s(s(elem!1)), s(z))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[3989, 7660])).
% 1.97/2.17 tff(7662,plain,
% 1.97/2.17 (~r(s(z), s(s(elem!1)))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[6725, 124, 7429, 7600])).
% 1.97/2.17 tff(7663,plain,
% 1.97/2.17 (b(s(z), s(s(elem!1)))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[3997, 43, 79, 7662])).
% 1.97/2.17 tff(7664,plain,
% 1.97/2.17 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7090, 7440, 2170, 808])).
% 1.97/2.17 tff(7665,plain,
% 1.97/2.17 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[143, 7440])).
% 1.97/2.17 tff(7666,plain,
% 1.97/2.17 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[659, 7664, 7429])).
% 1.97/2.17 tff(7667,plain,
% 1.97/2.17 (b(s(s(s(elem!1))), s(elem!1))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[664, 7666, 7665])).
% 1.97/2.18 tff(7668,plain,
% 1.97/2.18 (~r(z, s(s(s(elem!1))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[950, 437, 653])).
% 1.97/2.18 tff(7669,plain,
% 1.97/2.18 (b(z, s(s(s(elem!1))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[585, 7668])).
% 1.97/2.18 tff(7670,plain,
% 1.97/2.18 ($false),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[826, 7669, 6767, 815, 816, 759])).
% 1.97/2.18 tff(7671,plain,((~r(z, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.18 tff(7672,plain,
% 1.97/2.18 (~r(z, s(s(elem!1)))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[7671, 7667, 2323, 7419, 7664, 7429])).
% 1.97/2.18 tff(7673,plain,
% 1.97/2.18 (b(z, s(s(elem!1)))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[460, 7672])).
% 1.97/2.18 tff(7674,plain,
% 1.97/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(7675,plain,
% 1.97/2.18 (((~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(7676,plain,
% 1.97/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z)))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[7675])).
% 1.97/2.18 tff(7677,plain,
% 1.97/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))))),
% 1.97/2.18 inference(transitivity,[status(thm)],[7676, 7674])).
% 1.97/2.18 tff(7678,plain,
% 1.97/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))),
% 1.97/2.18 inference(quant_inst,[status(thm)],[])).
% 1.97/2.18 tff(7679,plain,
% 1.97/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z)))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[7678, 7677])).
% 1.97/2.18 tff(7680,plain,
% 1.97/2.18 ($false),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[7679, 306, 7441, 7673, 7663, 7661, 485])).
% 1.97/2.18 tff(7681,plain,((s(elem!1) = elem!1) | (~b(z, s(z))) | (~r(s(z), s(elem!1))) | (z = elem!1) | r(s(elem!1), elem!1) | r(s(s(elem!1)), elem!1) | b(s(s(elem!1)), s(elem!1)) | r(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.18 tff(7682,plain,
% 1.97/2.18 (s(elem!1) = elem!1),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[7681, 7656, 7659, 2252, 808, 6, 7093, 7654])).
% 1.97/2.18 tff(7683,plain,
% 1.97/2.18 (r(s(elem!1), z) <=> r(elem!1, z)),
% 1.97/2.18 inference(monotonicity,[status(thm)],[7682])).
% 1.97/2.18 tff(7684,plain,
% 1.97/2.18 (r(elem!1, z) <=> r(s(elem!1), z)),
% 1.97/2.18 inference(symmetry,[status(thm)],[7683])).
% 1.97/2.18 tff(7685,plain,
% 1.97/2.18 (r(s(elem!1), z)),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[2254, 7684])).
% 1.97/2.18 tff(7686,plain,
% 1.97/2.18 ($false),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[7531, 7685])).
% 1.97/2.18 tff(7687,plain,((~b(s(z), z)) | r(s(elem!1), elem!1) | r(s(s(elem!1)), elem!1) | b(s(s(elem!1)), s(elem!1)) | (~r(z, elem!1)) | (s(elem!1) = s(z)) | b(s(elem!1), s(z)) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.18 tff(7688,plain,
% 1.97/2.18 (~b(s(z), z)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[7687, 2609, 6, 7093, 374, 2249, 808, 2])).
% 1.97/2.18 tff(7689,plain,
% 1.97/2.18 (r(s(z), z)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[221, 7688])).
% 1.97/2.18 tff(7690,plain,
% 1.97/2.18 (~(s(elem!1) = elem!1)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[2641, 7689, 2609, 2254])).
% 1.97/2.18 tff(7691,plain,
% 1.97/2.18 (b(s(elem!1), elem!1)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[813, 7690, 808])).
% 1.97/2.18 tff(7692,plain,
% 1.97/2.18 (~(s(s(elem!1)) = s(elem!1))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[195, 7690])).
% 1.97/2.18 tff(7693,plain,
% 1.97/2.18 (r(s(s(elem!1)), s(elem!1))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[994, 7692, 7093])).
% 1.97/2.18 tff(7694,plain,
% 1.97/2.18 (~r(s(z), elem!1)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[1049, 7689, 2254])).
% 1.97/2.18 tff(7695,plain,
% 1.97/2.18 (b(s(z), elem!1)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[1500, 43, 7694, 7106])).
% 1.97/2.18 tff(7696,plain,
% 1.97/2.18 (r(elem!1, s(elem!1))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[7449, 7695, 6, 7093, 2249, 7690, 808])).
% 1.97/2.18 tff(7697,plain,
% 1.97/2.18 (~r(z, s(elem!1))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[5668, 7696, 374])).
% 1.97/2.18 tff(7698,plain,
% 1.97/2.18 (b(z, s(elem!1))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[275, 7697])).
% 1.97/2.18 tff(7699,plain,
% 1.97/2.18 (~r(s(elem!1), z)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[2634, 7689, 7096])).
% 1.97/2.18 tff(7700,plain,
% 1.97/2.18 (b(s(elem!1), z)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[2380, 7699])).
% 1.97/2.18 tff(7701,plain,
% 1.97/2.18 (~r(elem!1, s(z))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[2180, 124, 2254, 7689])).
% 1.97/2.18 tff(7702,plain,
% 1.97/2.18 (b(elem!1, s(z))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[96, 43, 7701, 7533])).
% 1.97/2.18 tff(7703,plain,
% 1.97/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(7704,plain,
% 1.97/2.18 (((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1)))) <=> ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(7705,plain,
% 1.97/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1)))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[7704])).
% 1.97/2.18 tff(7706,plain,
% 1.97/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1))))),
% 1.97/2.18 inference(transitivity,[status(thm)],[7705, 7703])).
% 1.97/2.18 tff(7707,plain,
% 1.97/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))),
% 1.97/2.18 inference(quant_inst,[status(thm)],[])).
% 1.97/2.18 tff(7708,plain,
% 1.97/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1)))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[7707, 7706])).
% 1.97/2.18 tff(7709,plain,
% 1.97/2.18 (~b(s(z), s(elem!1))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[7708, 306, 816, 2831, 4346])).
% 1.97/2.18 tff(7710,plain,
% 1.97/2.18 ((s(z) = s(elem!1)) | r(s(z), s(elem!1))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[4047, 43, 7709])).
% 1.97/2.18 tff(7711,plain,
% 1.97/2.18 (r(s(z), s(elem!1))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[7710, 7418])).
% 1.97/2.18 tff(7712,plain,
% 1.97/2.18 (~r(s(s(elem!1)), s(z))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[7432, 124, 244, 7711])).
% 1.97/2.18 tff(7713,plain,
% 1.97/2.18 (b(s(s(elem!1)), s(z))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[3989, 7712])).
% 1.97/2.18 tff(7714,plain,
% 1.97/2.18 (~b(s(s(elem!1)), elem!1)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[4380, 7713, 2831, 4346])).
% 1.97/2.18 tff(7715,plain,
% 1.97/2.18 (s(s(elem!1)) = elem!1),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[47, 7714, 6])).
% 1.97/2.18 tff(7716,plain,
% 1.97/2.18 (~(s(elem!1) = s(s(s(z))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[2356, 7715])).
% 1.97/2.18 tff(7717,plain,
% 1.97/2.18 (b(s(s(s(z))), z)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[2197, 1527])).
% 1.97/2.18 tff(7718,plain,
% 1.97/2.18 (~r(s(elem!1), s(s(s(z))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[5427, 124, 206, 2626])).
% 1.97/2.18 tff(7719,plain,
% 1.97/2.18 (b(s(elem!1), s(s(s(z))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[2367, 43, 7554, 7718])).
% 1.97/2.18 tff(7720,plain,
% 1.97/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(7721,plain,
% 1.97/2.18 (((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z)))))) <=> ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(7722,plain,
% 1.97/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[7721])).
% 1.97/2.18 tff(7723,plain,
% 1.97/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.97/2.18 inference(transitivity,[status(thm)],[7722, 7720])).
% 1.97/2.18 tff(7724,plain,
% 1.97/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))))),
% 1.97/2.18 inference(quant_inst,[status(thm)],[])).
% 1.97/2.18 tff(7725,plain,
% 1.97/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[7724, 7723])).
% 1.97/2.18 tff(7726,plain,
% 1.97/2.18 ($false),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[7725, 306, 1199, 817, 7719, 7717])).
% 1.97/2.18 tff(7727,plain,((~r(s(s(s(z))), s(z))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (s(elem!1) = s(s(s(z)))) | (~r(s(elem!1), s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.18 tff(7728,plain,
% 1.97/2.18 (~r(s(s(s(z))), s(z))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[7727, 7716, 817, 1199, 2626, 204])).
% 1.97/2.18 tff(7729,plain,
% 1.97/2.18 (b(s(s(s(z))), s(z))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[113, 7728])).
% 1.97/2.18 tff(7730,plain,
% 1.97/2.18 (((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(7731,plain,
% 1.97/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[7730])).
% 1.97/2.18 tff(7732,plain,
% 1.97/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.97/2.18 inference(transitivity,[status(thm)],[7731, 7562])).
% 1.97/2.18 tff(7733,plain,
% 1.97/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.97/2.18 inference(quant_inst,[status(thm)],[])).
% 1.97/2.18 tff(7734,plain,
% 1.97/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[7733, 7732])).
% 1.97/2.18 tff(7735,plain,
% 1.97/2.18 (~b(s(s(s(z))), elem!1)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[7734, 306, 7729, 2831, 4346])).
% 1.97/2.18 tff(7736,plain,
% 1.97/2.18 (r(s(s(s(z))), elem!1)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[1489, 7735, 1483])).
% 1.97/2.18 tff(7737,plain,
% 1.97/2.18 (~r(s(s(s(z))), z)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[6831, 7736, 374])).
% 1.97/2.18 tff(7738,plain,
% 1.97/2.18 (b(s(s(s(z))), z)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[2197, 7737])).
% 1.97/2.18 tff(7739,plain,
% 1.97/2.18 (~b(s(elem!1), s(s(s(z))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[7725, 306, 1199, 817, 7738])).
% 1.97/2.18 tff(7740,plain,
% 1.97/2.18 (r(s(elem!1), s(s(s(z))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[2367, 43, 7739, 7716])).
% 1.97/2.18 tff(7741,plain,
% 1.97/2.18 (~(elem!1 = s(s(s(z))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[1534, 7738, 2])).
% 1.97/2.18 tff(7742,plain,
% 1.97/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(7743,plain,
% 1.97/2.18 (((~b(elem!1, s(z))) | (~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(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(7744,plain,
% 1.97/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z)))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[7743])).
% 1.97/2.18 tff(7745,plain,
% 1.97/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))))),
% 1.97/2.18 inference(transitivity,[status(thm)],[7744, 7742])).
% 1.97/2.18 tff(7746,plain,
% 1.97/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))))),
% 1.97/2.18 inference(quant_inst,[status(thm)],[])).
% 1.97/2.18 tff(7747,plain,
% 1.97/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z)))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[7746, 7745])).
% 1.97/2.18 tff(7748,plain,
% 1.97/2.18 (~b(elem!1, s(s(s(z))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[7747, 306, 7729, 2831, 4346])).
% 1.97/2.18 tff(7749,plain,
% 1.97/2.18 (r(elem!1, s(s(s(z))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[131, 43, 7748, 7741])).
% 1.97/2.18 tff(7750,plain,
% 1.97/2.18 (r(s(s(elem!1)), s(elem!1)) <=> r(elem!1, s(elem!1))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[7715])).
% 1.97/2.18 tff(7751,plain,
% 1.97/2.18 (r(elem!1, s(elem!1))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[244, 7750])).
% 1.97/2.18 tff(7752,plain,
% 1.97/2.18 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(7753,plain,
% 1.97/2.18 (((~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(elem!1, s(s(s(z))))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(7754,plain,
% 1.97/2.18 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[7753])).
% 1.97/2.18 tff(7755,plain,
% 1.97/2.18 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.97/2.18 inference(transitivity,[status(thm)],[7754, 7752])).
% 1.97/2.18 tff(7756,plain,
% 1.97/2.18 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(elem!1))))),
% 1.97/2.18 inference(quant_inst,[status(thm)],[])).
% 1.97/2.18 tff(7757,plain,
% 1.97/2.18 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[7756, 7755])).
% 1.97/2.18 tff(7758,plain,
% 1.97/2.18 ($false),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[7757, 124, 7751, 7749, 7740])).
% 1.97/2.18 tff(7759,plain,((~b(elem!1, s(z))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | b(elem!1, z) | (~r(z, elem!1)) | (s(s(s(z))) = elem!1) | (~b(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(elem!1))) | r(s(s(elem!1)), elem!1) | (s(elem!1) = s(z)) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.18 tff(7760,plain,
% 1.97/2.18 (s(s(s(z))) = elem!1),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[7759, 7702, 7689, 2, 374, 7700, 7695, 7096, 7698, 7693, 6, 2249, 7691])).
% 1.97/2.18 tff(7761,plain,
% 1.97/2.18 ((s(s(elem!1)) = s(s(s(z)))) <=> (s(s(elem!1)) = elem!1)),
% 1.97/2.18 inference(monotonicity,[status(thm)],[7760])).
% 1.97/2.18 tff(7762,plain,
% 1.97/2.18 ((s(s(elem!1)) = elem!1) <=> (s(s(elem!1)) = s(s(s(z))))),
% 1.97/2.18 inference(symmetry,[status(thm)],[7761])).
% 1.97/2.18 tff(7763,plain,
% 1.97/2.18 ((s(s(elem!1)) = elem!1) <=> (s(s(s(z))) = s(s(elem!1)))),
% 1.97/2.18 inference(transitivity,[status(thm)],[7762, 7095])).
% 1.97/2.18 tff(7764,plain,
% 1.97/2.18 (~b(s(z), s(elem!1))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[7708, 306, 7691, 7695, 7702])).
% 1.97/2.18 tff(7765,plain,
% 1.97/2.18 ((s(z) = s(elem!1)) | r(s(z), s(elem!1))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[4047, 43, 7764])).
% 1.97/2.18 tff(7766,plain,
% 1.97/2.18 (r(s(z), s(elem!1))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[7765, 7418])).
% 1.97/2.18 tff(7767,plain,
% 1.97/2.18 (~r(s(s(elem!1)), s(z))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[7432, 124, 7693, 7766])).
% 1.97/2.18 tff(7768,plain,
% 1.97/2.18 (b(s(s(elem!1)), s(z))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[3989, 7767])).
% 1.97/2.18 tff(7769,plain,
% 1.97/2.18 (~b(s(s(elem!1)), elem!1)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[4380, 7768, 7702, 7695])).
% 1.97/2.18 tff(7770,plain,
% 1.97/2.18 (s(s(elem!1)) = elem!1),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[47, 7769, 6])).
% 1.97/2.18 tff(7771,plain,
% 1.97/2.18 (s(s(s(z))) = s(s(elem!1))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[7770, 7763])).
% 1.97/2.18 tff(7772,plain,
% 1.97/2.18 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[2974, 7533])).
% 1.97/2.18 tff(7773,plain,
% 1.97/2.18 ($false),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[7772, 7771])).
% 1.97/2.18 tff(7774,plain,(b(s(elem!1), s(z)) | r(s(s(elem!1)), elem!1) | (s(elem!1) = s(z)) | b(elem!1, z) | (~r(z, elem!1)) | b(s(s(elem!1)), s(elem!1)) | r(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.18 tff(7775,plain,
% 1.97/2.18 (r(s(s(elem!1)), elem!1)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[7774, 7093, 2, 2249, 374, 808, 2609])).
% 1.97/2.18 tff(7776,plain,
% 1.97/2.18 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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)))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(7777,plain,
% 1.97/2.18 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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)))))),
% 1.97/2.18 inference(quant_inst,[status(thm)],[])).
% 1.97/2.18 tff(7778,plain,
% 1.97/2.18 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[7777, 7776])).
% 1.97/2.18 tff(7779,plain,
% 1.97/2.18 ($false),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[7778, 124, 1730, 1627, 653])).
% 1.97/2.18 tff(7780,plain,((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.18 tff(7781,plain,
% 1.97/2.18 (~r(s(s(s(elem!1))), elem!1)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[7780, 7775, 653])).
% 1.97/2.18 tff(7782,plain,
% 1.97/2.18 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(7783,plain,
% 1.97/2.19 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))),
% 1.97/2.19 inference(quant_inst,[status(thm)],[])).
% 1.97/2.19 tff(7784,plain,
% 1.97/2.19 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[7783, 7782])).
% 1.97/2.19 tff(7785,plain,
% 1.97/2.19 ($false),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[7784, 124, 246, 1730, 465])).
% 1.97/2.19 tff(7786,plain,((~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.19 tff(7787,plain,
% 1.97/2.19 (~r(s(s(elem!1)), z)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[7786, 246, 1730])).
% 1.97/2.19 tff(7788,plain,
% 1.97/2.19 (b(s(s(elem!1)), z)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[476, 7787])).
% 1.97/2.19 tff(7789,assumption,(~r(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 1.97/2.19 tff(7790,plain,
% 1.97/2.19 (b(s(s(s(elem!1))), elem!1)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[1636, 1526, 7789])).
% 1.97/2.19 tff(7791,plain,
% 1.97/2.19 (b(elem!1, s(s(s(elem!1))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[3284, 1642, 536])).
% 1.97/2.19 tff(7792,plain,
% 1.97/2.19 ($false),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[6138, 7791, 7790, 816, 759])).
% 1.97/2.19 tff(7793,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(s(elem!1)))) | r(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.19 tff(7794,plain,
% 1.97/2.19 (r(elem!1, s(s(s(elem!1))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[7793, 1526, 759, 816, 7789])).
% 1.97/2.19 tff(7795,plain,
% 1.97/2.19 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[5766, 7794, 1730])).
% 1.97/2.19 tff(7796,plain,
% 1.97/2.19 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[891, 7795, 157])).
% 1.97/2.19 tff(7797,plain,
% 1.97/2.19 (~r(s(s(s(elem!1))), z)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[851, 7794, 246])).
% 1.97/2.19 tff(7798,plain,
% 1.97/2.19 (b(s(s(s(elem!1))), z)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[3033, 43, 579, 7797])).
% 1.97/2.19 tff(7799,plain,
% 1.97/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(7800,plain,
% 1.97/2.19 (((~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(7801,plain,
% 1.97/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[7800])).
% 1.97/2.19 tff(7802,plain,
% 1.97/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.97/2.19 inference(transitivity,[status(thm)],[7801, 7799])).
% 1.97/2.19 tff(7803,plain,
% 1.97/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.97/2.19 inference(quant_inst,[status(thm)],[])).
% 1.97/2.19 tff(7804,plain,
% 1.97/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[7803, 7802])).
% 1.97/2.19 tff(7805,plain,
% 1.97/2.19 ($false),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[7804, 306, 6445, 817, 1590, 816, 3968])).
% 1.97/2.19 tff(7806,plain,((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.19 tff(7807,plain,
% 1.97/2.19 (~b(z, s(elem!1))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[7806, 7798, 7796, 816, 7788])).
% 1.97/2.19 tff(7808,plain,
% 1.97/2.19 (r(z, s(elem!1))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[275, 7807])).
% 1.97/2.19 tff(7809,plain,
% 1.97/2.19 (~r(elem!1, s(elem!1))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[265, 7808, 246])).
% 1.97/2.19 tff(7810,plain,
% 1.97/2.19 (b(elem!1, s(elem!1))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[372, 7809, 366])).
% 1.97/2.19 tff(7811,plain,
% 1.97/2.19 ($false),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[6962, 306, 759, 7790, 816, 7810])).
% 1.97/2.19 tff(7812,plain,((s(s(s(elem!1))) = elem!1) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (elem!1 = s(elem!1)) | (~r(elem!1, z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | r(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.19 tff(7813,plain,
% 1.97/2.19 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[7812, 7775, 816, 366, 246, 1526, 232, 7781])).
% 1.97/2.19 tff(7814,plain,
% 1.97/2.19 (r(s(s(elem!1)), s(elem!1))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[994, 7093, 403])).
% 1.97/2.19 tff(7815,plain,
% 1.97/2.19 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[659, 7814, 653])).
% 1.97/2.19 tff(7816,plain,
% 1.97/2.19 ($false),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[664, 7815, 7813, 150])).
% 1.97/2.19 tff(7817,plain,(b(s(s(elem!1)), s(elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (elem!1 = s(elem!1)) | (~r(elem!1, z)) | (s(s(s(elem!1))) = elem!1) | (s(s(elem!1)) = s(elem!1)) | b(elem!1, z) | (s(elem!1) = s(z)) | (~r(z, elem!1)) | r(s(elem!1), elem!1) | b(s(elem!1), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.19 tff(7818,plain,
% 1.97/2.19 (b(s(s(elem!1)), s(elem!1))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[7817, 7092, 7091, 5591, 5613, 5612, 5611, 5593, 2, 3099, 374, 808, 5592])).
% 1.97/2.19 tff(7819,plain,
% 1.97/2.19 (r(z, s(elem!1)) <=> r(z, s(s(s(z))))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[5617])).
% 1.97/2.19 tff(7820,plain,
% 1.97/2.19 (r(z, s(s(s(z)))) <=> r(z, s(elem!1))),
% 1.97/2.19 inference(symmetry,[status(thm)],[7819])).
% 1.97/2.19 tff(7821,plain,
% 1.97/2.19 ((~r(z, s(s(s(z))))) <=> (~r(z, s(elem!1)))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[7820])).
% 1.97/2.19 tff(7822,plain,
% 1.97/2.19 (s(s(z)) = elem!1),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[5384, 5617])).
% 1.97/2.19 tff(7823,plain,
% 1.97/2.19 ((s(s(z)) = s(s(s(s(s(s(z))))))) <=> (elem!1 = s(s(s(s(s(s(z)))))))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[7822])).
% 1.97/2.19 tff(7824,plain,
% 1.97/2.19 ((s(s(z)) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = elem!1)),
% 1.97/2.19 inference(transitivity,[status(thm)],[7823, 3891])).
% 1.97/2.19 tff(7825,plain,
% 1.97/2.19 ((~(s(s(z)) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(s(s(s(s(z)))))) = elem!1))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[7824])).
% 1.97/2.19 tff(7826,plain,
% 1.97/2.19 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[2826, 7825])).
% 1.97/2.19 tff(7827,plain,
% 1.97/2.19 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[1144, 7826, 5378])).
% 1.97/2.19 tff(7828,plain,
% 1.97/2.19 (~r(z, s(s(s(s(s(s(z)))))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[5441, 124, 374, 7827])).
% 1.97/2.19 tff(7829,plain,
% 1.97/2.19 ((z = s(s(s(s(s(s(z))))))) | b(z, s(s(s(s(s(s(z)))))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[5445, 43, 7828])).
% 1.97/2.19 tff(7830,plain,
% 1.97/2.19 (b(z, s(s(s(s(s(s(z)))))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[7829, 5435])).
% 1.97/2.19 tff(7831,plain,
% 1.97/2.19 (~r(s(s(s(s(s(s(z)))))), z)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[5452, 7827, 374])).
% 1.97/2.19 tff(7832,plain,
% 1.97/2.19 (b(s(s(s(s(s(s(z)))))), z)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[4232, 7831])).
% 1.97/2.19 tff(7833,plain,
% 1.97/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(7834,plain,
% 1.97/2.19 (((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(z)))) <=> ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(7835,plain,
% 1.97/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z))))))))))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[7834])).
% 1.97/2.19 tff(7836,plain,
% 1.97/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 1.97/2.19 inference(transitivity,[status(thm)],[7835, 7833])).
% 1.97/2.19 tff(7837,plain,
% 1.97/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(z))))),
% 1.97/2.19 inference(quant_inst,[status(thm)],[])).
% 1.97/2.19 tff(7838,plain,
% 1.97/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z))))))))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[7837, 7836])).
% 1.97/2.19 tff(7839,plain,
% 1.97/2.19 (~b(z, s(z))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[7838, 306, 7832, 5558, 7830])).
% 1.97/2.19 tff(7840,plain,
% 1.97/2.19 (r(z, s(z))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[2263, 7839])).
% 1.97/2.19 tff(7841,plain,
% 1.97/2.19 (~r(z, s(s(s(z))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[5572, 124, 206, 7840])).
% 1.97/2.19 tff(7842,plain,
% 1.97/2.19 (~r(z, s(elem!1))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[7841, 7821])).
% 1.97/2.19 tff(7843,plain,
% 1.97/2.19 (b(z, s(elem!1))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[275, 7842])).
% 1.97/2.19 tff(7844,plain,
% 1.97/2.19 (~r(s(elem!1), z)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[2634, 5594, 204])).
% 1.97/2.19 tff(7845,plain,
% 1.97/2.19 (b(s(elem!1), z)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[2380, 7844])).
% 1.97/2.19 tff(7846,plain,
% 1.97/2.19 (~b(z, s(s(elem!1)))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[1218, 7818, 7845, 7843])).
% 1.97/2.19 tff(7847,plain,
% 1.97/2.19 (r(z, s(s(elem!1)))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[460, 7846])).
% 1.97/2.19 tff(7848,plain,
% 1.97/2.19 (~r(s(s(elem!1)), elem!1)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[5837, 7847, 374])).
% 1.97/2.19 tff(7849,plain,
% 1.97/2.19 (b(s(s(elem!1)), elem!1)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[47, 7848, 5618])).
% 1.97/2.19 tff(7850,plain,
% 1.97/2.19 (~(elem!1 = s(s(elem!1)))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[186, 5618])).
% 1.97/2.19 tff(7851,plain,
% 1.97/2.19 (~r(elem!1, s(s(elem!1)))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[1194, 7847, 374])).
% 1.97/2.19 tff(7852,plain,
% 1.97/2.19 (b(elem!1, s(s(elem!1)))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[516, 7851, 7850])).
% 1.97/2.19 tff(7853,plain,
% 1.97/2.19 ($false),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[1024, 7852, 7849, 5591, 7818])).
% 1.97/2.19 tff(7854,plain,(b(s(s(s(s(s(s(z)))))), s(s(s(z)))) | (~r(z, elem!1)) | b(elem!1, z) | r(s(elem!1), elem!1) | (~r(s(s(s(z))), s(z))) | (z = elem!1) | (~r(s(z), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~r(s(z), z)) | (~b(s(s(s(z))), z)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.19 tff(7855,plain,
% 1.97/2.19 ($false),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[7854, 5484, 5463, 2, 808, 206, 2170, 1034, 2831, 1967, 4346, 374, 1531, 87])).
% 1.97/2.19 tff(7856,plain,(r(s(elem!1), elem!1) | b(elem!1, z) | (~r(s(s(s(z))), s(z))) | (z = elem!1) | (~r(s(z), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~r(z, elem!1)) | (~b(s(s(s(z))), z)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.19 tff(7857,plain,
% 1.97/2.19 (r(s(elem!1), elem!1)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[7856, 2831, 206, 2170, 1034, 2, 1967, 4346, 374, 1531, 87])).
% 1.97/2.19 tff(7858,plain,
% 1.97/2.19 (r(s(elem!1), elem!1) <=> r(s(s(s(z))), elem!1)),
% 1.97/2.19 inference(monotonicity,[status(thm)],[2349])).
% 1.97/2.19 tff(7859,plain,
% 1.97/2.19 (r(s(s(s(z))), elem!1) <=> r(s(elem!1), elem!1)),
% 1.97/2.19 inference(symmetry,[status(thm)],[7858])).
% 1.97/2.19 tff(7860,plain,
% 1.97/2.19 ((~r(s(s(s(z))), elem!1)) <=> (~r(s(elem!1), elem!1))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[7859])).
% 1.97/2.19 tff(7861,plain,
% 1.97/2.19 (~r(s(elem!1), elem!1)),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[1484, 7860])).
% 1.97/2.19 tff(7862,plain,
% 1.97/2.19 ($false),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[802, 7861])).
% 1.97/2.19 tff(7863,plain,((~(s(elem!1) = s(s(s(z))))) | (~r(s(elem!1), elem!1)) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.19 tff(7864,plain,
% 1.97/2.19 (~(s(elem!1) = s(s(s(z))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[7863, 7857, 1484])).
% 1.97/2.19 tff(7865,plain,
% 1.97/2.19 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(7866,plain,
% 1.97/2.19 (((~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1)))) <=> ((~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(7867,plain,
% 1.97/2.19 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1))))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[7866])).
% 1.97/2.19 tff(7868,plain,
% 1.97/2.19 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)))),
% 1.97/2.19 inference(transitivity,[status(thm)],[7867, 7865])).
% 1.97/2.19 tff(7869,plain,
% 1.97/2.19 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))))),
% 1.97/2.19 inference(quant_inst,[status(thm)],[])).
% 1.97/2.19 tff(7870,plain,
% 1.97/2.19 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[7869, 7868])).
% 1.97/2.19 tff(7871,plain,
% 1.97/2.19 (~r(z, s(elem!1))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[7870, 124, 374, 7857])).
% 1.97/2.19 tff(7872,plain,
% 1.97/2.19 (b(z, s(elem!1))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[275, 7871])).
% 1.97/2.19 tff(7873,plain,
% 1.97/2.19 (~r(s(elem!1), z)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[416, 7857, 374])).
% 1.97/2.19 tff(7874,plain,
% 1.97/2.19 (b(s(elem!1), z)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[2380, 7873])).
% 1.97/2.19 tff(7875,plain,
% 1.97/2.19 (~b(s(elem!1), s(s(s(z))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[7725, 306, 7874, 7872, 1531])).
% 1.97/2.19 tff(7876,plain,
% 1.97/2.19 (r(s(elem!1), s(s(s(z))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[2367, 43, 7875, 7864])).
% 1.97/2.19 tff(7877,plain,
% 1.97/2.19 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(elem!1))))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(7878,plain,
% 1.97/2.19 (((~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(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(elem!1))))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(7879,plain,
% 1.97/2.19 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(elem!1)))))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[7878])).
% 1.97/2.19 tff(7880,plain,
% 1.97/2.19 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(elem!1))))),
% 1.97/2.19 inference(transitivity,[status(thm)],[7879, 7877])).
% 1.97/2.19 tff(7881,plain,
% 1.97/2.19 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(elem!1))))),
% 1.97/2.19 inference(quant_inst,[status(thm)],[])).
% 1.97/2.19 tff(7882,plain,
% 1.97/2.19 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(elem!1)))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[7881, 7880])).
% 1.97/2.19 tff(7883,plain,
% 1.97/2.19 (~r(s(z), s(elem!1))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[7882, 124, 1034, 7876])).
% 1.97/2.19 tff(7884,plain,
% 1.97/2.19 ((s(z) = s(elem!1)) | b(s(z), s(elem!1))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[4047, 43, 7883])).
% 1.97/2.19 tff(7885,plain,
% 1.97/2.19 (b(s(z), s(elem!1))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[7884, 4040])).
% 1.97/2.19 tff(7886,plain,
% 1.97/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(z, s(z))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(z, s(z))) | (~b(s(z), s(elem!1))))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(7887,plain,
% 1.97/2.19 (((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(z)))) <=> ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(z, s(z))) | (~b(s(z), s(elem!1))))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(7888,plain,
% 1.97/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(z, s(z))) | (~b(s(z), s(elem!1)))))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[7887])).
% 1.97/2.19 tff(7889,plain,
% 1.97/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(z, s(z))) | (~b(s(z), s(elem!1))))),
% 1.97/2.19 inference(transitivity,[status(thm)],[7888, 7886])).
% 1.97/2.19 tff(7890,plain,
% 1.97/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(z))))),
% 1.97/2.19 inference(quant_inst,[status(thm)],[])).
% 1.97/2.19 tff(7891,plain,
% 1.97/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(z, s(z))) | (~b(s(z), s(elem!1)))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[7890, 7889])).
% 1.97/2.19 tff(7892,plain,
% 1.97/2.19 (~b(z, s(z))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[7891, 306, 7874, 7872, 7885])).
% 1.97/2.19 tff(7893,plain,
% 1.97/2.19 (r(z, s(z))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[2263, 7892])).
% 1.97/2.19 tff(7894,plain,
% 1.97/2.19 (~r(z, s(s(s(z))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[5572, 124, 206, 7893])).
% 1.97/2.19 tff(7895,plain,
% 1.97/2.19 (b(z, s(s(s(z))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[2415, 43, 7894, 2405])).
% 1.97/2.19 tff(7896,assumption,(r(s(elem!1), s(s(s(z))))), introduced(assumption)).
% 1.97/2.19 tff(7897,plain,
% 1.97/2.19 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.97/2.20 inference(rewrite,[status(thm)],[])).
% 1.97/2.20 tff(7898,plain,
% 1.97/2.20 (((~r(elem!1, s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), elem!1))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.97/2.20 inference(rewrite,[status(thm)],[])).
% 1.97/2.20 tff(7899,plain,
% 1.97/2.20 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))))),
% 1.97/2.20 inference(monotonicity,[status(thm)],[7898])).
% 1.97/2.20 tff(7900,plain,
% 1.97/2.20 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.97/2.20 inference(transitivity,[status(thm)],[7899, 7897])).
% 1.97/2.20 tff(7901,plain,
% 1.97/2.20 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), elem!1)))),
% 1.97/2.20 inference(quant_inst,[status(thm)],[])).
% 1.97/2.20 tff(7902,plain,
% 1.97/2.20 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))),
% 1.97/2.20 inference(modus_ponens,[status(thm)],[7901, 7900])).
% 1.97/2.20 tff(7903,plain,
% 1.97/2.20 ($false),
% 1.97/2.20 inference(unit_resolution,[status(thm)],[7902, 124, 802, 3313, 7896])).
% 1.97/2.20 tff(7904,plain,((~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.20 tff(7905,plain,
% 1.97/2.20 (~r(elem!1, s(s(s(z))))),
% 1.97/2.20 inference(unit_resolution,[status(thm)],[7904, 7876, 7857])).
% 1.97/2.20 tff(7906,plain,
% 2.04/2.20 (b(elem!1, s(s(s(z))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[2304, 7905, 4939])).
% 2.04/2.20 tff(7907,plain,
% 2.04/2.20 (~b(s(s(z)), elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[5544, 306, 1967, 4346, 1470, 5503])).
% 2.04/2.20 tff(7908,plain,
% 2.04/2.20 ((elem!1 = s(s(z))) <=> (s(s(z)) = elem!1)),
% 2.04/2.20 inference(commutativity,[status(thm)],[])).
% 2.04/2.20 tff(7909,plain,
% 2.04/2.20 (b(s(s(s(s(s(s(z)))))), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[4273])).
% 2.04/2.20 tff(7910,plain,
% 2.04/2.20 (b(elem!1, s(s(s(z)))) <=> b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.04/2.20 inference(symmetry,[status(thm)],[7909])).
% 2.04/2.20 tff(7911,plain,
% 2.04/2.20 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[1470, 7910])).
% 2.04/2.20 tff(7912,plain,
% 2.04/2.20 ($false),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[2885, 7911])).
% 2.04/2.20 tff(7913,plain,((~(s(s(s(s(s(s(z)))))) = elem!1)) | b(s(s(s(s(s(s(z)))))), s(s(s(z)))) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.20 tff(7914,plain,
% 2.04/2.20 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[7913, 2885, 1470])).
% 2.04/2.20 tff(7915,plain,
% 2.04/2.20 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[1144, 7914, 5378])).
% 2.04/2.20 tff(7916,plain,
% 2.04/2.20 (~r(s(s(s(s(s(s(z)))))), z)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[5452, 7915, 374])).
% 2.04/2.20 tff(7917,plain,
% 2.04/2.20 (b(s(s(s(s(s(s(z)))))), z)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[4232, 7916])).
% 2.04/2.20 tff(7918,plain,
% 2.04/2.20 (~r(z, s(elem!1))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[7870, 124, 374, 802])).
% 2.04/2.20 tff(7919,plain,
% 2.04/2.20 (b(z, s(elem!1))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[275, 7918])).
% 2.04/2.20 tff(7920,plain,
% 2.04/2.20 (~r(s(elem!1), z)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[416, 802, 374])).
% 2.04/2.20 tff(7921,plain,
% 2.04/2.20 (b(s(elem!1), z)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[2380, 7920])).
% 2.04/2.20 tff(7922,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(7923,plain,
% 2.04/2.20 (((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1)))) <=> ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(7924,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1)))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[7923])).
% 2.04/2.20 tff(7925,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 2.04/2.20 inference(transitivity,[status(thm)],[7924, 7922])).
% 2.04/2.20 tff(7926,plain,
% 2.04/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 2.04/2.20 inference(quant_inst,[status(thm)],[])).
% 2.04/2.20 tff(7927,plain,
% 2.04/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1)))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[7926, 7925])).
% 2.04/2.20 tff(7928,plain,
% 2.04/2.20 (~b(s(s(s(s(s(s(z)))))), s(elem!1))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[7927, 306, 7921, 7919, 7917])).
% 2.04/2.20 tff(7929,plain,
% 2.04/2.20 (~r(s(s(s(s(s(s(z)))))), s(elem!1))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[3212, 124, 802, 7915])).
% 2.04/2.20 tff(7930,plain,
% 2.04/2.20 ((s(s(s(s(s(s(z)))))) = s(elem!1)) | b(s(s(s(s(s(s(z)))))), s(elem!1))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[3220, 43, 7929])).
% 2.04/2.20 tff(7931,plain,
% 2.04/2.20 (s(s(s(s(s(s(z)))))) = s(elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[7930, 7928])).
% 2.04/2.20 tff(7932,plain,
% 2.04/2.20 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(elem!1))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[7931])).
% 2.04/2.20 tff(7933,plain,
% 2.04/2.20 (s(s(s(s(s(z))))) = elem!1),
% 2.04/2.20 inference(transitivity,[status(thm)],[2823, 7932, 135])).
% 2.04/2.20 tff(7934,plain,
% 2.04/2.20 ((s(s(s(s(s(z))))) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[7933])).
% 2.04/2.20 tff(7935,plain,
% 2.04/2.20 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 2.04/2.20 inference(transitivity,[status(thm)],[7934, 7908])).
% 2.04/2.20 tff(7936,plain,
% 2.04/2.20 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[7935])).
% 2.04/2.20 tff(7937,plain,
% 2.04/2.20 (~(s(s(z)) = elem!1)),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[6464, 7936])).
% 2.04/2.20 tff(7938,plain,
% 2.04/2.20 (~b(s(s(z)), z)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[5582, 5503, 859, 1967, 1470])).
% 2.04/2.20 tff(7939,plain,
% 2.04/2.20 (r(s(s(z)), z)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[2531, 7938])).
% 2.04/2.20 tff(7940,plain,
% 2.04/2.20 (~r(s(s(z)), elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[7379, 124, 246, 7939])).
% 2.04/2.20 tff(7941,plain,
% 2.04/2.20 ($false),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[2545, 7940, 7937, 7907])).
% 2.04/2.20 tff(7942,plain,(b(s(s(s(s(s(s(z)))))), s(s(s(z)))) | (~r(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.20 tff(7943,plain,
% 2.04/2.20 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[7942, 7906, 1967, 4346, 5612, 7895, 2831, 1034, 7857, 374])).
% 2.04/2.20 tff(7944,plain,
% 2.04/2.20 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[5462, 7943, 1531, 374])).
% 2.04/2.20 tff(7945,plain,
% 2.04/2.20 (s(s(s(s(s(s(z)))))) = elem!1),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[1144, 7944, 5378])).
% 2.04/2.20 tff(7946,plain,
% 2.04/2.20 (elem!1 = s(s(s(s(s(s(z))))))),
% 2.04/2.20 inference(symmetry,[status(thm)],[7945])).
% 2.04/2.20 tff(7947,plain,
% 2.04/2.20 (~b(s(s(s(z))), s(elem!1))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[6777, 306, 7874, 7872, 1531])).
% 2.04/2.20 tff(7948,plain,
% 2.04/2.20 (~(s(s(s(z))) = s(elem!1))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[7556, 7864])).
% 2.04/2.20 tff(7949,plain,
% 2.04/2.20 (r(s(s(s(z))), s(elem!1))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[4132, 43, 7948, 7947])).
% 2.04/2.20 tff(7950,plain,
% 2.04/2.20 ((~(s(s(s(z))) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = s(s(s(z)))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[7094])).
% 2.04/2.20 tff(7951,plain,
% 2.04/2.20 (~(s(s(elem!1)) = s(s(s(z))))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[2976, 7950])).
% 2.04/2.20 tff(7952,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(7953,plain,
% 2.04/2.20 (((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(z)))))) <=> ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(7954,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[7953])).
% 2.04/2.20 tff(7955,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.04/2.20 inference(transitivity,[status(thm)],[7954, 7952])).
% 2.04/2.20 tff(7956,plain,
% 2.04/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.04/2.20 inference(quant_inst,[status(thm)],[])).
% 2.04/2.20 tff(7957,plain,
% 2.04/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[7956, 7955])).
% 2.04/2.20 tff(7958,plain,
% 2.04/2.20 ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[7957, 306])).
% 2.04/2.20 tff(7959,plain,
% 2.04/2.20 (~b(s(s(elem!1)), s(s(s(z))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[7958, 30, 2831, 1967, 4346])).
% 2.04/2.20 tff(7960,plain,
% 2.04/2.20 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(z)))) | b(s(s(elem!1)), s(s(s(z)))) | r(s(s(elem!1)), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(z)))) | b(s(s(elem!1)), s(s(s(z)))) | r(s(s(elem!1)), s(s(s(z)))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(7961,plain,
% 2.04/2.20 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(z)))) | b(s(s(elem!1)), s(s(s(z)))) | r(s(s(elem!1)), s(s(s(z)))))),
% 2.04/2.20 inference(quant_inst,[status(thm)],[])).
% 2.04/2.20 tff(7962,plain,
% 2.04/2.20 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(z)))) | b(s(s(elem!1)), s(s(s(z)))) | r(s(s(elem!1)), s(s(s(z))))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[7961, 7960])).
% 2.04/2.20 tff(7963,plain,
% 2.04/2.20 (r(s(s(elem!1)), s(s(s(z))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[7962, 43, 7959, 7951])).
% 2.04/2.20 tff(7964,plain,
% 2.04/2.20 (~b(s(s(elem!1)), s(z))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[4380, 30, 4346, 2831])).
% 2.04/2.20 tff(7965,plain,
% 2.04/2.20 (r(s(s(elem!1)), s(z))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[3989, 7964])).
% 2.04/2.20 tff(7966,plain,
% 2.04/2.20 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(7967,plain,
% 2.04/2.20 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.04/2.20 inference(quant_inst,[status(thm)],[])).
% 2.04/2.20 tff(7968,plain,
% 2.04/2.20 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[7967, 7966])).
% 2.04/2.20 tff(7969,plain,
% 2.04/2.20 ($false),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[7968, 124, 206, 7965, 7963])).
% 2.04/2.20 tff(7970,plain,((~b(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), s(z))) | (s(s(s(z))) = s(s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.20 tff(7971,plain,
% 2.04/2.20 (~b(s(s(elem!1)), elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[7970, 2831, 4270, 206, 1967, 4346])).
% 2.04/2.20 tff(7972,plain,
% 2.04/2.20 (~(s(elem!1) = elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[2422, 7906, 7875])).
% 2.04/2.20 tff(7973,plain,
% 2.04/2.20 (~(s(s(elem!1)) = s(elem!1))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[195, 7972])).
% 2.04/2.20 tff(7974,plain,
% 2.04/2.20 (r(s(s(elem!1)), elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[47, 91, 6481])).
% 2.04/2.20 tff(7975,plain,
% 2.04/2.20 (~r(z, s(s(elem!1)))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[5837, 7974, 374])).
% 2.04/2.20 tff(7976,assumption,(r(s(s(s(z))), s(elem!1))), introduced(assumption)).
% 2.04/2.20 tff(7977,plain,
% 2.04/2.20 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(7978,plain,
% 2.04/2.20 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.04/2.20 inference(quant_inst,[status(thm)],[])).
% 2.04/2.20 tff(7979,plain,
% 2.04/2.20 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(elem!1))))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[7978, 7977])).
% 2.04/2.20 tff(7980,plain,
% 2.04/2.20 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[7979, 124, 244, 7976])).
% 2.04/2.20 tff(7981,plain,
% 2.04/2.20 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(7982,plain,
% 2.04/2.20 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.04/2.20 inference(quant_inst,[status(thm)],[])).
% 2.04/2.20 tff(7983,plain,
% 2.04/2.20 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1)))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[7982, 7981])).
% 2.04/2.20 tff(7984,plain,
% 2.04/2.20 ($false),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[7983, 124, 802, 1730, 244])).
% 2.04/2.20 tff(7985,plain,((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.20 tff(7986,plain,
% 2.04/2.20 (~r(s(s(elem!1)), elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[7985, 244, 802])).
% 2.04/2.20 tff(7987,plain,
% 2.04/2.20 (b(s(s(elem!1)), elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[47, 7986, 91])).
% 2.04/2.20 tff(7988,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(7989,plain,
% 2.04/2.20 (((~b(s(z), elem!1)) | (~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))))) <=> ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(7990,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[7989])).
% 2.04/2.20 tff(7991,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.04/2.20 inference(transitivity,[status(thm)],[7990, 7988])).
% 2.04/2.20 tff(7992,plain,
% 2.04/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~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)))))),
% 2.04/2.20 inference(quant_inst,[status(thm)],[])).
% 2.04/2.20 tff(7993,plain,
% 2.04/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1))))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[7992, 7991])).
% 2.04/2.20 tff(7994,plain,
% 2.04/2.20 ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[7993, 306])).
% 2.04/2.20 tff(7995,plain,
% 2.04/2.20 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[7994, 7987, 2831, 1967, 4346])).
% 2.04/2.20 tff(7996,plain,
% 2.04/2.20 ($false),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[2986, 43, 7995, 7980, 2976])).
% 2.04/2.20 tff(7997,plain,((~r(s(s(elem!1)), s(elem!1))) | (s(s(s(z))) = s(s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (s(s(elem!1)) = elem!1) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.20 tff(7998,plain,
% 2.04/2.20 (~r(s(s(elem!1)), s(elem!1))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[7997, 91, 7976, 2831, 1967, 4346, 2976, 802])).
% 2.04/2.20 tff(7999,plain,
% 2.04/2.20 (b(s(s(elem!1)), s(elem!1))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[994, 7998, 403])).
% 2.04/2.20 tff(8000,plain,
% 2.04/2.20 (~b(z, s(s(elem!1)))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[1218, 7999, 7921, 7919])).
% 2.04/2.20 tff(8001,plain,
% 2.04/2.20 ($false),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[460, 8000, 7975])).
% 2.04/2.20 tff(8002,plain,((s(s(elem!1)) = elem!1) | (~r(z, elem!1)) | (s(s(elem!1)) = s(elem!1)) | b(s(s(elem!1)), elem!1) | (~r(s(s(s(z))), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (s(s(s(z))) = s(s(elem!1))) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.20 tff(8003,plain,
% 2.04/2.20 (s(s(elem!1)) = elem!1),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[8002, 7973, 374, 7971, 7949, 2831, 1967, 4346, 4270, 7857])).
% 2.04/2.20 tff(8004,plain,
% 2.04/2.20 (elem!1 = s(s(elem!1))),
% 2.04/2.20 inference(symmetry,[status(thm)],[8003])).
% 2.04/2.21 tff(8005,plain,
% 2.04/2.21 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 2.04/2.21 inference(transitivity,[status(thm)],[7945, 8004])).
% 2.04/2.21 tff(8006,plain,
% 2.04/2.21 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(elem!1)))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[8005])).
% 2.04/2.21 tff(8007,plain,
% 2.04/2.21 (s(s(s(s(s(z))))) = s(elem!1)),
% 2.04/2.21 inference(transitivity,[status(thm)],[2823, 8006, 66])).
% 2.04/2.21 tff(8008,plain,
% 2.04/2.21 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(elem!1))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[8007])).
% 2.04/2.21 tff(8009,plain,
% 2.04/2.21 (s(s(s(s(z)))) = s(s(s(s(s(s(z))))))),
% 2.04/2.21 inference(transitivity,[status(thm)],[497, 8008, 135, 7946])).
% 2.04/2.21 tff(8010,plain,
% 2.04/2.21 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(s(s(z)))))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[8009])).
% 2.04/2.21 tff(8011,plain,
% 2.04/2.21 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(s(s(z)))))),
% 2.04/2.21 inference(symmetry,[status(thm)],[8010])).
% 2.04/2.21 tff(8012,plain,
% 2.04/2.21 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(s(z)))))))),
% 2.04/2.21 inference(symmetry,[status(thm)],[8006])).
% 2.04/2.21 tff(8013,plain,
% 2.04/2.21 (s(elem!1) = s(s(s(z)))),
% 2.04/2.21 inference(transitivity,[status(thm)],[67, 8012, 8011, 320])).
% 2.04/2.21 tff(8014,plain,
% 2.04/2.21 ($false),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[7864, 8013])).
% 2.04/2.21 tff(8015,plain,((~b(s(z), elem!1)) | (~r(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | r(s(s(s(z))), elem!1) | (z = elem!1) | b(elem!1, z) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.21 tff(8016,plain,
% 2.04/2.21 (~b(s(z), elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[8015, 5330, 5335, 5333, 206, 5320, 1034, 1484, 2170, 2, 5331])).
% 2.04/2.21 tff(8017,plain,
% 2.04/2.21 (r(s(z), elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1500, 43, 8016, 3094])).
% 2.04/2.21 tff(8018,plain,
% 2.04/2.21 (~r(z, s(z))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[6096, 8017, 5330])).
% 2.04/2.21 tff(8019,plain,
% 2.04/2.21 (b(z, s(z))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[2263, 8018])).
% 2.04/2.21 tff(8020,plain,
% 2.04/2.21 (~r(s(z), z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1049, 8017, 5612])).
% 2.04/2.21 tff(8021,plain,
% 2.04/2.21 (b(s(z), z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[221, 8020])).
% 2.04/2.21 tff(8022,plain,
% 2.04/2.21 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[7186, 8021, 5330, 8017])).
% 2.04/2.21 tff(8023,plain,
% 2.04/2.21 (~(elem!1 = s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1534, 5320, 2])).
% 2.04/2.21 tff(8024,plain,
% 2.04/2.21 (~r(elem!1, s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[3347, 8017, 1034])).
% 2.04/2.21 tff(8025,plain,
% 2.04/2.21 (b(elem!1, s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[2304, 8024, 8023])).
% 2.04/2.21 tff(8026,assumption,(~r(s(s(s(s(s(s(z)))))), elem!1)), introduced(assumption)).
% 2.04/2.21 tff(8027,plain,
% 2.04/2.21 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1144, 7914, 8026])).
% 2.04/2.21 tff(8028,plain,
% 2.04/2.21 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[5367, 8027, 1034, 4346])).
% 2.04/2.21 tff(8029,plain,
% 2.04/2.21 ($false),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[4603, 43, 2885, 8028, 4577])).
% 2.04/2.21 tff(8030,plain,(b(s(s(s(s(s(s(z)))))), s(s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | r(s(s(s(s(s(s(z)))))), elem!1) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.21 tff(8031,plain,
% 2.04/2.21 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[8030, 8022, 5333, 1034, 8025])).
% 2.04/2.21 tff(8032,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(8033,plain,
% 2.04/2.21 (((~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), elem!1))) <=> ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(8034,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), elem!1))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[8033])).
% 2.04/2.21 tff(8035,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 2.04/2.21 inference(transitivity,[status(thm)],[8034, 8032])).
% 2.04/2.21 tff(8036,plain,
% 2.04/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 2.04/2.21 inference(quant_inst,[status(thm)],[])).
% 2.04/2.21 tff(8037,plain,
% 2.04/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), elem!1))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[8036, 8035])).
% 2.04/2.21 tff(8038,plain,
% 2.04/2.21 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[8037, 306, 5335, 5333, 8025, 8031])).
% 2.04/2.21 tff(8039,plain,
% 2.04/2.21 (s(s(s(s(s(s(z)))))) = elem!1),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1144, 8038, 8022])).
% 2.04/2.21 tff(8040,plain,
% 2.04/2.21 ((s(s(z)) = s(s(s(s(s(s(z))))))) <=> (s(s(z)) = elem!1)),
% 2.04/2.21 inference(monotonicity,[status(thm)],[8039])).
% 2.04/2.21 tff(8041,plain,
% 2.04/2.21 ((~(s(s(z)) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(z)) = elem!1))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[8040])).
% 2.04/2.21 tff(8042,plain,
% 2.04/2.21 (~(s(s(z)) = elem!1)),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[2826, 8041])).
% 2.04/2.21 tff(8043,plain,
% 2.04/2.21 (~(s(elem!1) = s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[5384, 8042])).
% 2.04/2.21 tff(8044,plain,
% 2.04/2.21 (r(s(z), elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[4192, 3094])).
% 2.04/2.21 tff(8045,plain,
% 2.04/2.21 (b(s(z), z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[221, 214])).
% 2.04/2.21 tff(8046,plain,
% 2.04/2.21 (~(z = elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1524, 214, 4])).
% 2.04/2.21 tff(8047,plain,
% 2.04/2.21 (~r(z, s(z))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[6096, 5330, 4])).
% 2.04/2.21 tff(8048,plain,
% 2.04/2.21 (b(z, s(z))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[2263, 8047])).
% 2.04/2.21 tff(8049,plain,
% 2.04/2.21 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[7186, 5330, 247, 4])).
% 2.04/2.21 tff(8050,plain,
% 2.04/2.21 (s(s(s(s(s(s(z)))))) = elem!1),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1144, 8049, 4269])).
% 2.04/2.21 tff(8051,plain,
% 2.04/2.21 ((s(s(z)) = s(s(s(s(s(s(z))))))) <=> (s(s(z)) = elem!1)),
% 2.04/2.21 inference(monotonicity,[status(thm)],[8050])).
% 2.04/2.21 tff(8052,plain,
% 2.04/2.21 ((~(s(s(z)) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(z)) = elem!1))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[8051])).
% 2.04/2.21 tff(8053,plain,
% 2.04/2.21 (~(s(s(z)) = elem!1)),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[2826, 8052])).
% 2.04/2.21 tff(8054,plain,
% 2.04/2.21 (~(s(elem!1) = s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[5384, 8053])).
% 2.04/2.21 tff(8055,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(z), z)))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(8056,plain,
% 2.04/2.21 (((~b(s(z), z)) | (~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(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(z), z)))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(8057,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(z), z))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[8056])).
% 2.04/2.21 tff(8058,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(z), z)))),
% 2.04/2.21 inference(transitivity,[status(thm)],[8057, 8055])).
% 2.04/2.21 tff(8059,plain,
% 2.04/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))))),
% 2.04/2.21 inference(quant_inst,[status(thm)],[])).
% 2.04/2.21 tff(8060,plain,
% 2.04/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(z), z))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[8059, 8058])).
% 2.04/2.21 tff(8061,plain,
% 2.04/2.21 (~b(s(elem!1), s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[8060, 306, 1199, 1531, 247, 485])).
% 2.04/2.21 tff(8062,plain,
% 2.04/2.21 (r(s(elem!1), s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[2367, 43, 8061, 7554])).
% 2.04/2.21 tff(8063,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(8064,plain,
% 2.04/2.21 (((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z)))) <=> ((~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(8065,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z)))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[8064])).
% 2.04/2.21 tff(8066,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))),
% 2.04/2.21 inference(transitivity,[status(thm)],[8065, 8063])).
% 2.04/2.21 tff(8067,plain,
% 2.04/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))),
% 2.04/2.21 inference(quant_inst,[status(thm)],[])).
% 2.04/2.21 tff(8068,plain,
% 2.04/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z)))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[8067, 8066])).
% 2.04/2.21 tff(8069,plain,
% 2.04/2.21 (~b(s(elem!1), s(z))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[8068, 306, 1199, 247, 485])).
% 2.04/2.21 tff(8070,plain,
% 2.04/2.21 (r(s(elem!1), s(z))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[2964, 8069, 2249])).
% 2.04/2.21 tff(8071,plain,
% 2.04/2.21 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(8072,plain,
% 2.04/2.21 (((~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(z)))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(8073,plain,
% 2.04/2.21 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z)))))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[8072])).
% 2.04/2.21 tff(8074,plain,
% 2.04/2.21 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))))),
% 2.04/2.21 inference(transitivity,[status(thm)],[8073, 8071])).
% 2.04/2.21 tff(8075,plain,
% 2.04/2.21 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(z))))),
% 2.04/2.21 inference(quant_inst,[status(thm)],[])).
% 2.04/2.21 tff(8076,plain,
% 2.04/2.21 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z)))))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[8075, 8074])).
% 2.04/2.21 tff(8077,plain,
% 2.04/2.21 ($false),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[8076, 124, 1034, 8070, 8062])).
% 2.04/2.21 tff(8078,plain,((~b(s(elem!1), z)) | (~r(s(z), s(s(s(z))))) | (s(elem!1) = s(s(s(z)))) | (s(elem!1) = s(z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.21 tff(8079,plain,
% 2.04/2.21 (~b(s(elem!1), z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[8078, 8054, 1034, 3099, 247, 8048, 1531])).
% 2.04/2.21 tff(8080,plain,
% 2.04/2.21 (r(s(elem!1), z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[2380, 8079])).
% 2.04/2.21 tff(8081,plain,
% 2.04/2.21 (~r(s(elem!1), elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[416, 8080, 5330])).
% 2.04/2.21 tff(8082,plain,
% 2.04/2.21 (s(elem!1) = elem!1),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[813, 8081, 807])).
% 2.04/2.21 tff(8083,plain,
% 2.04/2.21 (s(s(elem!1)) = elem!1),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[180, 8082])).
% 2.04/2.21 tff(8084,plain,
% 2.04/2.21 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[8083])).
% 2.04/2.21 tff(8085,plain,
% 2.04/2.21 ((elem!1 = s(s(s(elem!1)))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 2.04/2.21 inference(symmetry,[status(thm)],[8084])).
% 2.04/2.21 tff(8086,plain,
% 2.04/2.21 (elem!1 = s(s(elem!1))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1174, 8083])).
% 2.04/2.21 tff(8087,plain,
% 2.04/2.21 (s(s(s(elem!1))) = s(elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1168, 8086])).
% 2.04/2.21 tff(8088,plain,
% 2.04/2.21 ((elem!1 = s(s(s(elem!1)))) <=> (elem!1 = s(elem!1))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[8087])).
% 2.04/2.21 tff(8089,plain,
% 2.04/2.21 ((elem!1 = s(s(s(elem!1)))) <=> (s(elem!1) = elem!1)),
% 2.04/2.21 inference(transitivity,[status(thm)],[8088, 1162])).
% 2.04/2.21 tff(8090,plain,
% 2.04/2.21 ((s(elem!1) = elem!1) <=> (elem!1 = s(s(s(elem!1))))),
% 2.04/2.21 inference(symmetry,[status(thm)],[8089])).
% 2.04/2.21 tff(8091,plain,
% 2.04/2.21 ((s(elem!1) = elem!1) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 2.04/2.21 inference(transitivity,[status(thm)],[8090, 8085, 2425])).
% 2.04/2.21 tff(8092,plain,
% 2.04/2.21 (s(s(s(elem!1))) = s(s(elem!1))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[8082, 8091])).
% 2.04/2.21 tff(8093,plain,
% 2.04/2.21 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[5403, 8050])).
% 2.04/2.21 tff(8094,plain,
% 2.04/2.21 ($false),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[8093, 8092])).
% 2.04/2.21 tff(8095,plain,((z = elem!1) | b(s(elem!1), elem!1) | (~r(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | b(s(s(s(s(s(s(z)))))), elem!1) | (~r(s(z), elem!1)) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.04/2.21 tff(8096,plain,
% 2.04/2.21 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[8095, 8046, 1034, 8045, 1531, 807, 4, 5318])).
% 2.04/2.21 tff(8097,plain,
% 2.04/2.21 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[5367, 8096, 1034, 4346])).
% 2.04/2.21 tff(8098,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(8099,plain,
% 2.04/2.21 (((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))) <=> ((~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(8100,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), elem!1))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[8099])).
% 2.04/2.21 tff(8101,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 2.04/2.21 inference(transitivity,[status(thm)],[8100, 8098])).
% 2.04/2.21 tff(8102,plain,
% 2.04/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 2.04/2.21 inference(quant_inst,[status(thm)],[])).
% 2.04/2.21 tff(8103,plain,
% 2.04/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), elem!1))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[8102, 8101])).
% 2.04/2.21 tff(8104,plain,
% 2.04/2.21 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[8103, 306, 1967, 4346, 8045, 8096])).
% 2.04/2.21 tff(8105,plain,
% 2.04/2.21 ($false),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[4603, 43, 8104, 8097, 4577])).
% 2.04/2.21 tff(8106,plain,(r(s(z), z) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~r(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | b(s(elem!1), elem!1) | (~r(s(z), elem!1)) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.04/2.21 tff(8107,plain,
% 2.04/2.21 (r(s(z), z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[8106, 5333, 1967, 1034, 5320, 807, 8044, 5318])).
% 2.04/2.21 tff(8108,plain,
% 2.04/2.21 (~r(elem!1, z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1049, 8107, 8044])).
% 2.04/2.21 tff(8109,plain,
% 2.04/2.21 (elem!1 = z),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[174, 8108, 2])).
% 2.04/2.21 tff(8110,plain,
% 2.04/2.21 (z = elem!1),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[2172, 8109])).
% 2.04/2.21 tff(8111,plain,
% 2.04/2.21 (~(s(elem!1) = elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[2698, 8110])).
% 2.04/2.21 tff(8112,plain,
% 2.04/2.21 (r(s(elem!1), elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[813, 8111, 807])).
% 2.04/2.21 tff(8113,plain,
% 2.04/2.21 (s(elem!1) = s(z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[2251, 8110])).
% 2.04/2.21 tff(8114,plain,
% 2.04/2.21 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[2724, 8113])).
% 2.04/2.21 tff(8115,plain,
% 2.04/2.21 (~(elem!1 = s(s(elem!1)))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1168, 8114])).
% 2.04/2.21 tff(8116,plain,
% 2.04/2.21 (~(s(s(elem!1)) = elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1174, 8115])).
% 2.04/2.21 tff(8117,plain,
% 2.04/2.21 (b(elem!1, s(s(s(elem!1)))) <=> b(z, s(s(s(elem!1))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[8109])).
% 2.04/2.21 tff(8118,plain,
% 2.04/2.21 (b(z, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 2.04/2.21 inference(symmetry,[status(thm)],[8117])).
% 2.04/2.21 tff(8119,plain,
% 2.04/2.21 (s(elem!1) = s(z)),
% 2.04/2.21 inference(monotonicity,[status(thm)],[8109])).
% 2.04/2.21 tff(8120,plain,
% 2.04/2.21 (s(s(elem!1)) = s(s(z))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[8119])).
% 2.04/2.21 tff(8121,plain,
% 2.04/2.21 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[8120])).
% 2.04/2.21 tff(8122,plain,
% 2.04/2.21 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(s(z))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[8121])).
% 2.04/2.21 tff(8123,plain,
% 2.04/2.21 (b(z, s(s(s(z)))) <=> b(z, s(s(s(elem!1))))),
% 2.04/2.21 inference(symmetry,[status(thm)],[8122])).
% 2.04/2.21 tff(8124,plain,
% 2.04/2.21 (b(z, s(s(s(z)))) <=> b(elem!1, s(s(s(elem!1))))),
% 2.04/2.21 inference(transitivity,[status(thm)],[8123, 8118])).
% 2.04/2.21 tff(8125,plain,
% 2.04/2.21 (b(elem!1, s(s(s(z)))) <=> b(z, s(s(s(z))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[8109])).
% 2.04/2.21 tff(8126,plain,
% 2.04/2.21 (~r(elem!1, s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[3347, 8044, 1034])).
% 2.04/2.21 tff(8127,plain,
% 2.04/2.21 (b(elem!1, s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[2304, 8126, 8023])).
% 2.04/2.21 tff(8128,plain,
% 2.04/2.21 (b(z, s(s(s(z))))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[8127, 8125])).
% 2.04/2.21 tff(8129,plain,
% 2.04/2.21 (b(elem!1, s(s(s(elem!1))))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[8128, 8124])).
% 2.04/2.21 tff(8130,plain,
% 2.04/2.21 (~r(s(s(s(elem!1))), elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1631, 8109, 1629])).
% 2.04/2.21 tff(8131,plain,
% 2.04/2.21 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1511, 8110])).
% 2.04/2.21 tff(8132,plain,
% 2.04/2.21 (~(elem!1 = s(s(s(elem!1))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1518, 8131])).
% 2.04/2.21 tff(8133,plain,
% 2.04/2.21 (~(s(s(s(elem!1))) = elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[2187, 8132])).
% 2.04/2.21 tff(8134,plain,
% 2.04/2.21 (b(s(s(s(elem!1))), elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1636, 8133, 8130])).
% 2.04/2.21 tff(8135,plain,
% 2.04/2.21 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(z))), s(z))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[8121, 8119])).
% 2.04/2.21 tff(8136,plain,
% 2.04/2.21 (r(s(s(s(z))), s(z)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 2.04/2.22 inference(symmetry,[status(thm)],[8135])).
% 2.04/2.22 tff(8137,plain,
% 2.04/2.22 (r(s(s(s(elem!1))), s(elem!1))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[206, 8136])).
% 2.04/2.22 tff(8138,plain,
% 2.04/2.22 (~b(s(s(elem!1)), s(elem!1))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[3177, 30, 1502, 802, 4685, 1663, 1664, 4671])).
% 2.04/2.22 tff(8139,plain,
% 2.04/2.22 (r(s(s(elem!1)), s(elem!1))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[994, 8138, 4685])).
% 2.04/2.22 tff(8140,plain,
% 2.04/2.22 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1672, 30, 1664, 1663])).
% 2.04/2.22 tff(8141,plain,
% 2.04/2.22 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[610, 8140, 4671])).
% 2.04/2.22 tff(8142,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[659, 8141, 8139, 654])).
% 2.04/2.22 tff(8143,plain,((~b(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~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))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(8144,plain,
% 2.04/2.22 (~b(s(s(elem!1)), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[8143, 8137, 8134, 8129, 8110, 8112])).
% 2.04/2.22 tff(8145,plain,
% 2.04/2.22 (r(s(s(elem!1)), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[47, 8144, 8116])).
% 2.04/2.22 tff(8146,plain,
% 2.04/2.22 (~r(s(s(elem!1)), s(elem!1))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[7985, 8145, 8112])).
% 2.04/2.22 tff(8147,plain,
% 2.04/2.22 (~(s(s(elem!1)) = s(elem!1))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[195, 8111])).
% 2.04/2.22 tff(8148,plain,
% 2.04/2.22 (~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1655, 8132])).
% 2.04/2.22 tff(8149,plain,
% 2.04/2.22 (b(s(s(elem!1)), s(elem!1))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[994, 8146, 8147])).
% 2.04/2.22 tff(8150,plain,
% 2.04/2.22 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1964, 8149, 8110, 8137, 8148, 8129, 8134, 8112, 8147])).
% 2.04/2.22 tff(8151,plain,
% 2.04/2.22 (~b(s(elem!1), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[2718, 8110, 2715])).
% 2.04/2.22 tff(8152,plain,
% 2.04/2.22 (r(s(elem!1), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[2380, 8151])).
% 2.04/2.22 tff(8153,plain,
% 2.04/2.22 (~r(z, elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[416, 8152, 8112])).
% 2.04/2.22 tff(8154,plain,
% 2.04/2.22 (b(s(elem!1), s(s(elem!1))) <=> b(s(z), s(s(elem!1)))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[8119])).
% 2.04/2.22 tff(8155,plain,
% 2.04/2.22 (b(s(z), s(s(elem!1))) <=> b(s(elem!1), s(s(elem!1)))),
% 2.04/2.22 inference(symmetry,[status(thm)],[8154])).
% 2.04/2.22 tff(8156,plain,
% 2.04/2.22 (s(s(z)) = s(s(elem!1))),
% 2.04/2.22 inference(symmetry,[status(thm)],[8120])).
% 2.04/2.22 tff(8157,plain,
% 2.04/2.22 (b(s(z), s(s(z))) <=> b(s(z), s(s(elem!1)))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[8156])).
% 2.04/2.22 tff(8158,plain,
% 2.04/2.22 (b(s(z), s(s(z))) <=> b(s(elem!1), s(s(elem!1)))),
% 2.04/2.22 inference(transitivity,[status(thm)],[8157, 8155])).
% 2.04/2.22 tff(8159,plain,
% 2.04/2.22 (r(s(s(elem!1)), z) <=> r(s(s(z)), z)),
% 2.04/2.22 inference(monotonicity,[status(thm)],[8120])).
% 2.04/2.22 tff(8160,plain,
% 2.04/2.22 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), z)),
% 2.04/2.22 inference(monotonicity,[status(thm)],[8109])).
% 2.04/2.22 tff(8161,plain,
% 2.04/2.22 (r(s(s(elem!1)), elem!1) <=> r(s(s(z)), z)),
% 2.04/2.22 inference(transitivity,[status(thm)],[8160, 8159])).
% 2.04/2.22 tff(8162,plain,
% 2.04/2.22 (r(s(s(z)), z)),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[8145, 8161])).
% 2.04/2.22 tff(8163,plain,
% 2.04/2.22 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(8164,plain,
% 2.04/2.22 (((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(8165,plain,
% 2.04/2.22 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[8164])).
% 2.04/2.22 tff(8166,plain,
% 2.04/2.22 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)))),
% 2.04/2.22 inference(transitivity,[status(thm)],[8165, 8163])).
% 2.04/2.22 tff(8167,plain,
% 2.04/2.22 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))),
% 2.04/2.22 inference(quant_inst,[status(thm)],[])).
% 2.04/2.22 tff(8168,plain,
% 2.04/2.22 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[8167, 8166])).
% 2.04/2.22 tff(8169,plain,
% 2.04/2.22 (~r(s(z), s(s(z)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[8168, 124, 8107, 8162])).
% 2.04/2.22 tff(8170,plain,
% 2.04/2.22 (b(s(z), s(s(z)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4434, 8169])).
% 2.04/2.22 tff(8171,plain,
% 2.04/2.22 (b(s(elem!1), s(s(elem!1)))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[8170, 8158])).
% 2.04/2.22 tff(8172,plain,
% 2.04/2.22 (~b(elem!1, s(s(elem!1)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1803, 8171, 8110, 8145, 8129, 8134, 8112, 8149])).
% 2.04/2.22 tff(8173,plain,
% 2.04/2.22 (~b(z, s(s(elem!1)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[2757, 8172, 8110])).
% 2.04/2.22 tff(8174,assumption,(~b(z, s(s(elem!1)))), introduced(assumption)).
% 2.04/2.22 tff(8175,assumption,(~b(s(s(s(elem!1))), s(s(elem!1)))), introduced(assumption)).
% 2.04/2.22 tff(8176,plain,
% 2.04/2.22 (b(z, s(s(elem!1))) <=> b(z, elem!1)),
% 2.04/2.22 inference(monotonicity,[status(thm)],[1171])).
% 2.04/2.22 tff(8177,plain,
% 2.04/2.22 (b(z, elem!1) <=> b(z, s(s(elem!1)))),
% 2.04/2.22 inference(symmetry,[status(thm)],[8176])).
% 2.04/2.22 tff(8178,plain,
% 2.04/2.22 (b(z, s(s(elem!1)))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[838, 8177])).
% 2.04/2.22 tff(8179,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[8174, 8178])).
% 2.04/2.22 tff(8180,plain,((~(s(s(elem!1)) = elem!1)) | b(z, s(s(elem!1))) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(8181,plain,
% 2.04/2.22 (~(s(s(elem!1)) = elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[8180, 2255, 8174])).
% 2.04/2.22 tff(8182,plain,
% 2.04/2.22 (~(s(elem!1) = elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[180, 8181])).
% 2.04/2.22 tff(8183,plain,
% 2.04/2.22 (~(s(s(elem!1)) = s(elem!1))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[195, 8182])).
% 2.04/2.22 tff(8184,plain,
% 2.04/2.22 (b(s(s(elem!1)), s(elem!1))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[994, 8183, 3149])).
% 2.04/2.22 tff(8185,plain,
% 2.04/2.22 (b(elem!1, z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[174, 2253, 3062])).
% 2.04/2.22 tff(8186,plain,
% 2.04/2.22 (r(z, s(s(elem!1)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[460, 8174])).
% 2.04/2.22 tff(8187,plain,
% 2.04/2.22 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[143, 8181])).
% 2.04/2.22 tff(8188,plain,
% 2.04/2.22 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[152, 8187])).
% 2.04/2.22 tff(8189,plain,
% 2.04/2.22 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[159, 8188])).
% 2.04/2.22 tff(8190,plain,
% 2.04/2.22 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[610, 8189, 8175])).
% 2.04/2.22 tff(8191,plain,
% 2.04/2.22 (~r(z, s(s(s(elem!1))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[950, 8190, 8186])).
% 2.04/2.22 tff(8192,plain,
% 2.04/2.22 (b(z, s(s(s(elem!1))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[585, 8191])).
% 2.04/2.22 tff(8193,plain,
% 2.04/2.22 (~b(s(s(s(elem!1))), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[6150, 8192, 8185, 2255])).
% 2.04/2.22 tff(8194,plain,
% 2.04/2.22 (s(s(s(elem!1))) = elem!1),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1636, 8193, 7789])).
% 2.04/2.22 tff(8195,plain,
% 2.04/2.22 (s(s(s(s(elem!1)))) = s(elem!1)),
% 2.04/2.22 inference(monotonicity,[status(thm)],[8194])).
% 2.04/2.22 tff(8196,plain,
% 2.04/2.22 (b(s(s(s(s(elem!1)))), s(s(elem!1))) <=> b(s(elem!1), s(s(elem!1)))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[8195])).
% 2.04/2.22 tff(8197,plain,
% 2.04/2.22 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1284, 8187])).
% 2.04/2.22 tff(8198,plain,
% 2.04/2.22 (~(elem!1 = s(s(elem!1)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[186, 8181])).
% 2.04/2.22 tff(8199,plain,
% 2.04/2.22 (r(elem!1, s(s(elem!1)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[516, 8198, 2754])).
% 2.04/2.22 tff(8200,plain,
% 2.04/2.22 (r(s(s(s(s(elem!1)))), elem!1) <=> r(s(elem!1), elem!1)),
% 2.04/2.22 inference(monotonicity,[status(thm)],[8195])).
% 2.04/2.22 tff(8201,plain,
% 2.04/2.22 (r(s(elem!1), elem!1) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 2.04/2.22 inference(symmetry,[status(thm)],[8200])).
% 2.04/2.22 tff(8202,plain,
% 2.04/2.22 (r(s(elem!1), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[813, 8182, 807])).
% 2.04/2.22 tff(8203,plain,
% 2.04/2.22 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[8202, 8201])).
% 2.04/2.22 tff(8204,plain,
% 2.04/2.22 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1297, 8203, 8199])).
% 2.04/2.22 tff(8205,plain,
% 2.04/2.22 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1302, 8204, 8197])).
% 2.04/2.22 tff(8206,plain,
% 2.04/2.22 (b(s(elem!1), s(s(elem!1)))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[8205, 8196])).
% 2.04/2.22 tff(8207,plain,
% 2.04/2.22 ((s(z) = s(s(s(elem!1)))) <=> (s(z) = elem!1)),
% 2.04/2.22 inference(monotonicity,[status(thm)],[8194])).
% 2.04/2.22 tff(8208,plain,
% 2.04/2.22 ((s(z) = s(s(s(elem!1)))) <=> (elem!1 = s(z))),
% 2.04/2.22 inference(transitivity,[status(thm)],[8207, 84])).
% 2.04/2.22 tff(8209,plain,
% 2.04/2.22 ((~(s(z) = s(s(s(elem!1))))) <=> (~(elem!1 = s(z)))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[8208])).
% 2.04/2.22 tff(8210,plain,
% 2.04/2.22 (~(elem!1 = s(z))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[645, 8209])).
% 2.04/2.22 tff(8211,assumption,(r(s(z), s(s(elem!1)))), introduced(assumption)).
% 2.04/2.22 tff(8212,plain,
% 2.04/2.22 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(elem!1)))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(8213,plain,
% 2.04/2.22 (((~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(elem!1, s(z))) | (~r(s(z), s(s(elem!1)))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(8214,plain,
% 2.04/2.22 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(elem!1))))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[8213])).
% 2.04/2.22 tff(8215,plain,
% 2.04/2.22 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(elem!1)))))),
% 2.04/2.22 inference(transitivity,[status(thm)],[8214, 8212])).
% 2.04/2.22 tff(8216,plain,
% 2.04/2.22 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))))),
% 2.04/2.22 inference(quant_inst,[status(thm)],[])).
% 2.04/2.22 tff(8217,plain,
% 2.04/2.22 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(elem!1))))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[8216, 8215])).
% 2.04/2.22 tff(8218,plain,
% 2.04/2.22 (~r(elem!1, s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[8217, 124, 970, 8211])).
% 2.04/2.22 tff(8219,plain,
% 2.04/2.22 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(8220,plain,
% 2.04/2.22 (((~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), z))) <=> ((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(8221,plain,
% 2.04/2.22 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1))))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[8220])).
% 2.04/2.22 tff(8222,plain,
% 2.04/2.22 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))),
% 2.04/2.22 inference(transitivity,[status(thm)],[8221, 8219])).
% 2.04/2.22 tff(8223,plain,
% 2.04/2.22 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), z)))),
% 2.04/2.22 inference(quant_inst,[status(thm)],[])).
% 2.04/2.22 tff(8224,plain,
% 2.04/2.22 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1))))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[8223, 8222])).
% 2.04/2.22 tff(8225,plain,
% 2.04/2.22 (~r(s(z), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[8224, 124, 437, 8211])).
% 2.04/2.22 tff(8226,plain,
% 2.04/2.22 (b(s(z), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[221, 8225])).
% 2.04/2.22 tff(8227,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(8228,plain,
% 2.04/2.22 (((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(8229,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[8228])).
% 2.04/2.22 tff(8230,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)))),
% 2.04/2.22 inference(transitivity,[status(thm)],[8229, 8227])).
% 2.04/2.22 tff(8231,plain,
% 2.04/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))),
% 2.04/2.22 inference(quant_inst,[status(thm)],[])).
% 2.04/2.22 tff(8232,plain,
% 2.04/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[8231, 8230])).
% 2.04/2.22 tff(8233,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[8232, 306, 838, 4012, 4346, 247])).
% 2.04/2.22 tff(8234,plain,((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(8235,plain,
% 2.04/2.22 (~b(elem!1, s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[8234, 8226, 838, 4012])).
% 2.04/2.22 tff(8236,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[96, 43, 8235, 8218, 87])).
% 2.04/2.22 tff(8237,plain,((~r(s(z), s(s(elem!1)))) | (elem!1 = s(z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(8238,plain,
% 2.04/2.22 (~r(s(z), s(s(elem!1)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[8237, 8210, 2255, 8185, 8199, 8186])).
% 2.04/2.22 tff(8239,plain,
% 2.04/2.22 (b(s(z), s(s(elem!1)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[3997, 43, 79, 8238])).
% 2.04/2.22 tff(8240,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(8241,plain,
% 2.04/2.22 (((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(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)), s(elem!1))) | (~b(s(z), s(elem!1))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(8242,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1)))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[8241])).
% 2.04/2.22 tff(8243,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))))),
% 2.04/2.22 inference(transitivity,[status(thm)],[8242, 8240])).
% 2.04/2.22 tff(8244,plain,
% 2.04/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1))))),
% 2.04/2.22 inference(quant_inst,[status(thm)],[])).
% 2.04/2.22 tff(8245,plain,
% 2.04/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1)))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[8244, 8243])).
% 2.04/2.22 tff(8246,plain,
% 2.04/2.22 (~b(s(z), s(elem!1))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[8245, 306, 8184, 8239, 8206])).
% 2.04/2.22 tff(8247,plain,
% 2.04/2.22 ((s(z) = s(elem!1)) | r(s(z), s(elem!1))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4047, 43, 8246])).
% 2.04/2.22 tff(8248,plain,
% 2.04/2.22 (r(s(z), s(elem!1))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[8247, 7418])).
% 2.04/2.22 tff(8249,plain,
% 2.04/2.22 (~(s(s(s(z))) = elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4105, 8194, 2249])).
% 2.04/2.22 tff(8250,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(8251,plain,
% 2.04/2.22 (((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(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(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(8252,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z)))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[8251])).
% 2.04/2.22 tff(8253,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))))),
% 2.04/2.22 inference(transitivity,[status(thm)],[8252, 8250])).
% 2.04/2.22 tff(8254,plain,
% 2.04/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))))),
% 2.04/2.22 inference(quant_inst,[status(thm)],[])).
% 2.04/2.22 tff(8255,plain,
% 2.04/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z)))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[8254, 8253])).
% 2.04/2.22 tff(8256,plain,
% 2.04/2.22 (~b(s(elem!1), s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[8255, 306, 8184, 8239, 8206])).
% 2.04/2.22 tff(8257,plain,
% 2.04/2.22 (r(s(elem!1), s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[2612, 43, 8256, 2249])).
% 2.04/2.22 tff(8258,plain,
% 2.04/2.22 (~r(elem!1, s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[2960, 8202, 8257])).
% 2.04/2.22 tff(8259,plain,
% 2.04/2.22 (b(elem!1, s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[96, 43, 8258, 8210])).
% 2.04/2.22 tff(8260,plain,
% 2.04/2.22 (~(elem!1 = s(elem!1))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[364, 8182])).
% 2.04/2.22 tff(8261,plain,
% 2.04/2.22 (~b(s(z), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[8234, 8259, 2255, 8185])).
% 2.04/2.22 tff(8262,plain,
% 2.04/2.22 (r(s(z), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[221, 8261])).
% 2.04/2.22 tff(8263,plain,
% 2.04/2.22 (~r(s(elem!1), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[2634, 8262, 8257])).
% 2.04/2.22 tff(8264,plain,
% 2.04/2.22 (b(s(elem!1), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[2380, 8263])).
% 2.04/2.22 tff(8265,plain,
% 2.04/2.22 (~b(elem!1, s(elem!1))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4020, 8264, 8185, 2255])).
% 2.04/2.22 tff(8266,plain,
% 2.04/2.22 (r(elem!1, s(elem!1))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[372, 8265, 8260])).
% 2.04/2.22 tff(8267,plain,
% 2.04/2.22 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(8268,plain,
% 2.04/2.22 (((~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))), elem!1)) | (~r(s(s(s(z))), s(elem!1))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(8269,plain,
% 2.04/2.22 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1)))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[8268])).
% 2.04/2.23 tff(8270,plain,
% 2.04/2.23 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1))))),
% 2.04/2.23 inference(transitivity,[status(thm)],[8269, 8267])).
% 2.04/2.23 tff(8271,plain,
% 2.04/2.23 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)))),
% 2.04/2.23 inference(quant_inst,[status(thm)],[])).
% 2.04/2.23 tff(8272,plain,
% 2.04/2.23 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1)))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[8271, 8270])).
% 2.04/2.23 tff(8273,plain,
% 2.04/2.23 (~r(s(s(s(z))), elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[8272, 124, 255, 7976])).
% 2.04/2.23 tff(8274,plain,
% 2.04/2.23 (b(s(s(s(z))), elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[1489, 8273, 1483])).
% 2.04/2.23 tff(8275,plain,
% 2.04/2.23 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(z))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(8276,plain,
% 2.04/2.23 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(z))))),
% 2.04/2.23 inference(quant_inst,[status(thm)],[])).
% 2.04/2.23 tff(8277,plain,
% 2.04/2.23 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(z)))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[8276, 8275])).
% 2.04/2.23 tff(8278,plain,
% 2.04/2.23 (~r(s(s(s(z))), s(z))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[8277, 124, 7600, 7976])).
% 2.04/2.23 tff(8279,plain,
% 2.04/2.23 (b(s(s(s(z))), s(z))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[113, 8278])).
% 2.04/2.23 tff(8280,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(8281,plain,
% 2.04/2.23 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(8282,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(elem!1))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[8281])).
% 2.04/2.23 tff(8283,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(elem!1))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)))),
% 2.04/2.23 inference(transitivity,[status(thm)],[8282, 8280])).
% 2.04/2.23 tff(8284,plain,
% 2.04/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 2.04/2.23 inference(quant_inst,[status(thm)],[])).
% 2.04/2.23 tff(8285,plain,
% 2.04/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[8284, 8283])).
% 2.04/2.23 tff(8286,plain,
% 2.04/2.23 ($false),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[8285, 306, 1005, 8279, 3999, 8274, 4346])).
% 2.04/2.23 tff(8287,plain,((~r(s(s(s(z))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (s(s(s(z))) = elem!1) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.23 tff(8288,plain,
% 2.04/2.23 (~r(s(s(s(z))), s(elem!1))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[8287, 8266, 8239, 8259, 8249, 8248, 8184])).
% 2.04/2.23 tff(8289,plain,
% 2.04/2.23 ((s(z) = s(s(s(elem!1)))) <=> (s(z) = elem!1)),
% 2.04/2.23 inference(transitivity,[status(thm)],[8208, 3092])).
% 2.04/2.23 tff(8290,plain,
% 2.04/2.23 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(z) = elem!1))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[8289])).
% 2.04/2.23 tff(8291,plain,
% 2.04/2.23 (~(s(z) = elem!1)),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[645, 8290])).
% 2.04/2.23 tff(8292,plain,
% 2.04/2.23 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(8293,plain,
% 2.04/2.23 (((~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(z), s(elem!1))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(8294,plain,
% 2.04/2.23 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1)))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[8293])).
% 2.04/2.23 tff(8295,plain,
% 2.04/2.23 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))))),
% 2.04/2.23 inference(transitivity,[status(thm)],[8294, 8292])).
% 2.04/2.23 tff(8296,plain,
% 2.04/2.23 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), elem!1)))),
% 2.04/2.23 inference(quant_inst,[status(thm)],[])).
% 2.04/2.23 tff(8297,plain,
% 2.04/2.23 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1)))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[8296, 8295])).
% 2.04/2.23 tff(8298,plain,
% 2.04/2.23 (~r(s(z), elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[8297, 124, 8266, 8248])).
% 2.04/2.23 tff(8299,plain,
% 2.04/2.23 (b(s(z), elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[1500, 43, 8298, 8291])).
% 2.04/2.23 tff(8300,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(8301,plain,
% 2.04/2.23 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z)))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(8302,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z)))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[8301])).
% 2.04/2.23 tff(8303,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))))),
% 2.04/2.23 inference(transitivity,[status(thm)],[8302, 8300])).
% 2.04/2.23 tff(8304,plain,
% 2.04/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))),
% 2.04/2.23 inference(quant_inst,[status(thm)],[])).
% 2.04/2.23 tff(8305,plain,
% 2.04/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z)))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[8304, 8303])).
% 2.04/2.23 tff(8306,plain,
% 2.04/2.23 (~b(z, s(z))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[8305, 306, 2255, 8185, 8299])).
% 2.04/2.23 tff(8307,plain,
% 2.04/2.23 (r(z, s(z))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[389, 43, 8306, 2260])).
% 2.04/2.23 tff(8308,plain,
% 2.04/2.23 (~r(z, s(elem!1))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[7542, 124, 8307, 8257])).
% 2.04/2.23 tff(8309,plain,
% 2.04/2.23 (b(z, s(elem!1))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[275, 8308])).
% 2.04/2.23 tff(8310,plain,
% 2.04/2.23 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[2974, 8210])).
% 2.04/2.23 tff(8311,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(8312,plain,
% 2.04/2.23 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), z))) <=> ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(8313,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1)))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[8312])).
% 2.04/2.23 tff(8314,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.04/2.23 inference(transitivity,[status(thm)],[8313, 8311])).
% 2.04/2.23 tff(8315,plain,
% 2.04/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), z)))),
% 2.04/2.23 inference(quant_inst,[status(thm)],[])).
% 2.04/2.23 tff(8316,plain,
% 2.04/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1)))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[8315, 8314])).
% 2.04/2.23 tff(8317,plain,
% 2.04/2.23 (~b(s(s(elem!1)), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[8316, 306, 8309, 8184, 8206])).
% 2.04/2.23 tff(8318,plain,
% 2.04/2.23 (r(s(s(elem!1)), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[476, 8317])).
% 2.04/2.23 tff(8319,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(8320,plain,
% 2.04/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(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)))))),
% 2.04/2.23 inference(quant_inst,[status(thm)],[])).
% 2.04/2.23 tff(8321,plain,
% 2.04/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(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))))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[8320, 8319])).
% 2.04/2.23 tff(8322,plain,
% 2.04/2.23 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[8321, 306, 838, 1199, 1005, 2453])).
% 2.04/2.23 tff(8323,plain,
% 2.04/2.23 (r(s(s(s(z))), s(s(elem!1)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[2986, 43, 8322, 2976])).
% 2.04/2.23 tff(8324,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(8325,plain,
% 2.04/2.23 (((~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), z))) <=> ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(8326,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1)))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[8325])).
% 2.04/2.23 tff(8327,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))),
% 2.04/2.23 inference(transitivity,[status(thm)],[8326, 8324])).
% 2.04/2.23 tff(8328,plain,
% 2.04/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), z)))),
% 2.04/2.23 inference(quant_inst,[status(thm)],[])).
% 2.04/2.23 tff(8329,plain,
% 2.04/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1)))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[8328, 8327])).
% 2.04/2.23 tff(8330,plain,
% 2.04/2.23 ($false),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[8329, 306, 838, 1199, 817, 1531, 2453])).
% 2.04/2.23 tff(8331,plain,((~b(s(s(s(z))), s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.23 tff(8332,plain,
% 2.04/2.23 (~b(s(s(s(z))), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[8331, 2453, 1199, 817, 838])).
% 2.04/2.23 tff(8333,plain,
% 2.04/2.23 (r(s(s(s(z))), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[2197, 8332])).
% 2.04/2.23 tff(8334,plain,
% 2.04/2.23 ($false),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[3000, 124, 465, 8333, 8323])).
% 2.04/2.23 tff(8335,plain,((~b(s(s(s(z))), s(elem!1))) | (~r(s(s(elem!1)), z)) | (s(s(s(z))) = s(s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.23 tff(8336,plain,
% 2.04/2.23 (~b(s(s(s(z))), s(elem!1))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[8335, 8318, 8310, 2255, 8264, 8184, 8309])).
% 2.04/2.23 tff(8337,plain,
% 2.04/2.23 (~(s(s(s(z))) = s(elem!1))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[4128, 8194])).
% 2.04/2.23 tff(8338,plain,
% 2.04/2.23 ($false),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[4132, 43, 8337, 8336, 8288])).
% 2.04/2.23 tff(8339,plain,((s(elem!1) = s(z)) | r(s(s(s(elem!1))), elem!1) | b(s(s(s(elem!1))), s(s(elem!1))) | r(s(s(elem!1)), s(elem!1)) | b(s(elem!1), elem!1) | b(elem!1, s(s(elem!1))) | b(z, s(s(elem!1))) | r(elem!1, z) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.04/2.23 tff(8340,plain,
% 2.04/2.23 (s(elem!1) = s(z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[8339, 7789, 8175, 3149, 807, 2754, 8174, 3062, 7])).
% 2.04/2.23 tff(8341,plain,
% 2.04/2.23 (z = elem!1),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[2689, 8340])).
% 2.04/2.23 tff(8342,plain,
% 2.04/2.23 ((s(s(s(s(s(elem!1))))) = z) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 2.04/2.23 inference(monotonicity,[status(thm)],[8341])).
% 2.04/2.23 tff(8343,plain,
% 2.04/2.23 ((~(s(s(s(s(s(elem!1))))) = z)) <=> (~(s(s(s(s(s(elem!1))))) = elem!1))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[8342])).
% 2.04/2.23 tff(8344,plain,
% 2.04/2.23 (~(s(s(s(s(s(elem!1))))) = elem!1)),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[1822, 8343])).
% 2.04/2.23 tff(8345,plain,
% 2.04/2.23 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[2724, 8340])).
% 2.04/2.23 tff(8346,plain,
% 2.04/2.23 (~(s(s(elem!1)) = s(elem!1))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[1181, 8345])).
% 2.04/2.23 tff(8347,plain,
% 2.04/2.23 (b(s(s(elem!1)), s(elem!1))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[994, 8346, 3149])).
% 2.04/2.23 tff(8348,plain,
% 2.04/2.23 (~(elem!1 = s(s(elem!1)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[1168, 8345])).
% 2.04/2.23 tff(8349,plain,
% 2.04/2.23 (~(s(s(elem!1)) = elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[1174, 8348])).
% 2.04/2.23 tff(8350,plain,
% 2.04/2.23 (r(s(s(elem!1)), elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[47, 8349, 6481])).
% 2.04/2.23 tff(8351,plain,
% 2.04/2.23 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[1511, 8341])).
% 2.04/2.23 tff(8352,plain,
% 2.04/2.23 (~(elem!1 = s(s(s(elem!1))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[1518, 8351])).
% 2.04/2.23 tff(8353,plain,
% 2.04/2.23 (~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[1655, 8352])).
% 2.04/2.23 tff(8354,plain,
% 2.04/2.23 (~(s(elem!1) = elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[2698, 8341])).
% 2.04/2.23 tff(8355,plain,
% 2.04/2.23 (r(s(elem!1), elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[813, 8354, 807])).
% 2.04/2.23 tff(8356,plain,
% 2.04/2.23 (~(s(elem!1) = s(s(elem!1)))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[8346, 1658])).
% 2.04/2.23 tff(8357,plain,
% 2.04/2.23 (~r(s(elem!1), s(s(elem!1)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[1680, 124, 8355, 8350])).
% 2.04/2.23 tff(8358,plain,
% 2.04/2.23 ((s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[1684, 43, 8357])).
% 2.04/2.23 tff(8359,plain,
% 2.04/2.23 (b(s(elem!1), s(s(elem!1)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[8358, 8356])).
% 2.04/2.23 tff(8360,plain,
% 2.04/2.23 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[1850, 8359, 8355, 8353, 8341, 8350, 8347])).
% 2.04/2.23 tff(8361,plain,
% 2.04/2.23 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[1855, 8360, 8344])).
% 2.04/2.23 tff(8362,plain,
% 2.04/2.23 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 2.04/2.23 inference(monotonicity,[status(thm)],[8341])).
% 2.04/2.23 tff(8363,plain,
% 2.04/2.23 (r(s(s(s(s(elem!1)))), z) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 2.04/2.23 inference(monotonicity,[status(thm)],[8341])).
% 2.04/2.23 tff(8364,plain,
% 2.04/2.23 (r(s(s(s(s(elem!1)))), elem!1) <=> r(s(s(s(s(elem!1)))), z)),
% 2.04/2.23 inference(symmetry,[status(thm)],[8363])).
% 2.04/2.23 tff(8365,plain,
% 2.04/2.23 ((~r(s(s(s(s(elem!1)))), elem!1)) <=> (~r(s(s(s(s(elem!1)))), z))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[8364])).
% 2.04/2.23 tff(8366,plain,
% 2.04/2.23 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[1284, 8345])).
% 2.04/2.23 tff(8367,plain,
% 2.04/2.23 (r(elem!1, s(s(elem!1)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[516, 8348, 2754])).
% 2.04/2.23 tff(8368,plain,
% 2.04/2.23 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[152, 8345])).
% 2.04/2.23 tff(8369,plain,
% 2.04/2.23 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[159, 8368])).
% 2.04/2.23 tff(8370,plain,
% 2.04/2.23 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[610, 8369, 8175])).
% 2.04/2.23 tff(8371,plain,
% 2.04/2.23 (~(s(s(s(elem!1))) = elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[2187, 8352])).
% 2.04/2.23 tff(8372,plain,
% 2.04/2.23 (b(s(s(s(elem!1))), elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[1636, 8371, 7789])).
% 2.04/2.23 tff(8373,plain,
% 2.04/2.23 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[2053, 8372, 8370, 8367, 8341])).
% 2.04/2.23 tff(8374,plain,
% 2.04/2.23 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[1302, 8373, 8366])).
% 2.04/2.23 tff(8375,plain,
% 2.04/2.23 (~r(s(s(s(s(elem!1)))), elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[2000, 8374, 8341, 8347, 8355])).
% 2.04/2.23 tff(8376,plain,
% 2.04/2.23 (~r(s(s(s(s(elem!1)))), z)),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[8375, 8365])).
% 2.04/2.23 tff(8377,plain,
% 2.04/2.23 (b(s(s(s(s(elem!1)))), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[5723, 8376])).
% 2.04/2.23 tff(8378,plain,
% 2.04/2.23 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[8377, 8362])).
% 2.04/2.23 tff(8379,plain,
% 2.04/2.23 (b(z, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[8341])).
% 2.04/2.23 tff(8380,plain,
% 2.04/2.23 (~r(z, s(s(s(elem!1))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[950, 8370, 8186])).
% 2.04/2.23 tff(8381,plain,
% 2.04/2.23 (b(z, s(s(s(elem!1))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[585, 8380])).
% 2.04/2.23 tff(8382,plain,
% 2.04/2.23 (b(elem!1, s(s(s(elem!1))))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[8381, 8379])).
% 2.04/2.23 tff(8383,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), 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(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), 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(s(elem!1)))))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(8384,plain,
% 2.04/2.24 (((~b(s(s(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(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(8385,plain,
% 2.04/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), 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(s(elem!1))))))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[8384])).
% 2.04/2.24 tff(8386,plain,
% 2.04/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), 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(s(elem!1)))))))),
% 2.04/2.24 inference(transitivity,[status(thm)],[8385, 8383])).
% 2.04/2.24 tff(8387,plain,
% 2.04/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(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)))))))),
% 2.04/2.24 inference(quant_inst,[status(thm)],[])).
% 2.04/2.24 tff(8388,plain,
% 2.04/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(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(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[8387, 8386])).
% 2.04/2.24 tff(8389,plain,
% 2.04/2.24 (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[8388, 306, 8382, 8372, 8378, 8361])).
% 2.04/2.24 tff(8390,plain,
% 2.04/2.24 (~(s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1)))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1904, 8341])).
% 2.04/2.24 tff(8391,plain,
% 2.04/2.24 (r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1940, 43, 8390, 8389])).
% 2.04/2.24 tff(8392,plain,
% 2.04/2.24 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1862, 306, 8382, 8372, 8361])).
% 2.04/2.24 tff(8393,plain,
% 2.04/2.24 (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1719, 8366])).
% 2.04/2.24 tff(8394,plain,
% 2.04/2.24 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1867, 43, 8393, 8392])).
% 2.04/2.24 tff(8395,plain,
% 2.04/2.24 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1776, 306, 8382, 8372, 8378])).
% 2.04/2.24 tff(8396,plain,
% 2.04/2.24 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1954, 8341])).
% 2.04/2.24 tff(8397,plain,
% 2.04/2.24 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1958, 43, 8396, 8395])).
% 2.04/2.24 tff(8398,plain,
% 2.04/2.24 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(8399,plain,
% 2.04/2.24 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 2.04/2.24 inference(quant_inst,[status(thm)],[])).
% 2.04/2.24 tff(8400,plain,
% 2.04/2.24 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[8399, 8398])).
% 2.04/2.24 tff(8401,plain,
% 2.04/2.24 ($false),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[8400, 124, 8397, 8394, 8391])).
% 2.04/2.24 tff(8402,plain,(r(s(s(s(elem!1))), elem!1) | b(s(s(elem!1)), elem!1) | b(s(s(s(elem!1))), s(s(elem!1))) | b(s(elem!1), elem!1) | b(elem!1, s(s(elem!1))) | r(s(s(elem!1)), s(elem!1)) | b(z, s(s(elem!1))) | r(elem!1, z) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.04/2.24 tff(8403,plain,
% 2.04/2.24 ($false),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[8402, 8173, 8172, 807, 8153, 8144, 8150, 8130, 8146, 8108])).
% 2.04/2.24 tff(8404,plain,((s(z) = elem!1) | b(s(elem!1), elem!1) | (~r(s(s(s(z))), s(z))) | b(s(z), elem!1) | r(s(s(s(z))), z) | b(elem!1, z) | (~b(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | b(z, elem!1) | r(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.24 tff(8405,plain,
% 2.04/2.24 (b(s(elem!1), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[8404, 8016, 206, 3094, 1629, 2, 5335, 1034, 5318, 2607])).
% 2.04/2.24 tff(8406,plain,
% 2.04/2.24 (~b(s(elem!1), s(s(s(z))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[2363, 306, 8405, 5335, 8025])).
% 2.04/2.24 tff(8407,plain,
% 2.04/2.24 ((s(elem!1) = s(s(s(z)))) | r(s(elem!1), s(s(s(z))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[2367, 43, 8406])).
% 2.04/2.24 tff(8408,plain,
% 2.04/2.24 (r(s(elem!1), s(s(s(z))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[8407, 8043])).
% 2.04/2.24 tff(8409,plain,
% 2.04/2.24 (~r(s(elem!1), s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[8076, 124, 1034, 8408])).
% 2.04/2.24 tff(8410,plain,
% 2.04/2.24 (b(s(elem!1), s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[2964, 8409, 3099])).
% 2.04/2.24 tff(8411,plain,
% 2.04/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(8412,plain,
% 2.04/2.24 (((~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), elem!1))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(8413,plain,
% 2.04/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z)))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[8412])).
% 2.04/2.24 tff(8414,plain,
% 2.04/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))),
% 2.04/2.24 inference(transitivity,[status(thm)],[8413, 8411])).
% 2.04/2.24 tff(8415,plain,
% 2.04/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), elem!1)))),
% 2.04/2.24 inference(quant_inst,[status(thm)],[])).
% 2.04/2.24 tff(8416,plain,
% 2.04/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z)))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[8415, 8414])).
% 2.04/2.24 tff(8417,plain,
% 2.04/2.24 ($false),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[8416, 306, 8405, 5333, 8410, 8021, 8019])).
% 2.04/2.24 tff(8418,plain,((z = elem!1) | (~r(s(z), s(s(s(z))))) | (s(z) = elem!1) | (~r(s(s(s(z))), s(z))) | r(s(s(s(z))), z) | b(elem!1, z) | b(z, elem!1) | r(elem!1, s(z)) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.04/2.24 tff(8419,plain,
% 2.04/2.24 (z = elem!1),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[8418, 5329, 1034, 114, 1629, 2, 5318, 2607, 1484])).
% 2.04/2.24 tff(8420,plain,
% 2.04/2.24 (s(z) = s(elem!1)),
% 2.04/2.24 inference(monotonicity,[status(thm)],[8419])).
% 2.04/2.24 tff(8421,plain,
% 2.04/2.24 (s(s(z)) = s(s(elem!1))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[8420])).
% 2.04/2.24 tff(8422,plain,
% 2.04/2.24 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[8421])).
% 2.04/2.24 tff(8423,plain,
% 2.04/2.24 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[8422])).
% 2.04/2.24 tff(8424,plain,
% 2.04/2.24 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 2.04/2.24 inference(symmetry,[status(thm)],[8423])).
% 2.04/2.24 tff(8425,plain,
% 2.04/2.24 (r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z))))))) <=> r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[8424])).
% 2.04/2.24 tff(8426,plain,
% 2.04/2.24 (r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) <=> r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))),
% 2.04/2.24 inference(symmetry,[status(thm)],[8425])).
% 2.04/2.24 tff(8427,plain,
% 2.04/2.24 ((s(s(s(s(elem!1)))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(z)))) = s(s(s(s(s(s(z)))))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[8424])).
% 2.04/2.24 tff(8428,plain,
% 2.04/2.24 ((s(s(s(s(elem!1)))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = s(s(s(s(z)))))),
% 2.04/2.24 inference(transitivity,[status(thm)],[8427, 4708])).
% 2.04/2.24 tff(8429,plain,
% 2.04/2.24 ((s(s(s(s(elem!1)))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(z)))) = s(s(s(s(s(s(z)))))))),
% 2.04/2.24 inference(transitivity,[status(thm)],[8428, 4847])).
% 2.04/2.24 tff(8430,plain,
% 2.04/2.24 ((~(s(s(s(s(elem!1)))) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(s(s(z)))) = s(s(s(s(s(s(z))))))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[8429])).
% 2.04/2.24 tff(8431,plain,
% 2.04/2.24 (s(elem!1) = s(z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[2251, 8419])).
% 2.04/2.24 tff(8432,plain,
% 2.04/2.24 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[2724, 8431])).
% 2.04/2.24 tff(8433,plain,
% 2.04/2.24 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1284, 8432])).
% 2.04/2.24 tff(8434,plain,
% 2.04/2.24 (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1719, 8433])).
% 2.04/2.24 tff(8435,plain,
% 2.04/2.24 (~(s(s(s(s(elem!1)))) = s(s(s(s(s(s(z)))))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[3709, 8434, 8419])).
% 2.04/2.24 tff(8436,plain,
% 2.04/2.24 (~(s(s(s(s(z)))) = s(s(s(s(s(s(z)))))))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[8435, 8430])).
% 2.04/2.24 tff(8437,plain,
% 2.04/2.24 (b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z))))))) <=> b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[8424])).
% 2.04/2.24 tff(8438,plain,
% 2.04/2.24 ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))) <=> (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[8437])).
% 2.04/2.24 tff(8439,plain,
% 2.04/2.24 ((s(s(s(s(s(s(z)))))) = z) <=> (s(s(s(s(s(s(z)))))) = elem!1)),
% 2.04/2.24 inference(monotonicity,[status(thm)],[8419])).
% 2.04/2.24 tff(8440,plain,
% 2.04/2.24 ((~(s(s(s(s(s(s(z)))))) = z)) <=> (~(s(s(s(s(s(s(z)))))) = elem!1))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[8439])).
% 2.04/2.24 tff(8441,plain,
% 2.04/2.24 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[554, 8440])).
% 2.04/2.24 tff(8442,plain,
% 2.04/2.24 (~(elem!1 = s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[3096, 5329])).
% 2.04/2.24 tff(8443,plain,
% 2.04/2.24 (b(elem!1, s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[5332, 8442])).
% 2.04/2.24 tff(8444,plain,
% 2.04/2.24 (b(s(elem!1), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[8404, 2715, 206, 3094, 1629, 2, 1967, 1034, 5318, 2607])).
% 2.04/2.24 tff(8445,plain,
% 2.04/2.24 (~b(s(elem!1), z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[2718, 2715, 1502])).
% 2.04/2.24 tff(8446,plain,
% 2.04/2.24 ($false),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[2709, 8445, 8444, 1502])).
% 2.04/2.24 tff(8447,plain,(b(s(z), elem!1) | (~(z = elem!1)) | (~r(s(s(s(z))), s(z))) | (s(z) = elem!1) | r(s(s(s(z))), z) | b(elem!1, z) | (~b(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | b(z, elem!1) | r(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.24 tff(8448,plain,
% 2.04/2.24 (b(s(z), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[8447, 8419, 114, 5329, 1629, 2, 5328, 1034, 5318, 2607])).
% 2.04/2.24 tff(8449,plain,
% 2.04/2.24 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[5377, 8448, 5328, 8443, 1034])).
% 2.04/2.24 tff(8450,plain,
% 2.04/2.24 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1144, 8449, 8441])).
% 2.04/2.24 tff(8451,plain,
% 2.04/2.24 (~(elem!1 = s(s(elem!1)))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1168, 8432])).
% 2.04/2.24 tff(8452,plain,
% 2.04/2.24 (~(s(s(elem!1)) = elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1174, 8451])).
% 2.04/2.24 tff(8453,plain,
% 2.04/2.24 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[2974, 8442])).
% 2.04/2.24 tff(8454,plain,
% 2.04/2.24 (~b(s(s(elem!1)), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[7970, 8448, 8453, 114, 5328, 8443])).
% 2.04/2.24 tff(8455,plain,
% 2.04/2.24 (r(s(s(elem!1)), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[47, 8454, 8452])).
% 2.04/2.24 tff(8456,plain,
% 2.04/2.24 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(8457,plain,
% 2.04/2.24 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))))),
% 2.04/2.24 inference(quant_inst,[status(thm)],[])).
% 2.04/2.24 tff(8458,plain,
% 2.04/2.24 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1))))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[8457, 8456])).
% 2.04/2.24 tff(8459,plain,
% 2.04/2.24 (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[8458, 124, 8455, 8450])).
% 2.04/2.24 tff(8460,plain,
% 2.04/2.24 ((s(s(z)) = s(s(s(s(s(s(z))))))) <=> (s(s(elem!1)) = s(s(s(s(s(s(z)))))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[8421])).
% 2.04/2.24 tff(8461,plain,
% 2.04/2.24 ((s(s(z)) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = s(s(elem!1)))),
% 2.04/2.24 inference(transitivity,[status(thm)],[8460, 3240])).
% 2.04/2.24 tff(8462,plain,
% 2.04/2.24 ((~(s(s(z)) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(s(s(s(s(z)))))) = s(s(elem!1))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[8461])).
% 2.04/2.24 tff(8463,plain,
% 2.04/2.24 (~(s(s(s(s(s(s(z)))))) = s(s(elem!1)))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[2826, 8462])).
% 2.04/2.24 tff(8464,plain,
% 2.04/2.24 (b(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[3247, 43, 8463, 8459])).
% 2.04/2.24 tff(8465,plain,
% 2.04/2.24 (elem!1 = z),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1618, 8419])).
% 2.04/2.24 tff(8466,plain,
% 2.04/2.24 (~r(s(s(s(elem!1))), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1631, 8465, 1629])).
% 2.04/2.24 tff(8467,plain,
% 2.04/2.24 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1511, 8419])).
% 2.04/2.24 tff(8468,plain,
% 2.04/2.24 (~(elem!1 = s(s(s(elem!1))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1518, 8467])).
% 2.04/2.24 tff(8469,plain,
% 2.04/2.24 (~(s(s(s(elem!1))) = elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[2187, 8468])).
% 2.04/2.24 tff(8470,plain,
% 2.04/2.24 (b(s(s(s(elem!1))), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1636, 8469, 8466])).
% 2.04/2.24 tff(8471,plain,
% 2.04/2.24 (r(z, s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[8419])).
% 2.04/2.24 tff(8472,plain,
% 2.04/2.24 (b(z, s(elem!1))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[4412, 8419, 8443])).
% 2.04/2.24 tff(8473,plain,
% 2.04/2.24 (b(s(elem!1), z) <=> b(s(elem!1), elem!1)),
% 2.04/2.24 inference(monotonicity,[status(thm)],[8419])).
% 2.04/2.24 tff(8474,plain,
% 2.04/2.24 (b(s(elem!1), elem!1) <=> b(s(elem!1), z)),
% 2.04/2.24 inference(symmetry,[status(thm)],[8473])).
% 2.04/2.24 tff(8475,plain,
% 2.04/2.24 (b(s(z), elem!1) <=> b(s(elem!1), elem!1)),
% 2.04/2.24 inference(monotonicity,[status(thm)],[8420])).
% 2.04/2.24 tff(8476,plain,
% 2.04/2.24 (b(s(z), elem!1) <=> b(s(elem!1), z)),
% 2.04/2.24 inference(transitivity,[status(thm)],[8475, 8474])).
% 2.04/2.24 tff(8477,plain,
% 2.04/2.24 (b(s(elem!1), z)),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[8448, 8476])).
% 2.04/2.24 tff(8478,plain,
% 2.04/2.24 (~(s(elem!1) = elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[2698, 8419])).
% 2.04/2.24 tff(8479,plain,
% 2.04/2.24 (~(s(s(elem!1)) = s(elem!1))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[195, 8478])).
% 2.04/2.24 tff(8480,plain,
% 2.04/2.24 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.04/2.24 inference(symmetry,[status(thm)],[8422])).
% 2.04/2.24 tff(8481,plain,
% 2.04/2.24 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(z))), s(elem!1))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[8480])).
% 2.04/2.24 tff(8482,plain,
% 2.04/2.24 (r(s(s(s(z))), s(elem!1)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 2.04/2.24 inference(symmetry,[status(thm)],[8481])).
% 2.04/2.24 tff(8483,plain,
% 2.04/2.24 (r(s(s(s(z))), s(z)) <=> r(s(s(s(z))), s(elem!1))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[8420])).
% 2.04/2.24 tff(8484,plain,
% 2.04/2.24 (r(s(s(s(z))), s(elem!1))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[114, 8483])).
% 2.04/2.24 tff(8485,plain,
% 2.04/2.24 (r(s(s(s(elem!1))), s(elem!1))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[8484, 8482])).
% 2.04/2.24 tff(8486,plain,
% 2.04/2.24 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[152, 8432])).
% 2.04/2.24 tff(8487,plain,
% 2.04/2.24 ((s(s(s(s(s(s(z)))))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(s(s(s(z)))))))),
% 2.04/2.24 inference(symmetry,[status(thm)],[3240])).
% 2.04/2.24 tff(8488,plain,
% 2.04/2.24 ((~(s(s(s(s(s(s(z)))))) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = s(s(s(s(s(s(z))))))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[8487])).
% 2.04/2.24 tff(8489,plain,
% 2.04/2.24 (~(s(s(elem!1)) = s(s(s(s(s(s(z)))))))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[8463, 8488])).
% 2.04/2.24 tff(8490,plain,
% 2.04/2.24 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(z)))))))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(8491,plain,
% 2.04/2.24 (((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(z)))))))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(8492,plain,
% 2.04/2.24 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(z))))))))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[8491])).
% 2.04/2.24 tff(8493,plain,
% 2.04/2.24 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(z)))))))))),
% 2.04/2.24 inference(transitivity,[status(thm)],[8492, 8490])).
% 2.04/2.24 tff(8494,plain,
% 2.04/2.24 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(z)))))))))),
% 2.04/2.24 inference(quant_inst,[status(thm)],[])).
% 2.04/2.24 tff(8495,plain,
% 2.04/2.24 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(z))))))))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[8494, 8493])).
% 2.04/2.24 tff(8496,plain,
% 2.04/2.24 (~r(s(s(elem!1)), s(s(s(s(s(s(z)))))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[8495, 124, 8455, 8450])).
% 2.04/2.24 tff(8497,plain,
% 2.04/2.24 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(s(s(z))))))) | b(s(s(elem!1)), s(s(s(s(s(s(z))))))) | r(s(s(elem!1)), s(s(s(s(s(s(z))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(s(s(z))))))) | b(s(s(elem!1)), s(s(s(s(s(s(z))))))) | r(s(s(elem!1)), s(s(s(s(s(s(z))))))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(8498,plain,
% 2.04/2.24 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(s(s(z))))))) | b(s(s(elem!1)), s(s(s(s(s(s(z))))))) | r(s(s(elem!1)), s(s(s(s(s(s(z))))))))),
% 2.04/2.24 inference(quant_inst,[status(thm)],[])).
% 2.04/2.24 tff(8499,plain,
% 2.04/2.24 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(s(s(z))))))) | b(s(s(elem!1)), s(s(s(s(s(s(z))))))) | r(s(s(elem!1)), s(s(s(s(s(s(z)))))))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[8498, 8497])).
% 2.04/2.24 tff(8500,plain,
% 2.04/2.24 ((s(s(elem!1)) = s(s(s(s(s(s(z))))))) | b(s(s(elem!1)), s(s(s(s(s(s(z)))))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[8499, 43, 8496])).
% 2.04/2.24 tff(8501,plain,
% 2.04/2.24 (b(s(s(elem!1)), s(s(s(s(s(s(z)))))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[8500, 8489])).
% 2.04/2.24 tff(8502,assumption,(b(s(s(s(s(s(s(z)))))), s(s(elem!1)))), introduced(assumption)).
% 2.04/2.24 tff(8503,assumption,(b(s(s(elem!1)), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 2.04/2.24 tff(8504,plain,
% 2.04/2.24 (r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[5336, 2870])).
% 2.04/2.24 tff(8505,plain,
% 2.04/2.24 (r(s(elem!1), s(s(s(z)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[1507])).
% 2.04/2.24 tff(8506,plain,
% 2.04/2.24 (r(s(z), s(s(s(z)))) <=> r(s(elem!1), s(s(s(z))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[1503])).
% 2.04/2.24 tff(8507,plain,
% 2.04/2.24 (r(s(elem!1), s(s(s(z))))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[1034, 8506])).
% 2.04/2.24 tff(8508,plain,
% 2.04/2.24 (r(s(elem!1), s(s(s(elem!1))))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[8507, 8505])).
% 2.04/2.24 tff(8509,plain,
% 2.04/2.24 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(8510,plain,
% 2.04/2.24 (((~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(s(s(z))))))))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(8511,plain,
% 2.04/2.24 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[8510])).
% 2.04/2.25 tff(8512,plain,
% 2.04/2.25 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 2.04/2.25 inference(transitivity,[status(thm)],[8511, 8509])).
% 2.04/2.25 tff(8513,plain,
% 2.04/2.25 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(s(s(z)))))))))),
% 2.04/2.25 inference(quant_inst,[status(thm)],[])).
% 2.04/2.25 tff(8514,plain,
% 2.04/2.25 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[8513, 8512])).
% 2.04/2.25 tff(8515,plain,
% 2.04/2.25 (~r(s(elem!1), s(s(s(s(s(s(z)))))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[8514, 124, 8508, 8504])).
% 2.04/2.25 tff(8516,plain,
% 2.04/2.25 ((s(elem!1) = s(s(s(s(s(s(z))))))) | b(s(elem!1), s(s(s(s(s(s(z)))))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[3862, 43, 8515])).
% 2.04/2.25 tff(8517,plain,
% 2.04/2.25 (b(s(elem!1), s(s(s(s(s(s(z)))))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[8516, 3852])).
% 2.04/2.25 tff(8518,plain,
% 2.04/2.25 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(8519,plain,
% 2.04/2.25 (((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1)))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(8520,plain,
% 2.04/2.25 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[8519])).
% 2.04/2.25 tff(8521,plain,
% 2.04/2.25 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 2.04/2.25 inference(transitivity,[status(thm)],[8520, 8518])).
% 2.04/2.25 tff(8522,plain,
% 2.04/2.25 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 2.04/2.25 inference(quant_inst,[status(thm)],[])).
% 2.04/2.25 tff(8523,plain,
% 2.04/2.25 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[8522, 8521])).
% 2.04/2.25 tff(8524,plain,
% 2.04/2.25 (~r(s(s(s(s(s(s(z)))))), s(elem!1))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[8523, 124, 8508, 8504])).
% 2.04/2.25 tff(8525,plain,
% 2.04/2.25 (b(s(s(s(s(s(s(z)))))), s(elem!1))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[3220, 43, 3217, 8524])).
% 2.04/2.25 tff(8526,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(8527,plain,
% 2.04/2.25 (((~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(z)))))))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~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(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(8528,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(z)))))))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(z))))))))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[8527])).
% 2.04/2.25 tff(8529,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(z)))))))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))))),
% 2.04/2.25 inference(transitivity,[status(thm)],[8528, 8526])).
% 2.04/2.25 tff(8530,plain,
% 2.04/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(z)))))))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(s(elem!1), s(s(elem!1)))))),
% 2.04/2.25 inference(quant_inst,[status(thm)],[])).
% 2.04/2.25 tff(8531,plain,
% 2.04/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(z))))))))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[8530, 8529])).
% 2.04/2.25 tff(8532,plain,
% 2.04/2.25 (~b(s(elem!1), s(s(elem!1)))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[8531, 306, 8525, 8517, 8503])).
% 2.04/2.25 tff(8533,plain,
% 2.04/2.25 (r(s(elem!1), s(s(elem!1)))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[1684, 43, 8532, 4690])).
% 2.04/2.25 tff(8534,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(8535,plain,
% 2.04/2.25 (((~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(z)))))))) | (~b(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(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(8536,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(z)))))))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(z))))))))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[8535])).
% 2.04/2.25 tff(8537,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(z)))))))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))))),
% 2.04/2.25 inference(transitivity,[status(thm)],[8536, 8534])).
% 2.04/2.25 tff(8538,plain,
% 2.04/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(z)))))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.04/2.25 inference(quant_inst,[status(thm)],[])).
% 2.04/2.25 tff(8539,plain,
% 2.04/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(z))))))))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[8538, 8537])).
% 2.04/2.25 tff(8540,plain,
% 2.04/2.25 (~b(s(s(elem!1)), s(elem!1))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[8539, 306, 8525, 8517, 8503])).
% 2.04/2.25 tff(8541,plain,
% 2.04/2.25 (r(s(s(elem!1)), s(elem!1))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[994, 8540, 4685])).
% 2.04/2.25 tff(8542,plain,
% 2.04/2.25 (~r(s(elem!1), elem!1)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[7985, 8541, 1730])).
% 2.04/2.25 tff(8543,plain,
% 2.04/2.25 (b(s(elem!1), elem!1)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[813, 8542, 4675])).
% 2.04/2.25 tff(8544,plain,
% 2.04/2.25 (r(z, s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[1502])).
% 2.04/2.25 tff(8545,plain,
% 2.04/2.25 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[1726])).
% 2.04/2.25 tff(8546,plain,
% 2.04/2.25 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.04/2.25 inference(symmetry,[status(thm)],[8545])).
% 2.04/2.25 tff(8547,plain,
% 2.04/2.25 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[1506])).
% 2.04/2.25 tff(8548,plain,
% 2.04/2.25 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.04/2.25 inference(transitivity,[status(thm)],[8547, 8546])).
% 2.04/2.25 tff(8549,plain,
% 2.04/2.25 (~r(s(s(z)), s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[5501, 5336, 4346, 2831, 1034])).
% 2.04/2.25 tff(8550,plain,
% 2.04/2.25 (b(s(s(z)), s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[2514, 8549])).
% 2.04/2.25 tff(8551,plain,
% 2.04/2.25 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[8550, 8548])).
% 2.04/2.25 tff(8552,plain,
% 2.04/2.25 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[659, 8541, 654])).
% 2.04/2.25 tff(8553,plain,
% 2.04/2.25 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[610, 8552, 4671])).
% 2.04/2.25 tff(8554,plain,
% 2.04/2.25 (r(z, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[1502])).
% 2.04/2.25 tff(8555,plain,
% 2.04/2.25 (r(elem!1, s(s(s(elem!1)))) <=> r(z, s(s(s(elem!1))))),
% 2.04/2.25 inference(symmetry,[status(thm)],[8554])).
% 2.04/2.25 tff(8556,plain,
% 2.04/2.25 ((~r(elem!1, s(s(s(elem!1))))) <=> (~r(z, s(s(s(elem!1)))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[8555])).
% 2.04/2.25 tff(8557,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(8558,plain,
% 2.04/2.25 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(8559,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z))))))))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[8558])).
% 2.04/2.25 tff(8560,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))),
% 2.04/2.25 inference(transitivity,[status(thm)],[8559, 8557])).
% 2.04/2.25 tff(8561,plain,
% 2.04/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))),
% 2.04/2.25 inference(quant_inst,[status(thm)],[])).
% 2.04/2.25 tff(8562,plain,
% 2.04/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z))))))))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[8561, 8560])).
% 2.04/2.25 tff(8563,plain,
% 2.04/2.25 (~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[8562, 306, 8551, 1664, 8553, 8502])).
% 2.04/2.25 tff(8564,plain,
% 2.04/2.25 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[8563, 3925])).
% 2.04/2.25 tff(8565,plain,
% 2.04/2.25 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[3207, 8564])).
% 2.04/2.25 tff(8566,plain,
% 2.04/2.25 (r(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[8565, 3924])).
% 2.04/2.25 tff(8567,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(8568,plain,
% 2.04/2.25 (((~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(z))))))))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(8569,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(elem!1), s(s(s(s(s(s(z))))))))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[8568])).
% 2.04/2.25 tff(8570,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))))),
% 2.04/2.25 inference(transitivity,[status(thm)],[8569, 8567])).
% 2.04/2.25 tff(8571,plain,
% 2.04/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))),
% 2.04/2.25 inference(quant_inst,[status(thm)],[])).
% 2.04/2.25 tff(8572,plain,
% 2.04/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(elem!1), s(s(s(s(s(s(z))))))))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[8571, 8570])).
% 2.04/2.25 tff(8573,plain,
% 2.04/2.25 (~b(elem!1, s(s(s(s(s(s(z)))))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[8572, 306, 4677, 8525, 8517])).
% 2.04/2.25 tff(8574,plain,
% 2.04/2.25 ((elem!1 = s(s(s(s(s(s(z))))))) | r(elem!1, s(s(s(s(s(s(z)))))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[3921, 43, 8573])).
% 2.04/2.25 tff(8575,plain,
% 2.04/2.25 (r(elem!1, s(s(s(s(s(s(z)))))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[8574, 3894])).
% 2.04/2.25 tff(8576,plain,
% 2.04/2.25 (~r(elem!1, s(s(s(elem!1))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[3935, 124, 8575, 8566])).
% 2.04/2.25 tff(8577,plain,
% 2.04/2.25 (~r(z, s(s(s(elem!1))))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[8576, 8556])).
% 2.04/2.25 tff(8578,plain,
% 2.04/2.25 (b(z, s(s(s(elem!1))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[585, 8577])).
% 2.04/2.25 tff(8579,plain,
% 2.04/2.25 (~b(z, s(s(elem!1)))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[1598, 8578, 8553, 8551])).
% 2.04/2.25 tff(8580,plain,
% 2.04/2.25 (r(z, s(s(elem!1)))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[460, 8579])).
% 2.04/2.25 tff(8581,plain,
% 2.04/2.25 (r(elem!1, s(s(elem!1)))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[8580, 8544])).
% 2.04/2.25 tff(8582,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(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(s(s(s(elem!1)))))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(8583,plain,
% 2.04/2.25 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(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(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(s(s(s(elem!1)))))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(8584,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(s(s(s(elem!1))))))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[8583])).
% 2.04/2.25 tff(8585,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(s(s(s(elem!1)))))))),
% 2.04/2.25 inference(transitivity,[status(thm)],[8584, 8582])).
% 2.04/2.25 tff(8586,plain,
% 2.04/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(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))))),
% 2.04/2.25 inference(quant_inst,[status(thm)],[])).
% 2.04/2.25 tff(8587,plain,
% 2.04/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[8586, 8585])).
% 2.04/2.25 tff(8588,plain,
% 2.04/2.25 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[8587, 306, 1924, 816, 1908])).
% 2.04/2.25 tff(8589,plain,
% 2.04/2.25 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[4456, 124, 1288, 4445])).
% 2.04/2.25 tff(8590,plain,
% 2.04/2.25 ($false),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[1767, 43, 1516, 8589, 8588])).
% 2.04/2.25 tff(8591,plain,((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (s(s(s(s(elem!1)))) = s(elem!1)) | (~b(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (elem!1 = s(s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = elem!1) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.25 tff(8592,plain,
% 2.04/2.25 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[8591, 8581, 8543, 8533, 1807, 1550, 1512])).
% 2.04/2.25 tff(8593,plain,
% 2.04/2.25 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[1302, 8592, 4684])).
% 2.04/2.25 tff(8594,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), 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(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), 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(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(8595,plain,
% 2.04/2.26 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), 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(s(z))))))))) <=> ((~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(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(8596,plain,
% 2.04/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), 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(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z))))))))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[8595])).
% 2.04/2.26 tff(8597,plain,
% 2.04/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), 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(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))))),
% 2.04/2.26 inference(transitivity,[status(thm)],[8596, 8594])).
% 2.04/2.26 tff(8598,plain,
% 2.04/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), 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(s(z)))))))))),
% 2.04/2.26 inference(quant_inst,[status(thm)],[])).
% 2.04/2.26 tff(8599,plain,
% 2.04/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), 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(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z))))))))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[8598, 8597])).
% 2.04/2.26 tff(8600,plain,
% 2.04/2.26 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[8599, 306, 8551, 1664, 8593, 8502])).
% 2.04/2.26 tff(8601,plain,
% 2.04/2.26 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[8600, 4852])).
% 2.04/2.26 tff(8602,plain,
% 2.04/2.26 (r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[4864, 8601, 4850])).
% 2.04/2.26 tff(8603,plain,
% 2.04/2.26 (r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[8602, 4846])).
% 2.04/2.26 tff(8604,plain,
% 2.04/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(8605,plain,
% 2.04/2.26 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(8606,plain,
% 2.04/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), 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(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[8605])).
% 2.04/2.26 tff(8607,plain,
% 2.04/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), 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(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.04/2.26 inference(transitivity,[status(thm)],[8606, 8604])).
% 2.04/2.26 tff(8608,plain,
% 2.04/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), 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(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.04/2.26 inference(quant_inst,[status(thm)],[])).
% 2.04/2.26 tff(8609,plain,
% 2.04/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[8608, 8607])).
% 2.04/2.26 tff(8610,plain,
% 2.04/2.26 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[8609, 306, 8551, 1664, 8553, 8593])).
% 2.04/2.26 tff(8611,plain,
% 2.04/2.26 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[1958, 43, 1955, 8610])).
% 2.04/2.26 tff(8612,plain,
% 2.04/2.26 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(8613,plain,
% 2.04/2.26 (((~r(s(s(s(s(s(s(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)))), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(8614,plain,
% 2.04/2.26 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(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)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[8613])).
% 2.04/2.26 tff(8615,plain,
% 2.04/2.26 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(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)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 2.04/2.26 inference(transitivity,[status(thm)],[8614, 8612])).
% 2.04/2.26 tff(8616,plain,
% 2.04/2.26 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(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)))), s(s(s(s(s(s(z)))))))))),
% 2.04/2.26 inference(quant_inst,[status(thm)],[])).
% 2.04/2.26 tff(8617,plain,
% 2.04/2.26 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[8616, 8615])).
% 2.04/2.26 tff(8618,plain,
% 2.04/2.26 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[8617, 124, 8504, 8611])).
% 2.04/2.26 tff(8619,plain,
% 2.04/2.26 ($false),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[8618, 8603])).
% 2.04/2.26 tff(8620,plain,((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~(z = elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.26 tff(8621,plain,
% 2.04/2.26 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[8620, 8419, 8470, 8464, 8485, 8455, 8501, 8443, 8448, 1034])).
% 2.04/2.26 tff(8622,plain,
% 2.04/2.26 (b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[2880, 8621, 8419])).
% 2.04/2.26 tff(8623,plain,
% 2.04/2.26 (b(z, s(elem!1)) <=> b(elem!1, s(elem!1))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[8419])).
% 2.04/2.26 tff(8624,plain,
% 2.04/2.26 (b(elem!1, s(elem!1))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[8472, 8623])).
% 2.04/2.26 tff(8625,plain,
% 2.04/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(8626,plain,
% 2.04/2.26 (((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(z))))))))) <=> ((~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)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(8627,plain,
% 2.04/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[8626])).
% 2.04/2.26 tff(8628,plain,
% 2.04/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 2.04/2.26 inference(transitivity,[status(thm)],[8627, 8625])).
% 2.04/2.26 tff(8629,plain,
% 2.04/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(z)))))))))),
% 2.04/2.26 inference(quant_inst,[status(thm)],[])).
% 2.04/2.26 tff(8630,plain,
% 2.04/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[8629, 8628])).
% 2.04/2.26 tff(8631,plain,
% 2.04/2.26 ($false),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[8630, 306, 1590, 1664, 815, 8503, 2887])).
% 2.04/2.26 tff(8632,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.26 tff(8633,plain,
% 2.04/2.26 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[8632, 8470, 8624, 8501, 8622])).
% 2.04/2.26 tff(8634,plain,
% 2.04/2.26 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[891, 8633, 8486])).
% 2.04/2.26 tff(8635,plain,
% 2.04/2.26 (~r(s(s(elem!1)), s(elem!1))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[886, 8634, 8485])).
% 2.04/2.26 tff(8636,plain,
% 2.04/2.26 (b(s(s(elem!1)), s(elem!1))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[994, 8635, 8479])).
% 2.04/2.26 tff(8637,plain,
% 2.04/2.26 (~b(z, s(s(elem!1)))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[1218, 8636, 8477, 8472])).
% 2.04/2.26 tff(8638,plain,
% 2.04/2.26 (r(z, s(s(elem!1)))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[460, 8637])).
% 2.04/2.26 tff(8639,plain,
% 2.04/2.26 (r(elem!1, s(s(elem!1)))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[8638, 8471])).
% 2.04/2.26 tff(8640,plain,
% 2.04/2.26 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[159, 8486])).
% 2.04/2.26 tff(8641,plain,
% 2.04/2.26 (b(s(s(s(elem!1))), s(s(s(s(s(s(z))))))) <=> b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[8480])).
% 2.04/2.26 tff(8642,plain,
% 2.04/2.26 (b(s(s(s(z))), s(s(s(s(s(s(z))))))) <=> b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))),
% 2.04/2.26 inference(symmetry,[status(thm)],[8641])).
% 2.04/2.26 tff(8643,plain,
% 2.04/2.26 (r(s(s(s(elem!1))), s(s(s(s(s(s(z))))))) <=> r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[8480])).
% 2.04/2.26 tff(8644,plain,
% 2.04/2.26 ((~r(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))) <=> (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[8643])).
% 2.04/2.26 tff(8645,plain,
% 2.04/2.26 (~(s(elem!1) = s(s(elem!1)))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[4689, 8479])).
% 2.04/2.26 tff(8646,plain,
% 2.04/2.26 (r(s(elem!1), s(s(s(z)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[8422])).
% 2.04/2.27 tff(8647,plain,
% 2.04/2.27 (r(s(z), s(s(s(z)))) <=> r(s(elem!1), s(s(s(z))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[8420])).
% 2.04/2.27 tff(8648,plain,
% 2.04/2.27 (r(s(elem!1), s(s(s(z))))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[1034, 8647])).
% 2.04/2.27 tff(8649,plain,
% 2.04/2.27 (r(s(elem!1), s(s(s(elem!1))))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[8648, 8646])).
% 2.04/2.27 tff(8650,plain,
% 2.04/2.27 (~r(s(elem!1), s(s(elem!1)))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[2109, 124, 8634, 8649])).
% 2.04/2.27 tff(8651,plain,
% 2.04/2.27 (b(s(elem!1), s(s(elem!1)))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[1684, 43, 8650, 8645])).
% 2.04/2.27 tff(8652,plain,
% 2.04/2.27 (b(s(elem!1), elem!1)),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[8448, 8475])).
% 2.04/2.27 tff(8653,plain,
% 2.04/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(8654,plain,
% 2.04/2.27 (((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(8655,plain,
% 2.04/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1)))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[8654])).
% 2.04/2.27 tff(8656,plain,
% 2.04/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 2.04/2.27 inference(transitivity,[status(thm)],[8655, 8653])).
% 2.04/2.27 tff(8657,plain,
% 2.04/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 2.04/2.27 inference(quant_inst,[status(thm)],[])).
% 2.04/2.27 tff(8658,plain,
% 2.04/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1)))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[8657, 8656])).
% 2.04/2.27 tff(8659,plain,
% 2.04/2.27 (~b(s(s(s(s(s(s(z)))))), s(elem!1))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[8658, 306, 8636, 8652, 8651, 8464])).
% 2.04/2.27 tff(8660,plain,
% 2.04/2.27 (s(elem!1) = s(z)),
% 2.04/2.27 inference(symmetry,[status(thm)],[8420])).
% 2.04/2.27 tff(8661,plain,
% 2.04/2.27 ((s(s(s(s(s(s(z)))))) = s(elem!1)) <=> (s(s(s(s(s(s(z)))))) = s(z))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[8660])).
% 2.04/2.27 tff(8662,plain,
% 2.04/2.27 ((s(s(s(s(s(s(z)))))) = s(z)) <=> (s(s(s(s(s(s(z)))))) = s(elem!1))),
% 2.04/2.27 inference(symmetry,[status(thm)],[8661])).
% 2.04/2.27 tff(8663,plain,
% 2.04/2.27 ((~(s(s(s(s(s(s(z)))))) = s(z))) <=> (~(s(s(s(s(s(s(z)))))) = s(elem!1)))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[8662])).
% 2.04/2.27 tff(8664,plain,
% 2.04/2.27 (~(s(s(s(s(s(s(z)))))) = s(elem!1))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[2844, 8663])).
% 2.04/2.27 tff(8665,plain,
% 2.04/2.27 (r(s(s(s(s(s(s(z)))))), s(elem!1))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[3220, 43, 8664, 8659])).
% 2.04/2.27 tff(8666,plain,
% 2.04/2.27 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(8667,plain,
% 2.04/2.27 (((~r(s(s(s(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(s(s(s(z))))))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(8668,plain,
% 2.04/2.27 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(z))))))))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[8667])).
% 2.04/2.27 tff(8669,plain,
% 2.04/2.27 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))),
% 2.04/2.27 inference(transitivity,[status(thm)],[8668, 8666])).
% 2.04/2.27 tff(8670,plain,
% 2.04/2.27 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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(s(s(s(z)))))))))),
% 2.04/2.27 inference(quant_inst,[status(thm)],[])).
% 2.04/2.27 tff(8671,plain,
% 2.04/2.27 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(z))))))))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[8670, 8669])).
% 2.04/2.27 tff(8672,plain,
% 2.04/2.27 (~r(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[8671, 124, 8485, 8665])).
% 2.04/2.27 tff(8673,plain,
% 2.04/2.27 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[8672, 8644])).
% 2.04/2.27 tff(8674,plain,
% 2.04/2.27 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[3207, 8673])).
% 2.04/2.27 tff(8675,plain,
% 2.04/2.27 (b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[8674, 8642])).
% 2.04/2.27 tff(8676,plain,
% 2.04/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(8677,plain,
% 2.04/2.27 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(8678,plain,
% 2.04/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z))))))))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[8677])).
% 2.04/2.27 tff(8679,plain,
% 2.04/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))),
% 2.04/2.27 inference(transitivity,[status(thm)],[8678, 8676])).
% 2.04/2.27 tff(8680,plain,
% 2.04/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.04/2.27 inference(quant_inst,[status(thm)],[])).
% 2.04/2.27 tff(8681,plain,
% 2.04/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z))))))))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[8680, 8679])).
% 2.04/2.27 tff(8682,plain,
% 2.04/2.27 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[8681, 306, 8470, 8501, 8622, 8675])).
% 2.04/2.27 tff(8683,plain,
% 2.04/2.27 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[610, 8682, 8640])).
% 2.04/2.27 tff(8684,plain,
% 2.04/2.27 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[2053, 8683, 8419, 8639, 8470])).
% 2.04/2.27 tff(8685,plain,
% 2.04/2.27 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[1302, 8684, 8433])).
% 2.04/2.27 tff(8686,plain,
% 2.04/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(8687,plain,
% 2.04/2.27 (((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), 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(s(z))))))))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(8688,plain,
% 2.04/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), 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(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z))))))))))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[8687])).
% 2.04/2.28 tff(8689,plain,
% 2.04/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), 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(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))))),
% 2.04/2.28 inference(transitivity,[status(thm)],[8688, 8686])).
% 2.04/2.28 tff(8690,plain,
% 2.04/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), 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(s(z)))))))))),
% 2.04/2.28 inference(quant_inst,[status(thm)],[])).
% 2.04/2.28 tff(8691,plain,
% 2.04/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z))))))))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[8690, 8689])).
% 2.04/2.28 tff(8692,plain,
% 2.04/2.28 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[8691, 306, 8636, 8652, 8685, 8464])).
% 2.04/2.28 tff(8693,plain,
% 2.04/2.28 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[8692, 8438])).
% 2.04/2.28 tff(8694,plain,
% 2.04/2.28 (r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[4864, 8693, 8436])).
% 2.04/2.28 tff(8695,plain,
% 2.04/2.28 (r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[8694, 8426])).
% 2.04/2.28 tff(8696,plain,
% 2.04/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), 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))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), 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))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(8697,plain,
% 2.04/2.28 (((~b(s(elem!1), elem!1)) | (~b(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(s(s(elem!1)))), s(elem!1)))) <=> ((~b(s(s(s(s(elem!1)))), 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))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(8698,plain,
% 2.04/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(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(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), 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))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[8697])).
% 2.04/2.28 tff(8699,plain,
% 2.04/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(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(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), 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))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.04/2.28 inference(transitivity,[status(thm)],[8698, 8696])).
% 2.04/2.28 tff(8700,plain,
% 2.04/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(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(s(s(elem!1)))), s(elem!1))))),
% 2.04/2.28 inference(quant_inst,[status(thm)],[])).
% 2.04/2.28 tff(8701,plain,
% 2.04/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), 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))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[8700, 8699])).
% 2.04/2.28 tff(8702,plain,
% 2.04/2.28 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[8701, 306, 8636, 8652, 8685, 8651])).
% 2.04/2.28 tff(8703,plain,
% 2.04/2.28 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[1767, 43, 8467, 8702])).
% 2.04/2.28 tff(8704,plain,
% 2.04/2.28 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(8705,plain,
% 2.04/2.28 (((~r(s(s(s(s(s(s(z)))))), 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(s(z))))))))) <=> ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(8706,plain,
% 2.04/2.28 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), 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(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z))))))))))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[8705])).
% 2.04/2.28 tff(8707,plain,
% 2.04/2.28 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), 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(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))))),
% 2.04/2.28 inference(transitivity,[status(thm)],[8706, 8704])).
% 2.04/2.28 tff(8708,plain,
% 2.04/2.28 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), 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(s(z)))))))))),
% 2.04/2.28 inference(quant_inst,[status(thm)],[])).
% 2.04/2.28 tff(8709,plain,
% 2.04/2.28 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z))))))))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[8708, 8707])).
% 2.04/2.28 tff(8710,plain,
% 2.04/2.28 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(z)))))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[8709, 124, 8665, 8703])).
% 2.04/2.28 tff(8711,plain,
% 2.04/2.28 ($false),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[8710, 8695])).
% 2.04/2.28 tff(8712,plain,(r(elem!1, s(z)) | (~r(s(z), s(s(s(z))))) | r(s(s(s(z))), z) | b(elem!1, z) | b(z, elem!1) | r(s(s(s(z))), elem!1) | b(s(s(s(z))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.28 tff(8713,plain,
% 2.04/2.28 (r(elem!1, s(z))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[8712, 1629, 1034, 2, 5318, 1484, 9])).
% 2.04/2.28 tff(8714,plain,
% 2.04/2.28 (~r(s(z), z)),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[1049, 5612, 4])).
% 2.04/2.28 tff(8715,plain,
% 2.04/2.28 (b(s(z), z)),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[221, 8714])).
% 2.04/2.28 tff(8716,plain,
% 2.04/2.28 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[7186, 8715, 5330, 4])).
% 2.04/2.28 tff(8717,plain,
% 2.04/2.28 (~r(z, s(z))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[385, 5330, 359])).
% 2.04/2.28 tff(8718,plain,
% 2.04/2.28 (b(z, s(z))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[2263, 8717])).
% 2.04/2.28 tff(8719,plain,
% 2.04/2.28 (~r(elem!1, s(s(s(z))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[3293, 359, 1034])).
% 2.04/2.28 tff(8720,plain,
% 2.04/2.28 (b(elem!1, s(s(s(z))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[2304, 8719, 4939])).
% 2.04/2.28 tff(8721,plain,
% 2.04/2.28 (~(s(elem!1) = s(s(s(z))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[7863, 802, 1484])).
% 2.04/2.28 tff(8722,plain,
% 2.04/2.28 (~b(s(elem!1), s(s(s(z))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[7725, 306, 7921, 7919, 1531])).
% 2.04/2.28 tff(8723,plain,
% 2.04/2.28 (r(s(elem!1), s(s(s(z))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[2367, 43, 8722, 8721])).
% 2.04/2.28 tff(8724,plain,
% 2.04/2.28 (~r(s(z), s(elem!1))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[7882, 124, 1034, 8723])).
% 2.04/2.28 tff(8725,plain,
% 2.04/2.28 ((s(z) = s(elem!1)) | b(s(z), s(elem!1))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[4047, 43, 8724])).
% 2.04/2.28 tff(8726,plain,
% 2.04/2.28 (b(s(z), s(elem!1))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[8725, 7418])).
% 2.04/2.28 tff(8727,plain,
% 2.04/2.28 (((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), z))) <=> ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(8728,plain,
% 2.04/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(z), s(elem!1)))))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[8727])).
% 2.04/2.28 tff(8729,plain,
% 2.04/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))),
% 2.04/2.28 inference(transitivity,[status(thm)],[8728, 6796])).
% 2.04/2.28 tff(8730,plain,
% 2.04/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), z)))),
% 2.04/2.28 inference(quant_inst,[status(thm)],[])).
% 2.04/2.28 tff(8731,plain,
% 2.04/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(z), s(elem!1)))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[8730, 8729])).
% 2.04/2.28 tff(8732,plain,
% 2.04/2.28 ($false),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[8731, 306, 7921, 7919, 247, 8726])).
% 2.04/2.28 tff(8733,plain,((~r(s(elem!1), elem!1)) | (~b(s(z), z)) | (s(elem!1) = s(z)) | (~r(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~r(z, elem!1)) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.04/2.28 tff(8734,plain,
% 2.04/2.28 (~r(s(elem!1), elem!1)),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[8733, 8715, 3099, 1034, 1531, 5330, 1484])).
% 2.04/2.28 tff(8735,plain,
% 2.04/2.28 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[7309, 306, 1967, 2812, 1470])).
% 2.04/2.28 tff(8736,plain,
% 2.04/2.28 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[4603, 43, 8735, 4577])).
% 2.04/2.28 tff(8737,plain,
% 2.04/2.28 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[5339, 124, 1034, 8736])).
% 2.04/2.28 tff(8738,plain,
% 2.04/2.28 (b(s(s(s(s(s(s(z)))))), s(z))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[651, 43, 2844, 8737])).
% 2.04/2.28 tff(8739,plain,
% 2.04/2.28 (~b(z, s(s(s(s(s(s(z)))))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[7330, 306, 247, 485, 8738])).
% 2.04/2.28 tff(8740,plain,
% 2.04/2.28 ((z = s(s(s(s(s(s(z))))))) | r(z, s(s(s(s(s(s(z)))))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[5445, 43, 8739])).
% 2.04/2.28 tff(8741,plain,
% 2.04/2.28 (r(z, s(s(s(s(s(s(z)))))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[8740, 5435])).
% 2.04/2.28 tff(8742,plain,
% 2.04/2.28 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[7320, 306, 1967, 2812, 1470])).
% 2.04/2.28 tff(8743,plain,
% 2.04/2.28 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[3207, 8742])).
% 2.04/2.28 tff(8744,plain,
% 2.04/2.28 (~r(z, s(s(s(z))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[7341, 124, 8743, 8741])).
% 2.04/2.28 tff(8745,plain,
% 2.04/2.28 (b(z, s(s(s(z))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[2415, 43, 8744, 2405])).
% 2.04/2.28 tff(8746,plain,
% 2.04/2.28 (~r(s(s(z)), s(s(s(z))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[7352, 8745, 247, 1034, 8736, 8738])).
% 2.04/2.28 tff(8747,plain,
% 2.04/2.28 (b(s(s(z)), s(s(s(z))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[2514, 8746])).
% 2.04/2.28 tff(8748,plain,
% 2.04/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(8749,plain,
% 2.04/2.28 (((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1))) <=> ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(8750,plain,
% 2.04/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1))))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[8749])).
% 2.04/2.28 tff(8751,plain,
% 2.04/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 2.04/2.29 inference(transitivity,[status(thm)],[8750, 8748])).
% 2.04/2.29 tff(8752,plain,
% 2.04/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 2.04/2.29 inference(quant_inst,[status(thm)],[])).
% 2.04/2.29 tff(8753,plain,
% 2.04/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[8752, 8751])).
% 2.04/2.29 tff(8754,plain,
% 2.04/2.29 (~b(s(s(z)), elem!1)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[8753, 306, 1531, 8745, 1470, 8747])).
% 2.04/2.29 tff(8755,plain,
% 2.04/2.29 (~b(s(s(z)), z)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[7374, 8745, 247, 485, 1034, 1967, 1470])).
% 2.04/2.29 tff(8756,plain,
% 2.04/2.29 (r(s(s(z)), z)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[2531, 8755])).
% 2.04/2.29 tff(8757,plain,
% 2.04/2.29 (~r(s(s(z)), elem!1)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[7379, 124, 5612, 8756])).
% 2.04/2.29 tff(8758,plain,
% 2.04/2.29 (s(s(z)) = elem!1),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[2545, 8757, 8754])).
% 2.04/2.29 tff(8759,plain,
% 2.04/2.29 (s(s(s(z))) = s(elem!1)),
% 2.04/2.29 inference(monotonicity,[status(thm)],[8758])).
% 2.04/2.29 tff(8760,plain,
% 2.04/2.29 (b(s(s(s(z))), s(z)) <=> b(s(elem!1), s(z))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[8759])).
% 2.04/2.29 tff(8761,plain,
% 2.04/2.29 ((~b(s(s(s(z))), s(z))) <=> (~b(s(elem!1), s(z)))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[8760])).
% 2.04/2.29 tff(8762,plain,
% 2.04/2.29 (~b(s(elem!1), s(z))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[9, 8761])).
% 2.04/2.29 tff(8763,plain,
% 2.04/2.29 (~(s(z) = elem!1)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[2235, 1967, 9])).
% 2.04/2.29 tff(8764,plain,
% 2.04/2.29 (~(elem!1 = s(z))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[3096, 8763])).
% 2.04/2.29 tff(8765,plain,
% 2.04/2.29 (~(s(elem!1) = elem!1)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[2398, 8758, 8764])).
% 2.04/2.29 tff(8766,plain,
% 2.04/2.29 (~(s(s(elem!1)) = s(elem!1))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[195, 8765])).
% 2.04/2.29 tff(8767,plain,
% 2.04/2.29 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[8759])).
% 2.04/2.29 tff(8768,plain,
% 2.04/2.29 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[8767])).
% 2.04/2.29 tff(8769,plain,
% 2.04/2.29 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(s(elem!1))) = elem!1)),
% 2.04/2.29 inference(monotonicity,[status(thm)],[8768, 8758])).
% 2.04/2.29 tff(8770,plain,
% 2.04/2.29 ((s(s(s(s(s(z))))) = s(s(z))) <=> (elem!1 = s(s(s(elem!1))))),
% 2.04/2.29 inference(transitivity,[status(thm)],[8769, 1554])).
% 2.04/2.29 tff(8771,plain,
% 2.04/2.29 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(s(elem!1))) = elem!1)),
% 2.04/2.29 inference(transitivity,[status(thm)],[8770, 1555])).
% 2.04/2.29 tff(8772,plain,
% 2.04/2.29 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[8771])).
% 2.04/2.29 tff(8773,plain,
% 2.04/2.29 (~(s(s(s(elem!1))) = elem!1)),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[6464, 8772])).
% 2.04/2.29 tff(8774,plain,
% 2.04/2.29 (s(s(elem!1)) = s(s(s(s(z))))),
% 2.04/2.29 inference(symmetry,[status(thm)],[8767])).
% 2.04/2.29 tff(8775,plain,
% 2.04/2.29 ((s(s(elem!1)) = elem!1) <=> (s(s(s(s(z)))) = elem!1)),
% 2.04/2.29 inference(monotonicity,[status(thm)],[8774])).
% 2.04/2.29 tff(8776,plain,
% 2.04/2.29 ((s(s(s(s(z)))) = elem!1) <=> (s(s(elem!1)) = elem!1)),
% 2.04/2.29 inference(symmetry,[status(thm)],[8775])).
% 2.04/2.29 tff(8777,plain,
% 2.04/2.29 ((~(s(s(s(s(z)))) = elem!1)) <=> (~(s(s(elem!1)) = elem!1))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[8776])).
% 2.04/2.29 tff(8778,plain,
% 2.04/2.29 ((elem!1 = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = elem!1)),
% 2.04/2.29 inference(commutativity,[status(thm)],[])).
% 2.04/2.29 tff(8779,plain,
% 2.04/2.29 ((s(s(z)) = s(s(s(s(z))))) <=> (elem!1 = s(s(s(s(z)))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[8758])).
% 2.04/2.29 tff(8780,plain,
% 2.04/2.29 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = elem!1)),
% 2.04/2.29 inference(transitivity,[status(thm)],[8779, 8778])).
% 2.04/2.29 tff(8781,plain,
% 2.04/2.29 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[8780])).
% 2.04/2.29 tff(8782,plain,
% 2.04/2.29 (~(s(s(s(s(z)))) = elem!1)),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[1612, 8781])).
% 2.04/2.29 tff(8783,plain,
% 2.04/2.29 (~(s(s(elem!1)) = elem!1)),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[8782, 8777])).
% 2.04/2.29 tff(8784,plain,
% 2.04/2.29 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[143, 8783])).
% 2.04/2.29 tff(8785,plain,
% 2.04/2.29 (~(elem!1 = s(elem!1))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[364, 8765])).
% 2.04/2.29 tff(8786,plain,
% 2.04/2.29 (b(s(elem!1), elem!1)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[813, 8765, 808])).
% 2.04/2.29 tff(8787,plain,
% 2.04/2.29 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[7090, 8783, 2170, 808])).
% 2.04/2.29 tff(8788,plain,
% 2.04/2.29 (b(s(s(elem!1)), s(elem!1))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[7817, 8787, 5612, 8786, 8785, 8784, 8773, 8766, 2, 3099, 374, 808, 8762])).
% 2.04/2.29 tff(8789,plain,
% 2.04/2.29 (b(z, s(s(s(z)))) <=> b(z, s(elem!1))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[8759])).
% 2.04/2.29 tff(8790,plain,
% 2.04/2.29 (b(z, s(elem!1))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[8745, 8789])).
% 2.04/2.29 tff(8791,plain,
% 2.04/2.29 (b(s(s(s(z))), z) <=> b(s(elem!1), z)),
% 2.04/2.29 inference(monotonicity,[status(thm)],[8759])).
% 2.04/2.29 tff(8792,plain,
% 2.04/2.29 (b(s(elem!1), z)),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[1531, 8791])).
% 2.04/2.29 tff(8793,plain,
% 2.04/2.29 (~b(z, s(s(elem!1)))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[1218, 8788, 8792, 8790])).
% 2.04/2.29 tff(8794,plain,
% 2.04/2.29 (r(z, s(s(elem!1)))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[460, 8793])).
% 2.04/2.29 tff(8795,plain,
% 2.04/2.29 (~r(s(s(elem!1)), elem!1)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[5837, 8794, 374])).
% 2.04/2.29 tff(8796,plain,
% 2.04/2.29 (b(s(s(elem!1)), elem!1)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[47, 8795, 8783])).
% 2.04/2.29 tff(8797,plain,
% 2.04/2.29 ((s(s(s(s(z)))) = elem!1) <=> (elem!1 = s(s(elem!1)))),
% 2.04/2.29 inference(transitivity,[status(thm)],[8776, 1170])).
% 2.04/2.29 tff(8798,plain,
% 2.04/2.29 ((~(s(s(s(s(z)))) = elem!1)) <=> (~(elem!1 = s(s(elem!1))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[8797])).
% 2.04/2.29 tff(8799,plain,
% 2.04/2.29 (~(elem!1 = s(s(elem!1)))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[8782, 8798])).
% 2.04/2.29 tff(8800,plain,
% 2.04/2.29 (~r(elem!1, s(s(elem!1)))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[1194, 8794, 374])).
% 2.04/2.29 tff(8801,plain,
% 2.04/2.29 (b(elem!1, s(s(elem!1)))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[516, 8800, 8799])).
% 2.04/2.29 tff(8802,plain,
% 2.04/2.29 ($false),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[1024, 8801, 8796, 8786, 8788])).
% 2.04/2.29 tff(8803,plain,((~b(s(s(s(s(s(s(z)))))), elem!1)) | (~r(z, elem!1)) | b(elem!1, z) | r(s(elem!1), elem!1) | (z = elem!1) | (~b(s(s(s(z))), z)) | b(s(s(s(z))), s(z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.29 tff(8804,plain,
% 2.04/2.29 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[8803, 5330, 2, 8734, 2170, 1531, 9, 8720, 8715, 1034, 8718, 1967])).
% 2.04/2.29 tff(8805,plain,
% 2.04/2.29 (s(s(s(s(s(s(z)))))) = elem!1),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[1144, 8804, 8716])).
% 2.04/2.29 tff(8806,plain,
% 2.04/2.29 (elem!1 = s(s(s(s(s(s(z))))))),
% 2.04/2.29 inference(symmetry,[status(thm)],[8805])).
% 2.04/2.29 tff(8807,plain,
% 2.04/2.29 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[5403, 8805])).
% 2.04/2.29 tff(8808,plain,
% 2.04/2.29 (~(s(elem!1) = elem!1)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[2436, 8807])).
% 2.04/2.29 tff(8809,plain,
% 2.04/2.29 (b(s(elem!1), elem!1)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[8095, 8804, 1034, 2170, 1531, 4, 8715, 5318])).
% 2.04/2.29 tff(8810,plain,
% 2.04/2.29 (~(elem!1 = s(elem!1))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[364, 8808])).
% 2.04/2.29 tff(8811,plain,
% 2.04/2.29 ((s(s(z)) = s(s(s(s(s(s(z))))))) <=> (s(s(z)) = elem!1)),
% 2.04/2.29 inference(monotonicity,[status(thm)],[8805])).
% 2.04/2.29 tff(8812,plain,
% 2.04/2.29 ((~(s(s(z)) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(z)) = elem!1))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[8811])).
% 2.04/2.29 tff(8813,plain,
% 2.04/2.29 (~(s(s(z)) = elem!1)),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[2826, 8812])).
% 2.04/2.29 tff(8814,plain,
% 2.04/2.29 (~(s(elem!1) = s(s(s(z))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[5384, 8813])).
% 2.04/2.29 tff(8815,plain,
% 2.04/2.29 (~b(s(elem!1), z)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[8078, 8814, 1034, 3099, 8718, 8715, 1531])).
% 2.04/2.29 tff(8816,plain,
% 2.04/2.29 (r(s(elem!1), z)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[2380, 8815])).
% 2.04/2.29 tff(8817,plain,
% 2.04/2.29 (~r(elem!1, s(elem!1))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[287, 8816, 5612])).
% 2.04/2.29 tff(8818,plain,
% 2.04/2.29 (b(elem!1, s(elem!1))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[372, 8817, 8810])).
% 2.04/2.29 tff(8819,plain,
% 2.04/2.29 (~r(s(z), z)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[1049, 246, 4])).
% 2.04/2.29 tff(8820,plain,
% 2.04/2.29 (b(s(z), z)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[221, 8819])).
% 2.04/2.29 tff(8821,assumption,(r(s(s(elem!1)), s(z))), introduced(assumption)).
% 2.04/2.29 tff(8822,plain,
% 2.04/2.29 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(8823,plain,
% 2.04/2.29 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))))),
% 2.04/2.29 inference(quant_inst,[status(thm)],[])).
% 2.04/2.29 tff(8824,plain,
% 2.04/2.29 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z)))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[8823, 8822])).
% 2.04/2.29 tff(8825,plain,
% 2.04/2.29 ($false),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[8824, 124, 1730, 4, 8821])).
% 2.04/2.29 tff(8826,plain,((~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.29 tff(8827,plain,
% 2.04/2.29 (~r(s(s(elem!1)), s(z))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[8826, 1730, 4])).
% 2.04/2.29 tff(8828,plain,
% 2.04/2.29 (b(s(s(elem!1)), s(z))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[3989, 8827])).
% 2.04/2.29 tff(8829,plain,
% 2.04/2.29 (~r(s(s(elem!1)), z)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[7786, 1730, 246])).
% 2.04/2.29 tff(8830,plain,
% 2.04/2.29 (b(s(s(elem!1)), z)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[476, 8829])).
% 2.04/2.29 tff(8831,plain,
% 2.04/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(8832,plain,
% 2.04/2.29 (((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(8833,plain,
% 2.04/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[8832])).
% 2.04/2.29 tff(8834,plain,
% 2.04/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)))),
% 2.04/2.29 inference(transitivity,[status(thm)],[8833, 8831])).
% 2.04/2.29 tff(8835,plain,
% 2.04/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))),
% 2.04/2.29 inference(quant_inst,[status(thm)],[])).
% 2.04/2.29 tff(8836,plain,
% 2.04/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[8835, 8834])).
% 2.04/2.29 tff(8837,plain,
% 2.04/2.29 ($false),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[8836, 306, 6699, 8830, 8828, 8820])).
% 2.04/2.29 tff(8838,plain,((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.29 tff(8839,plain,
% 2.04/2.29 (~r(s(s(elem!1)), elem!1)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[8838, 5612, 5330, 4])).
% 2.04/2.29 tff(8840,plain,
% 2.04/2.29 (b(s(elem!1), s(z))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[7774, 2249, 6, 2, 374, 7093, 808])).
% 2.04/2.29 tff(8841,plain,
% 2.04/2.29 (~(s(elem!1) = s(s(elem!1)))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[4689, 392])).
% 2.04/2.29 tff(8842,plain,
% 2.04/2.29 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 2.04/2.29 inference(monotonicity,[status(thm)],[85])).
% 2.04/2.29 tff(8843,plain,
% 2.04/2.29 ((s(s(elem!1)) = s(z)) <=> (elem!1 = s(s(elem!1)))),
% 2.04/2.29 inference(transitivity,[status(thm)],[8842, 1170])).
% 2.04/2.29 tff(8844,plain,
% 2.04/2.29 ((~(s(s(elem!1)) = s(z))) <=> (~(elem!1 = s(s(elem!1))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[8843])).
% 2.04/2.29 tff(8845,plain,
% 2.04/2.29 (~(elem!1 = s(s(elem!1)))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[80, 8844])).
% 2.04/2.29 tff(8846,plain,
% 2.04/2.29 ((s(z) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[85])).
% 2.04/2.29 tff(8847,plain,
% 2.04/2.29 ((~(s(z) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[8846])).
% 2.04/2.29 tff(8848,plain,
% 2.04/2.29 (~(elem!1 = s(s(s(elem!1))))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[645, 8847])).
% 2.04/2.29 tff(8849,plain,
% 2.04/2.29 (s(s(z)) = s(elem!1)),
% 2.04/2.29 inference(monotonicity,[status(thm)],[85])).
% 2.04/2.29 tff(8850,plain,
% 2.04/2.29 (s(s(s(z))) = s(s(elem!1))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[8849])).
% 2.04/2.29 tff(8851,plain,
% 2.04/2.29 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[8850])).
% 2.04/2.29 tff(8852,plain,
% 2.04/2.29 ((s(s(z)) = s(s(s(s(z))))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[8849, 8851])).
% 2.04/2.29 tff(8853,plain,
% 2.04/2.29 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 2.04/2.29 inference(transitivity,[status(thm)],[8852, 1573])).
% 2.04/2.29 tff(8854,plain,
% 2.04/2.29 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[8853])).
% 2.04/2.29 tff(8855,plain,
% 2.04/2.29 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[1612, 8854])).
% 2.04/2.29 tff(8856,plain,
% 2.04/2.29 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = elem!1))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[8842])).
% 2.04/2.29 tff(8857,plain,
% 2.04/2.29 (~(s(s(elem!1)) = elem!1)),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[80, 8856])).
% 2.04/2.29 tff(8858,plain,
% 2.04/2.29 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[7090, 8857, 2170, 808])).
% 2.04/2.29 tff(8859,plain,
% 2.04/2.29 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[659, 8858, 244])).
% 2.04/2.29 tff(8860,plain,
% 2.04/2.29 (b(s(s(s(elem!1))), s(elem!1))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[664, 8859, 8855])).
% 2.04/2.29 tff(8861,plain,
% 2.04/2.29 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 2.04/2.29 inference(transitivity,[status(thm)],[8846, 1555])).
% 2.04/2.29 tff(8862,plain,
% 2.04/2.29 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[8861])).
% 2.04/2.29 tff(8863,plain,
% 2.04/2.29 (~(s(s(s(elem!1))) = elem!1)),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[645, 8862])).
% 2.04/2.29 tff(8864,plain,
% 2.04/2.29 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[152, 8855])).
% 2.04/2.29 tff(8865,plain,
% 2.04/2.29 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[3437, 8864])).
% 2.04/2.29 tff(8866,plain,
% 2.04/2.29 (elem!1 = s(z)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[89, 85])).
% 2.04/2.29 tff(8867,plain,
% 2.04/2.29 (~(s(s(s(s(elem!1)))) = elem!1)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[6321, 8866])).
% 2.04/2.29 tff(8868,plain,
% 2.04/2.29 (b(s(s(elem!1)), elem!1)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[47, 8857, 6])).
% 2.04/2.29 tff(8869,plain,
% 2.04/2.29 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[1284, 8855])).
% 2.04/2.29 tff(8870,assumption,(~(s(elem!1) = s(s(elem!1)))), introduced(assumption)).
% 2.04/2.29 tff(8871,plain,
% 2.04/2.29 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[8851])).
% 2.04/2.29 tff(8872,plain,
% 2.04/2.29 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[8871, 8849])).
% 2.04/2.29 tff(8873,plain,
% 2.04/2.29 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(s(s(elem!1)))) = s(elem!1)))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[8872])).
% 2.04/2.29 tff(8874,plain,
% 2.04/2.29 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[6464, 8873])).
% 2.04/2.29 tff(8875,plain,
% 2.04/2.29 (~b(elem!1, s(s(s(elem!1))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[6617, 815, 816, 759])).
% 2.04/2.29 tff(8876,plain,
% 2.04/2.29 (r(elem!1, s(s(s(elem!1))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[3284, 8875, 1653])).
% 2.04/2.29 tff(8877,plain,
% 2.04/2.29 (~r(s(s(s(elem!1))), z)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[851, 8876, 246])).
% 2.04/2.29 tff(8878,plain,
% 2.04/2.29 (b(s(s(s(elem!1))), z)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[3033, 43, 579, 8877])).
% 2.04/2.29 tff(8879,plain,
% 2.04/2.29 (~r(z, s(s(s(elem!1))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[573, 8876, 374])).
% 2.04/2.29 tff(8880,plain,
% 2.04/2.29 (b(z, s(s(s(elem!1))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[585, 8879])).
% 2.04/2.29 tff(8881,plain,
% 2.04/2.29 (~b(s(s(s(elem!1))), elem!1)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[6962, 306, 759, 816, 815])).
% 2.04/2.29 tff(8882,plain,
% 2.04/2.29 (r(s(s(s(elem!1))), elem!1)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[1636, 8881, 1526])).
% 2.04/2.29 tff(8883,plain,
% 2.04/2.29 (~r(s(s(s(s(elem!1)))), elem!1)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[6453, 8882, 8880, 3476, 8878, 374])).
% 2.04/2.29 tff(8884,plain,
% 2.04/2.29 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[1736, 8883, 1731])).
% 2.04/2.29 tff(8885,plain,
% 2.04/2.29 (~r(s(elem!1), s(s(elem!1)))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[4458, 8884, 1516, 1717, 816, 30, 815])).
% 2.04/2.29 tff(8886,plain,
% 2.04/2.29 ($false),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[1684, 43, 4697, 8885, 8870])).
% 2.04/2.29 tff(8887,plain,((~b(elem!1, s(elem!1))) | (s(elem!1) = s(s(elem!1))) | (s(s(s(s(elem!1)))) = s(elem!1)) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (s(s(s(s(elem!1)))) = elem!1) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~r(z, elem!1)) | (s(s(s(elem!1))) = elem!1) | (~b(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, z)) | (elem!1 = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.29 tff(8888,plain,
% 2.04/2.29 (~b(elem!1, s(elem!1))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[8887, 8874, 8870, 8869, 816, 8868, 8867, 8865, 374, 8863, 8860, 246, 8848])).
% 2.04/2.29 tff(8889,plain,
% 2.04/2.29 (r(elem!1, s(elem!1))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[372, 8888, 366])).
% 2.04/2.29 tff(8890,plain,
% 2.04/2.29 (~r(elem!1, s(s(elem!1)))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[1238, 8889, 244])).
% 2.04/2.29 tff(8891,plain,
% 2.04/2.29 (b(elem!1, s(s(elem!1)))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[516, 8890, 8845])).
% 2.04/2.29 tff(8892,plain,
% 2.04/2.29 (~r(z, s(elem!1))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[5668, 8889, 374])).
% 2.04/2.29 tff(8893,plain,
% 2.04/2.29 (b(z, s(elem!1))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[275, 8892])).
% 2.04/2.29 tff(8894,plain,
% 2.04/2.29 (~b(s(s(s(elem!1))), z)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[5789, 306, 8860, 8893, 8891, 816])).
% 2.04/2.29 tff(8895,plain,
% 2.04/2.29 (~r(s(elem!1), z)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[287, 8889, 246])).
% 2.04/2.29 tff(8896,plain,
% 2.04/2.29 (b(s(elem!1), z)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[2380, 8895])).
% 2.04/2.29 tff(8897,plain,
% 2.04/2.29 (~r(elem!1, s(s(s(elem!1))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[6042, 8893, 8855, 8889, 374, 8896])).
% 2.04/2.29 tff(8898,plain,
% 2.04/2.29 (b(elem!1, s(s(s(elem!1))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[3284, 8897, 8848])).
% 2.04/2.29 tff(8899,plain,
% 2.04/2.29 (~b(s(s(s(elem!1))), elem!1)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[6138, 8898, 816, 8860])).
% 2.04/2.29 tff(8900,plain,
% 2.04/2.29 (r(s(s(s(elem!1))), elem!1)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[1636, 8899, 8863])).
% 2.04/2.29 tff(8901,plain,
% 2.04/2.29 (~r(s(s(s(elem!1))), z)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[3029, 8900, 246])).
% 2.04/2.29 tff(8902,plain,
% 2.04/2.29 ($false),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[3033, 43, 579, 8901, 8894])).
% 2.04/2.29 tff(8903,plain,((~(s(z) = elem!1)) | (~b(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (elem!1 = s(elem!1)) | (s(elem!1) = s(s(elem!1))) | (z = elem!1) | r(s(elem!1), elem!1) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.04/2.29 tff(8904,plain,
% 2.04/2.29 (~(s(z) = elem!1)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[8903, 2323, 2254, 374, 7429, 365, 8841, 2252, 808, 6])).
% 2.04/2.29 tff(8905,plain,
% 2.04/2.29 (~r(s(z), elem!1)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[1049, 204, 2254])).
% 2.04/2.29 tff(8906,plain,
% 2.04/2.29 (b(s(z), elem!1)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[1500, 43, 8905, 8904])).
% 2.04/2.29 tff(8907,plain,
% 2.04/2.29 (r(elem!1, s(elem!1))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[7449, 8906, 6, 7093, 2249, 193, 808])).
% 2.04/2.29 tff(8908,plain,
% 2.04/2.29 (~r(elem!1, s(s(elem!1)))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[1238, 8907, 7429])).
% 2.04/2.29 tff(8909,assumption,(~r(elem!1, s(s(elem!1)))), introduced(assumption)).
% 2.04/2.29 tff(8910,plain,
% 2.04/2.29 (b(elem!1, s(s(elem!1)))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[516, 187, 8909])).
% 2.04/2.29 tff(8911,plain,
% 2.04/2.29 ($false),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[6417, 306, 92, 8910, 816, 2831, 2647])).
% 2.04/2.29 tff(8912,plain,((s(s(elem!1)) = elem!1) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | r(elem!1, s(s(elem!1))) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.04/2.29 tff(8913,plain,
% 2.04/2.29 (s(s(elem!1)) = elem!1),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[8912, 8906, 2323, 8840, 8908, 6])).
% 2.04/2.29 tff(8914,plain,
% 2.04/2.29 (elem!1 = s(s(elem!1))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[1174, 8913])).
% 2.04/2.29 tff(8915,plain,
% 2.04/2.29 (s(s(s(elem!1))) = s(elem!1)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[1168, 8914])).
% 2.04/2.29 tff(8916,plain,
% 2.04/2.29 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[8915])).
% 2.04/2.29 tff(8917,plain,
% 2.04/2.29 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 2.04/2.29 inference(symmetry,[status(thm)],[8916])).
% 2.04/2.29 tff(8918,plain,
% 2.04/2.29 (elem!1 = s(s(elem!1))),
% 2.04/2.29 inference(symmetry,[status(thm)],[8913])).
% 2.04/2.29 tff(8919,plain,
% 2.04/2.29 (elem!1 = s(s(s(s(elem!1))))),
% 2.04/2.29 inference(transitivity,[status(thm)],[8918, 8917])).
% 2.04/2.29 tff(8920,plain,
% 2.04/2.29 (~(s(s(s(z))) = elem!1)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[1443, 8919])).
% 2.04/2.29 tff(8921,plain,
% 2.04/2.29 (~(elem!1 = s(s(s(z))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[4555, 8920])).
% 2.04/2.29 tff(8922,plain,
% 2.04/2.29 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(elem!1))), elem!1)),
% 2.04/2.29 inference(monotonicity,[status(thm)],[8913])).
% 2.04/2.29 tff(8923,plain,
% 2.04/2.29 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.04/2.29 inference(symmetry,[status(thm)],[8922])).
% 2.04/2.29 tff(8924,plain,
% 2.04/2.29 (r(s(s(s(elem!1))), elem!1) <=> r(s(elem!1), elem!1)),
% 2.04/2.29 inference(monotonicity,[status(thm)],[8915])).
% 2.04/2.29 tff(8925,plain,
% 2.04/2.29 (r(s(elem!1), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 2.04/2.29 inference(symmetry,[status(thm)],[8924])).
% 2.04/2.29 tff(8926,plain,
% 2.04/2.29 (r(s(elem!1), elem!1) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.04/2.29 inference(transitivity,[status(thm)],[8925, 8923])).
% 2.04/2.29 tff(8927,plain,
% 2.04/2.29 ((~r(s(elem!1), elem!1)) <=> (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[8926])).
% 2.04/2.29 tff(8928,plain,
% 2.04/2.29 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[808, 8927])).
% 2.04/2.29 tff(8929,plain,
% 2.04/2.29 (r(z, s(s(elem!1))) <=> r(z, elem!1)),
% 2.04/2.29 inference(monotonicity,[status(thm)],[8913])).
% 2.04/2.29 tff(8930,plain,
% 2.04/2.29 (r(z, elem!1) <=> r(z, s(s(elem!1)))),
% 2.04/2.29 inference(symmetry,[status(thm)],[8929])).
% 2.04/2.29 tff(8931,plain,
% 2.04/2.29 (r(z, s(s(elem!1)))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[374, 8930])).
% 2.04/2.29 tff(8932,plain,
% 2.04/2.29 ((elem!1 = s(s(s(elem!1)))) <=> (elem!1 = s(elem!1))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[8915])).
% 2.04/2.29 tff(8933,plain,
% 2.04/2.29 ((elem!1 = s(s(s(elem!1)))) <=> (s(elem!1) = elem!1)),
% 2.04/2.29 inference(transitivity,[status(thm)],[8932, 1162])).
% 2.04/2.29 tff(8934,plain,
% 2.04/2.29 ((s(elem!1) = elem!1) <=> (elem!1 = s(s(s(elem!1))))),
% 2.04/2.29 inference(symmetry,[status(thm)],[8933])).
% 2.04/2.29 tff(8935,plain,
% 2.04/2.29 ((s(elem!1) = elem!1) <=> (s(s(s(elem!1))) = elem!1)),
% 2.04/2.29 inference(transitivity,[status(thm)],[8934, 1555])).
% 2.04/2.29 tff(8936,plain,
% 2.04/2.29 ((~(s(elem!1) = elem!1)) <=> (~(s(s(s(elem!1))) = elem!1))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[8935])).
% 2.04/2.29 tff(8937,plain,
% 2.04/2.29 (~(s(s(s(elem!1))) = elem!1)),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[193, 8936])).
% 2.04/2.29 tff(8938,plain,
% 2.04/2.29 (~b(elem!1, s(z))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[5422, 8906, 2323, 8840])).
% 2.04/2.29 tff(8939,plain,
% 2.04/2.29 (b(elem!1, s(s(s(z))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[1455, 6, 5, 2, 9])).
% 2.04/2.29 tff(8940,plain,
% 2.04/2.29 ((s(s(elem!1)) = z) <=> (elem!1 = z)),
% 2.04/2.29 inference(monotonicity,[status(thm)],[1171])).
% 2.04/2.29 tff(8941,plain,
% 2.04/2.29 ((s(s(elem!1)) = z) <=> (z = elem!1)),
% 2.04/2.29 inference(transitivity,[status(thm)],[8940, 161])).
% 2.04/2.29 tff(8942,plain,
% 2.04/2.29 ((s(s(elem!1)) = z) <=> (elem!1 = z)),
% 2.04/2.29 inference(transitivity,[status(thm)],[8941, 162])).
% 2.04/2.29 tff(8943,plain,
% 2.04/2.29 ((~(s(s(elem!1)) = z)) <=> (~(elem!1 = z))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[8942])).
% 2.04/2.29 tff(8944,plain,
% 2.04/2.29 (~(elem!1 = z)),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[454, 8943])).
% 2.04/2.29 tff(8945,plain,
% 2.04/2.29 (r(elem!1, z)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[174, 8944, 2])).
% 2.04/2.29 tff(8946,plain,
% 2.04/2.29 (~r(s(z), elem!1)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[1049, 8945, 204])).
% 2.04/2.29 tff(8947,plain,
% 2.04/2.29 ((s(s(elem!1)) = s(elem!1)) <=> (elem!1 = s(elem!1))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[1171])).
% 2.04/2.29 tff(8948,plain,
% 2.04/2.29 ((s(s(elem!1)) = s(elem!1)) <=> (s(elem!1) = elem!1)),
% 2.04/2.29 inference(transitivity,[status(thm)],[8947, 1162])).
% 2.04/2.29 tff(8949,plain,
% 2.04/2.29 ((~(s(s(elem!1)) = s(elem!1))) <=> (~(s(elem!1) = elem!1))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[8948])).
% 2.04/2.29 tff(8950,plain,
% 2.04/2.29 (~(s(elem!1) = elem!1)),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[403, 8949])).
% 2.04/2.29 tff(8951,plain,
% 2.04/2.29 (s(elem!1) = s(s(s(elem!1)))),
% 2.04/2.29 inference(symmetry,[status(thm)],[1424])).
% 2.04/2.29 tff(8952,plain,
% 2.04/2.29 (r(s(elem!1), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 2.04/2.29 inference(monotonicity,[status(thm)],[8951])).
% 2.04/2.29 tff(8953,plain,
% 2.04/2.29 (r(s(s(s(elem!1))), elem!1) <=> r(s(elem!1), elem!1)),
% 2.04/2.29 inference(symmetry,[status(thm)],[8952])).
% 2.04/2.29 tff(8954,plain,
% 2.04/2.29 ((~r(s(s(s(elem!1))), elem!1)) <=> (~r(s(elem!1), elem!1))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[8953])).
% 2.04/2.29 tff(8955,plain,
% 2.04/2.29 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(elem!1))), elem!1)),
% 2.04/2.29 inference(monotonicity,[status(thm)],[1171])).
% 2.04/2.29 tff(8956,plain,
% 2.04/2.29 ((~r(s(s(s(elem!1))), s(s(elem!1)))) <=> (~r(s(s(s(elem!1))), elem!1))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[8955])).
% 2.04/2.29 tff(8957,plain,
% 2.04/2.29 (~r(s(s(s(elem!1))), elem!1)),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[3314, 8956])).
% 2.04/2.29 tff(8958,plain,
% 2.04/2.29 (~r(s(elem!1), elem!1)),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[8957, 8954])).
% 2.04/2.29 tff(8959,plain,
% 2.04/2.29 (b(s(elem!1), elem!1)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[813, 8958, 8950])).
% 2.04/2.29 tff(8960,plain,
% 2.04/2.29 (~(s(elem!1) = s(z))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[2724, 1424])).
% 2.04/2.29 tff(8961,plain,
% 2.04/2.29 (~r(s(s(s(z))), elem!1)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[1481, 4287, 206])).
% 2.04/2.29 tff(8962,plain,
% 2.04/2.29 (b(s(s(s(z))), elem!1)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[1489, 8961, 1483])).
% 2.04/2.29 tff(8963,plain,
% 2.04/2.29 (~b(s(elem!1), s(s(s(z))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[2363, 306, 816, 8962, 1470])).
% 2.04/2.29 tff(8964,plain,
% 2.04/2.29 (r(s(elem!1), s(s(s(z))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[2367, 43, 8963, 7554])).
% 2.04/2.29 tff(8965,plain,
% 2.04/2.29 (~(s(z) = elem!1)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[89, 87])).
% 2.04/2.29 tff(8966,assumption,(~r(s(z), elem!1)), introduced(assumption)).
% 2.04/2.29 tff(8967,plain,
% 2.04/2.29 ((s(z) = elem!1) | b(s(z), elem!1)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[1500, 43, 8966])).
% 2.04/2.29 tff(8968,plain,
% 2.04/2.29 (b(s(z), elem!1)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[8967, 8965])).
% 2.04/2.29 tff(8969,plain,
% 2.04/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(z))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(8970,plain,
% 2.04/2.29 (((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(z))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(8971,plain,
% 2.04/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(z)))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[8970])).
% 2.04/2.29 tff(8972,plain,
% 2.04/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(z))))),
% 2.04/2.30 inference(transitivity,[status(thm)],[8971, 8969])).
% 2.04/2.30 tff(8973,plain,
% 2.04/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))),
% 2.04/2.30 inference(quant_inst,[status(thm)],[])).
% 2.04/2.30 tff(8974,plain,
% 2.04/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(z)))),
% 2.04/2.30 inference(modus_ponens,[status(thm)],[8973, 8972])).
% 2.04/2.30 tff(8975,plain,
% 2.04/2.30 (~b(s(elem!1), s(z))),
% 2.04/2.30 inference(unit_resolution,[status(thm)],[8974, 306, 816, 8968, 8962, 1470])).
% 2.04/2.30 tff(8976,plain,
% 2.04/2.30 (r(s(elem!1), s(z))),
% 2.04/2.30 inference(unit_resolution,[status(thm)],[2612, 43, 8975, 2249])).
% 2.04/2.30 tff(8977,plain,
% 2.04/2.30 (~b(s(z), s(s(s(z))))),
% 2.04/2.30 inference(unit_resolution,[status(thm)],[2939, 8968, 8962, 1531, 1470])).
% 2.04/2.30 tff(8978,plain,
% 2.04/2.30 (r(s(z), s(s(s(z))))),
% 2.04/2.30 inference(unit_resolution,[status(thm)],[3302, 8977])).
% 2.04/2.30 tff(8979,plain,
% 2.04/2.30 ($false),
% 2.04/2.30 inference(unit_resolution,[status(thm)],[8076, 124, 8978, 8976, 8964])).
% 2.04/2.30 tff(8980,plain,((elem!1 = s(z)) | (s(elem!1) = s(z)) | (s(elem!1) = s(s(s(z)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (s(s(s(z))) = elem!1) | r(s(z), elem!1) | (~r(s(s(s(z))), s(z))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.30 tff(8981,plain,
% 2.04/2.30 (elem!1 = s(z)),
% 2.04/2.30 inference(unit_resolution,[status(thm)],[8980, 8960, 4282, 8959, 1470, 1528, 1444, 8946, 206, 5])).
% 2.04/2.30 tff(8982,plain,
% 2.04/2.30 (s(z) = elem!1),
% 2.04/2.30 inference(symmetry,[status(thm)],[8981])).
% 2.04/2.30 tff(8983,plain,
% 2.04/2.30 (s(z) = s(s(elem!1))),
% 2.04/2.30 inference(transitivity,[status(thm)],[8982, 1427])).
% 2.04/2.30 tff(8984,plain,
% 2.04/2.30 (inj_0(s(z)) = inj_0(s(s(elem!1)))),
% 2.04/2.30 inference(monotonicity,[status(thm)],[8983])).
% 2.04/2.30 tff(8985,plain,
% 2.04/2.30 (inj_0(s(s(elem!1))) = inj_0(s(z))),
% 2.04/2.30 inference(symmetry,[status(thm)],[8984])).
% 2.04/2.30 tff(8986,plain,
% 2.04/2.30 (s(elem!1) = z),
% 2.04/2.30 inference(transitivity,[status(thm)],[67, 8985, 61])).
% 2.04/2.30 tff(8987,plain,
% 2.04/2.30 ($false),
% 2.04/2.30 inference(unit_resolution,[status(thm)],[77, 8986])).
% 2.04/2.30 tff(8988,plain,((~(s(s(elem!1)) = elem!1)) | (~b(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | b(elem!1, s(z)) | (~r(s(z), z)) | b(elem!1, z) | r(s(s(s(elem!1))), s(s(elem!1))) | (s(s(elem!1)) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.30 tff(8989,plain,
% 2.04/2.30 (~(s(s(elem!1)) = elem!1)),
% 2.04/2.30 inference(unit_resolution,[status(thm)],[8988, 8939, 114, 5, 204, 2, 3314, 1565])).
% 2.04/2.30 tff(8990,plain,
% 2.04/2.30 (~(elem!1 = s(s(elem!1)))),
% 2.04/2.30 inference(unit_resolution,[status(thm)],[186, 8989])).
% 2.04/2.30 tff(8991,plain,
% 2.04/2.30 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.04/2.30 inference(unit_resolution,[status(thm)],[143, 8989])).
% 2.04/2.30 tff(8992,plain,
% 2.04/2.30 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.04/2.30 inference(unit_resolution,[status(thm)],[152, 8991])).
% 2.04/2.30 tff(8993,plain,
% 2.04/2.30 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 2.04/2.30 inference(unit_resolution,[status(thm)],[159, 8992])).
% 2.04/2.30 tff(8994,plain,
% 2.04/2.30 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.04/2.30 inference(unit_resolution,[status(thm)],[610, 8993, 3314])).
% 2.04/2.30 tff(8995,plain,
% 2.04/2.30 (b(s(s(elem!1)), elem!1)),
% 2.04/2.30 inference(unit_resolution,[status(thm)],[47, 8989, 6])).
% 2.04/2.30 tff(8996,plain,
% 2.04/2.30 (~(elem!1 = s(z))),
% 2.04/2.30 inference(unit_resolution,[status(thm)],[32, 8995, 9])).
% 2.04/2.30 tff(8997,plain,
% 2.04/2.30 (~(s(elem!1) = elem!1)),
% 2.04/2.30 inference(unit_resolution,[status(thm)],[180, 8989])).
% 2.04/2.30 tff(8998,plain,
% 2.04/2.30 (r(elem!1, z)),
% 2.04/2.30 inference(unit_resolution,[status(thm)],[174, 1616, 2])).
% 2.04/2.30 tff(8999,plain,
% 2.04/2.30 (~r(elem!1, s(s(elem!1)))),
% 2.04/2.30 inference(unit_resolution,[status(thm)],[978, 8998, 437])).
% 2.04/2.30 tff(9000,plain,
% 2.04/2.30 (b(elem!1, s(s(elem!1)))),
% 2.04/2.30 inference(unit_resolution,[status(thm)],[516, 8999, 360])).
% 2.14/2.30 tff(9001,plain,
% 2.14/2.30 (~b(s(s(s(elem!1))), elem!1)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[6386, 306, 30, 9000, 601])).
% 2.14/2.30 tff(9002,plain,
% 2.14/2.30 (r(s(s(s(elem!1))), elem!1)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[1636, 9001, 1526])).
% 2.14/2.30 tff(9003,plain,
% 2.14/2.30 (~(z = elem!1)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[1618, 1616])).
% 2.14/2.30 tff(9004,plain,
% 2.14/2.30 (~(s(elem!1) = s(z))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[2689, 9003])).
% 2.14/2.30 tff(9005,plain,
% 2.14/2.30 (~(s(s(s(z))) = elem!1)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[2204, 8998, 1527])).
% 2.14/2.30 tff(9006,plain,
% 2.14/2.30 (~r(s(z), elem!1)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[1049, 8998, 204])).
% 2.14/2.30 tff(9007,plain,
% 2.14/2.30 (s(elem!1) = s(s(s(z)))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[8980, 816, 87, 8966, 1470, 1531, 1483, 2249, 206, 5])).
% 2.14/2.30 tff(9008,plain,
% 2.14/2.30 (s(s(elem!1)) = s(s(s(s(z))))),
% 2.14/2.30 inference(monotonicity,[status(thm)],[9007])).
% 2.14/2.30 tff(9009,plain,
% 2.14/2.30 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.14/2.30 inference(symmetry,[status(thm)],[9008])).
% 2.14/2.30 tff(9010,plain,
% 2.14/2.30 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(elem!1)), s(s(s(z))))),
% 2.14/2.30 inference(monotonicity,[status(thm)],[9009])).
% 2.14/2.30 tff(9011,plain,
% 2.14/2.30 (r(s(s(elem!1)), s(s(s(z)))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 2.14/2.30 inference(symmetry,[status(thm)],[9010])).
% 2.14/2.30 tff(9012,plain,
% 2.14/2.30 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(elem!1)), s(s(s(z))))),
% 2.14/2.30 inference(monotonicity,[status(thm)],[9007])).
% 2.14/2.30 tff(9013,plain,
% 2.14/2.30 (~b(s(s(elem!1)), s(elem!1))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[1024, 816, 30, 1003])).
% 2.14/2.30 tff(9014,plain,
% 2.14/2.30 (r(s(s(elem!1)), s(elem!1))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[994, 9013, 403])).
% 2.14/2.30 tff(9015,plain,
% 2.14/2.30 (r(s(s(elem!1)), s(s(s(z))))),
% 2.14/2.30 inference(modus_ponens,[status(thm)],[9014, 9012])).
% 2.14/2.30 tff(9016,plain,
% 2.14/2.30 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.14/2.30 inference(modus_ponens,[status(thm)],[9015, 9011])).
% 2.14/2.30 tff(9017,plain,
% 2.14/2.30 (b(s(z), elem!1)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[1500, 43, 8966, 8965])).
% 2.14/2.30 tff(9018,plain,
% 2.14/2.30 (b(s(s(s(z))), elem!1)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[1489, 1483, 8961])).
% 2.14/2.30 tff(9019,plain,
% 2.14/2.30 (~b(s(z), s(s(s(z))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[2939, 9018, 9017, 1531, 1470])).
% 2.14/2.30 tff(9020,plain,
% 2.14/2.30 (r(s(z), s(s(s(z))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[3302, 9019])).
% 2.14/2.30 tff(9021,plain,
% 2.14/2.30 (~r(s(z), s(s(s(s(z)))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[3585, 124, 9020, 9016])).
% 2.14/2.30 tff(9022,plain,
% 2.14/2.30 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(s(s(z)))))),
% 2.14/2.30 inference(monotonicity,[status(thm)],[9008])).
% 2.14/2.30 tff(9023,plain,
% 2.14/2.30 ((~b(s(z), s(s(elem!1)))) <=> (~b(s(z), s(s(s(s(z))))))),
% 2.14/2.30 inference(monotonicity,[status(thm)],[9022])).
% 2.14/2.30 tff(9024,plain,
% 2.14/2.30 (~b(s(z), s(s(elem!1)))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[6409, 306, 30, 1003, 9017])).
% 2.14/2.30 tff(9025,plain,
% 2.14/2.30 (~b(s(z), s(s(s(s(z)))))),
% 2.14/2.30 inference(modus_ponens,[status(thm)],[9024, 9023])).
% 2.14/2.30 tff(9026,plain,
% 2.14/2.30 ($false),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[680, 43, 9025, 9021, 5134])).
% 2.14/2.30 tff(9027,plain,((~b(s(elem!1), elem!1)) | (s(s(elem!1)) = s(elem!1)) | (elem!1 = s(z)) | r(s(z), elem!1) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (s(s(s(z))) = elem!1) | (s(elem!1) = s(z)) | (~r(s(s(s(z))), s(z))) | b(elem!1, s(z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.30 tff(9028,plain,
% 2.14/2.30 (~b(s(elem!1), elem!1)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[9027, 9006, 87, 1565, 1470, 1528, 9005, 9004, 206, 5, 30, 9000])).
% 2.14/2.30 tff(9029,plain,
% 2.14/2.30 (r(s(elem!1), elem!1)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[813, 9028, 193])).
% 2.14/2.30 tff(9030,plain,
% 2.14/2.30 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(9031,plain,
% 2.14/2.30 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 2.14/2.30 inference(quant_inst,[status(thm)],[])).
% 2.14/2.30 tff(9032,plain,
% 2.14/2.30 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1)))),
% 2.14/2.30 inference(modus_ponens,[status(thm)],[9031, 9030])).
% 2.14/2.30 tff(9033,plain,
% 2.14/2.30 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[9032, 124, 9029, 9002])).
% 2.14/2.30 tff(9034,plain,
% 2.14/2.30 (b(s(s(s(z))), elem!1)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[1489, 9005, 8961])).
% 2.14/2.30 tff(9035,plain,
% 2.14/2.30 (~b(z, elem!1)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[4143, 9000, 30, 9034, 1528])).
% 2.14/2.30 tff(9036,plain,
% 2.14/2.30 (r(z, elem!1)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[835, 9035, 9003])).
% 2.14/2.30 tff(9037,plain,
% 2.14/2.30 (~r(s(elem!1), z)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[416, 9029, 9036])).
% 2.14/2.30 tff(9038,plain,
% 2.14/2.30 (b(s(elem!1), z)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[2380, 9037])).
% 2.14/2.30 tff(9039,plain,
% 2.14/2.30 (~b(elem!1, s(s(s(elem!1))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[6394, 306, 30, 9000, 601])).
% 2.14/2.30 tff(9040,plain,
% 2.14/2.30 (r(elem!1, s(s(s(elem!1))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[1260, 43, 9039, 1642])).
% 2.14/2.30 tff(9041,plain,
% 2.14/2.30 (~r(s(s(s(elem!1))), z)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[851, 9040, 8998])).
% 2.14/2.30 tff(9042,plain,
% 2.14/2.30 (b(s(s(s(elem!1))), z)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[3033, 43, 579, 9041])).
% 2.14/2.30 tff(9043,plain,
% 2.14/2.30 (~r(z, s(s(s(elem!1))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[573, 9036, 9040])).
% 2.14/2.30 tff(9044,plain,
% 2.14/2.30 (b(z, s(s(s(elem!1))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[585, 9043])).
% 2.14/2.30 tff(9045,plain,
% 2.14/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(9046,plain,
% 2.14/2.30 (((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(9047,plain,
% 2.14/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z))))),
% 2.14/2.30 inference(monotonicity,[status(thm)],[9046])).
% 2.14/2.30 tff(9048,plain,
% 2.14/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)))),
% 2.14/2.30 inference(transitivity,[status(thm)],[9047, 9045])).
% 2.14/2.30 tff(9049,plain,
% 2.14/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 2.14/2.30 inference(quant_inst,[status(thm)],[])).
% 2.14/2.30 tff(9050,plain,
% 2.14/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z))),
% 2.14/2.30 inference(modus_ponens,[status(thm)],[9049, 9048])).
% 2.14/2.30 tff(9051,plain,
% 2.14/2.30 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[9050, 306, 9044, 9042, 9038])).
% 2.14/2.30 tff(9052,plain,
% 2.14/2.30 ($false),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[664, 9051, 9033, 150])).
% 2.14/2.30 tff(9053,plain,((elem!1 = z) | (s(s(s(elem!1))) = s(elem!1)) | (s(elem!1) = elem!1) | (elem!1 = s(z)) | (~b(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | b(elem!1, s(z)) | (~b(s(s(elem!1)), elem!1)) | (s(s(s(elem!1))) = elem!1) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (elem!1 = s(s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 2.14/2.30 tff(9054,plain,
% 2.14/2.30 (elem!1 = z),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[9053, 8991, 8997, 8996, 8939, 114, 5, 8995, 1526, 8994, 8990, 437, 204, 2])).
% 2.14/2.30 tff(9055,plain,
% 2.14/2.30 (s(elem!1) = s(z)),
% 2.14/2.30 inference(monotonicity,[status(thm)],[9054])).
% 2.14/2.30 tff(9056,plain,
% 2.14/2.30 (s(s(elem!1)) = s(s(z))),
% 2.14/2.30 inference(monotonicity,[status(thm)],[9055])).
% 2.14/2.30 tff(9057,plain,
% 2.14/2.30 (s(s(z)) = s(s(elem!1))),
% 2.14/2.30 inference(symmetry,[status(thm)],[9056])).
% 2.14/2.30 tff(9058,plain,
% 2.14/2.30 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 2.14/2.30 inference(monotonicity,[status(thm)],[9057])).
% 2.14/2.30 tff(9059,plain,
% 2.14/2.30 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(z)))),
% 2.14/2.30 inference(symmetry,[status(thm)],[9058])).
% 2.14/2.30 tff(9060,plain,
% 2.14/2.30 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.14/2.30 inference(monotonicity,[status(thm)],[9056])).
% 2.14/2.30 tff(9061,plain,
% 2.14/2.30 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 2.14/2.30 inference(monotonicity,[status(thm)],[9060])).
% 2.14/2.30 tff(9062,plain,
% 2.14/2.30 (b(s(s(s(z))), s(s(elem!1)))),
% 2.14/2.30 inference(modus_ponens,[status(thm)],[8994, 9061])).
% 2.14/2.30 tff(9063,plain,
% 2.14/2.30 (b(s(s(s(z))), s(s(z)))),
% 2.14/2.30 inference(modus_ponens,[status(thm)],[9062, 9059])).
% 2.14/2.30 tff(9064,plain,
% 2.14/2.30 (b(elem!1, s(s(s(z)))) <=> b(z, s(s(s(z))))),
% 2.14/2.30 inference(monotonicity,[status(thm)],[9054])).
% 2.14/2.30 tff(9065,plain,
% 2.14/2.30 (b(z, s(s(s(z))))),
% 2.14/2.30 inference(modus_ponens,[status(thm)],[8939, 9064])).
% 2.14/2.30 tff(9066,plain,
% 2.14/2.30 (~r(s(s(s(z))), z)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[211, 114, 204])).
% 2.14/2.30 tff(9067,plain,
% 2.14/2.30 (b(s(s(s(z))), z)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[202, 43, 169, 9066])).
% 2.14/2.30 tff(9068,plain,
% 2.14/2.30 (b(s(s(elem!1)), z) <=> b(s(s(z)), z)),
% 2.14/2.30 inference(monotonicity,[status(thm)],[9056])).
% 2.14/2.30 tff(9069,plain,
% 2.14/2.30 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), z)),
% 2.14/2.30 inference(monotonicity,[status(thm)],[9054])).
% 2.14/2.30 tff(9070,plain,
% 2.14/2.30 (b(s(s(elem!1)), z)),
% 2.14/2.30 inference(modus_ponens,[status(thm)],[8995, 9069])).
% 2.14/2.30 tff(9071,plain,
% 2.14/2.30 (b(s(s(z)), z)),
% 2.14/2.30 inference(modus_ponens,[status(thm)],[9070, 9068])).
% 2.14/2.30 tff(9072,plain,
% 2.14/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(9073,plain,
% 2.14/2.30 (((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(9074,plain,
% 2.14/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))))),
% 2.14/2.30 inference(monotonicity,[status(thm)],[9073])).
% 2.14/2.30 tff(9075,plain,
% 2.14/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.14/2.30 inference(transitivity,[status(thm)],[9074, 9072])).
% 2.14/2.30 tff(9076,plain,
% 2.14/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 2.14/2.30 inference(quant_inst,[status(thm)],[])).
% 2.14/2.30 tff(9077,plain,
% 2.14/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))),
% 2.14/2.30 inference(modus_ponens,[status(thm)],[9076, 9075])).
% 2.14/2.30 tff(9078,plain,
% 2.14/2.30 (~b(s(s(s(z))), s(s(z)))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[9077, 306, 9071, 9067, 9065])).
% 2.14/2.30 tff(9079,plain,
% 2.14/2.30 ($false),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[9078, 9063])).
% 2.14/2.30 tff(9080,plain,(r(s(s(elem!1)), elem!1) | b(elem!1, s(z)) | (s(s(s(elem!1))) = elem!1) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | b(elem!1, z) | r(s(s(s(elem!1))), s(s(elem!1))) | b(s(s(s(z))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.30 tff(9081,plain,
% 2.14/2.30 (b(s(s(s(z))), s(z))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[9080, 8938, 8937, 204, 6, 2, 8931, 8928])).
% 2.14/2.30 tff(9082,plain,
% 2.14/2.30 (~(elem!1 = s(s(s(z))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[4555, 1483])).
% 2.14/2.30 tff(9083,plain,
% 2.14/2.30 (b(elem!1, s(s(s(z))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[131, 43, 6884, 9082])).
% 2.14/2.30 tff(9084,plain,
% 2.14/2.30 (((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(9085,plain,
% 2.14/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))))),
% 2.14/2.30 inference(monotonicity,[status(thm)],[9084])).
% 2.14/2.30 tff(9086,plain,
% 2.14/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.14/2.30 inference(transitivity,[status(thm)],[9085, 7505])).
% 2.14/2.30 tff(9087,plain,
% 2.14/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 2.14/2.30 inference(quant_inst,[status(thm)],[])).
% 2.14/2.30 tff(9088,plain,
% 2.14/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 2.14/2.30 inference(modus_ponens,[status(thm)],[9087, 9086])).
% 2.14/2.30 tff(9089,plain,
% 2.14/2.30 ($false),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[9088, 306, 2284, 2831, 6887, 9083])).
% 2.14/2.30 tff(9090,plain,((~r(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (s(s(s(z))) = elem!1) | (~r(elem!1, z)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.30 tff(9091,plain,
% 2.14/2.30 (~r(s(s(s(z))), z)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[9090, 9081, 8906, 8920, 2254, 374])).
% 2.14/2.30 tff(9092,plain,
% 2.14/2.30 (b(s(s(s(z))), z)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[2197, 9091])).
% 2.14/2.30 tff(9093,plain,
% 2.14/2.30 (~r(z, s(elem!1))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[5668, 8907, 374])).
% 2.14/2.30 tff(9094,plain,
% 2.14/2.30 (b(z, s(elem!1))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[275, 9093])).
% 2.14/2.30 tff(9095,plain,
% 2.14/2.30 (~r(s(elem!1), z)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[287, 8907, 2254])).
% 2.14/2.30 tff(9096,plain,
% 2.14/2.30 (b(s(elem!1), z)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[2380, 9095])).
% 2.14/2.30 tff(9097,plain,
% 2.14/2.30 (~b(s(s(s(z))), s(elem!1))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[6777, 306, 9096, 9094, 9092])).
% 2.14/2.30 tff(9098,plain,
% 2.14/2.30 (~(s(elem!1) = s(s(s(z))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[2356, 8913])).
% 2.14/2.30 tff(9099,plain,
% 2.14/2.30 (~(s(s(s(z))) = s(elem!1))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[7556, 9098])).
% 2.14/2.30 tff(9100,plain,
% 2.14/2.30 (r(s(s(s(z))), s(elem!1))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[4132, 43, 9099, 9097])).
% 2.14/2.30 tff(9101,plain,
% 2.14/2.30 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1))))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(9102,plain,
% 2.14/2.30 (((~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(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(9103,plain,
% 2.14/2.31 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1)))))),
% 2.14/2.31 inference(monotonicity,[status(thm)],[9102])).
% 2.14/2.31 tff(9104,plain,
% 2.14/2.31 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1))))),
% 2.14/2.31 inference(transitivity,[status(thm)],[9103, 9101])).
% 2.14/2.31 tff(9105,plain,
% 2.14/2.31 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(z))))))),
% 2.14/2.31 inference(quant_inst,[status(thm)],[])).
% 2.14/2.31 tff(9106,plain,
% 2.14/2.31 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1)))),
% 2.14/2.31 inference(modus_ponens,[status(thm)],[9105, 9104])).
% 2.14/2.31 tff(9107,plain,
% 2.14/2.31 (~r(elem!1, s(s(s(z))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[9106, 124, 8907, 9100])).
% 2.14/2.31 tff(9108,plain,
% 2.14/2.31 (b(elem!1, s(s(s(z))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[131, 43, 9107, 8921])).
% 2.14/2.31 tff(9109,plain,
% 2.14/2.31 (~r(s(s(s(z))), elem!1)),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[8272, 124, 8907, 9100])).
% 2.14/2.31 tff(9110,plain,
% 2.14/2.31 (b(s(s(s(z))), elem!1)),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[1489, 9109, 8920])).
% 2.14/2.31 tff(9111,plain,
% 2.14/2.31 ($false),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[9088, 306, 9081, 8906, 9110, 9108])).
% 2.14/2.31 tff(9112,plain,((~r(s(z), z)) | (~r(z, elem!1)) | r(s(s(elem!1)), elem!1) | b(elem!1, z) | r(s(elem!1), elem!1) | (s(elem!1) = elem!1) | b(s(s(elem!1)), s(elem!1)) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.31 tff(9113,plain,
% 2.14/2.31 (~r(s(z), z)),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[9112, 193, 6, 2, 808, 374, 7093, 2249])).
% 2.14/2.31 tff(9114,plain,
% 2.14/2.31 (b(s(z), z)),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[221, 9113])).
% 2.14/2.31 tff(9115,plain,
% 2.14/2.31 (((~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z))) <=> ((~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(9116,plain,
% 2.14/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z)))))),
% 2.14/2.31 inference(monotonicity,[status(thm)],[9115])).
% 2.14/2.31 tff(9117,plain,
% 2.14/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))),
% 2.14/2.31 inference(transitivity,[status(thm)],[9116, 8063])).
% 2.14/2.31 tff(9118,plain,
% 2.14/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)))),
% 2.14/2.31 inference(quant_inst,[status(thm)],[])).
% 2.14/2.31 tff(9119,plain,
% 2.14/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z)))),
% 2.14/2.31 inference(modus_ponens,[status(thm)],[9118, 9117])).
% 2.14/2.31 tff(9120,plain,
% 2.14/2.31 (~b(s(elem!1), z)),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[9119, 306, 2647, 247, 485])).
% 2.14/2.31 tff(9121,plain,
% 2.14/2.31 (r(s(elem!1), z)),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[2380, 9120])).
% 2.14/2.31 tff(9122,plain,
% 2.14/2.31 (~r(s(s(elem!1)), z)),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[471, 9121, 244])).
% 2.14/2.31 tff(9123,plain,
% 2.14/2.31 (b(s(s(elem!1)), z)),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[476, 9122])).
% 2.14/2.31 tff(9124,plain,
% 2.14/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(9125,plain,
% 2.14/2.31 (((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1)))) <=> ((~b(z, s(elem!1))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(9126,plain,
% 2.14/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z)))))),
% 2.14/2.31 inference(monotonicity,[status(thm)],[9125])).
% 2.14/2.31 tff(9127,plain,
% 2.14/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))),
% 2.14/2.31 inference(transitivity,[status(thm)],[9126, 9124])).
% 2.14/2.31 tff(9128,plain,
% 2.14/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))))),
% 2.14/2.31 inference(quant_inst,[status(thm)],[])).
% 2.14/2.31 tff(9129,plain,
% 2.14/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z)))),
% 2.14/2.31 inference(modus_ponens,[status(thm)],[9128, 9127])).
% 2.14/2.31 tff(9130,plain,
% 2.14/2.31 (~b(z, s(elem!1))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[9129, 306, 2647, 247, 485])).
% 2.14/2.31 tff(9131,plain,
% 2.14/2.31 (r(z, s(elem!1))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[275, 9130])).
% 2.14/2.31 tff(9132,plain,
% 2.14/2.31 (~r(z, s(s(elem!1)))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[799, 9131, 244])).
% 2.14/2.31 tff(9133,plain,
% 2.14/2.31 (b(z, s(s(elem!1)))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[460, 9132])).
% 2.14/2.31 tff(9134,plain,
% 2.14/2.31 (~r(elem!1, s(elem!1))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[265, 9131, 246])).
% 2.14/2.31 tff(9135,plain,
% 2.14/2.31 (b(elem!1, s(elem!1))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[372, 9134, 366])).
% 2.14/2.31 tff(9136,plain,
% 2.14/2.31 (~(s(s(elem!1)) = elem!1)),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[7439, 9135, 7093])).
% 2.14/2.31 tff(9137,plain,
% 2.14/2.31 (b(s(s(elem!1)), elem!1)),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[47, 9136, 6])).
% 2.14/2.31 tff(9138,plain,
% 2.14/2.31 (~b(s(z), s(s(elem!1)))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[6863, 306, 9137, 9133, 9123, 247])).
% 2.14/2.31 tff(9139,plain,
% 2.14/2.31 (r(s(z), s(s(elem!1)))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[3997, 43, 9138, 79])).
% 2.14/2.31 tff(9140,plain,
% 2.14/2.31 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[7090, 9136, 2170, 808])).
% 2.14/2.31 tff(9141,plain,
% 2.14/2.31 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(elem!1)))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(9142,plain,
% 2.14/2.31 (((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z)))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(elem!1)))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(9143,plain,
% 2.14/2.31 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(elem!1))))))),
% 2.14/2.31 inference(monotonicity,[status(thm)],[9142])).
% 2.14/2.31 tff(9144,plain,
% 2.14/2.31 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(elem!1)))))),
% 2.14/2.31 inference(transitivity,[status(thm)],[9143, 9141])).
% 2.14/2.31 tff(9145,plain,
% 2.14/2.31 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))),
% 2.14/2.31 inference(quant_inst,[status(thm)],[])).
% 2.14/2.31 tff(9146,plain,
% 2.14/2.31 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(elem!1))))),
% 2.14/2.31 inference(modus_ponens,[status(thm)],[9145, 9144])).
% 2.14/2.31 tff(9147,plain,
% 2.14/2.31 (~r(s(s(s(elem!1))), s(z))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[9146, 124, 9140, 9139])).
% 2.14/2.31 tff(9148,plain,
% 2.14/2.31 ((s(s(s(elem!1))) = s(z)) | b(s(s(s(elem!1))), s(z))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[5924, 43, 9147])).
% 2.14/2.31 tff(9149,plain,
% 2.14/2.31 (b(s(s(s(elem!1))), s(z))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[9148, 5909])).
% 2.14/2.31 tff(9150,plain,
% 2.14/2.31 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[143, 9136])).
% 2.14/2.31 tff(9151,plain,
% 2.14/2.31 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[659, 9140, 244])).
% 2.14/2.31 tff(9152,plain,
% 2.14/2.31 (b(s(s(s(elem!1))), s(elem!1))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[664, 9151, 9150])).
% 2.14/2.31 tff(9153,plain,
% 2.14/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(9154,plain,
% 2.14/2.31 (((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(9155,plain,
% 2.14/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z)))))),
% 2.14/2.31 inference(monotonicity,[status(thm)],[9154])).
% 2.14/2.31 tff(9156,plain,
% 2.14/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.14/2.31 inference(transitivity,[status(thm)],[9155, 9153])).
% 2.14/2.31 tff(9157,plain,
% 2.14/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 2.14/2.31 inference(quant_inst,[status(thm)],[])).
% 2.14/2.31 tff(9158,plain,
% 2.14/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z)))),
% 2.14/2.31 inference(modus_ponens,[status(thm)],[9157, 9156])).
% 2.14/2.31 tff(9159,plain,
% 2.14/2.31 ($false),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[9158, 306, 9152, 9133, 2647, 247, 9149])).
% 2.14/2.31 tff(9160,plain,((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~r(s(s(elem!1)), s(elem!1))) | (z = elem!1) | r(s(elem!1), elem!1) | r(s(s(elem!1)), elem!1) | b(s(s(elem!1)), s(elem!1)) | (elem!1 = s(elem!1)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.31 tff(9161,plain,
% 2.14/2.31 (~b(z, s(z))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[9160, 9114, 8840, 7429, 2252, 808, 6, 7093, 365, 2254])).
% 2.14/2.31 tff(9162,plain,
% 2.14/2.31 (r(z, s(z))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[2263, 9161])).
% 2.14/2.31 tff(9163,plain,
% 2.14/2.31 (~r(s(z), elem!1)),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[6096, 9162, 374])).
% 2.14/2.31 tff(9164,plain,
% 2.14/2.31 (b(s(z), elem!1)),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[1500, 43, 9163, 8904])).
% 2.14/2.31 tff(9165,plain,
% 2.14/2.31 (~(elem!1 = s(z))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[3096, 8904])).
% 2.14/2.31 tff(9166,plain,
% 2.14/2.31 (~r(elem!1, s(z))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[385, 9162, 374])).
% 2.14/2.31 tff(9167,plain,
% 2.14/2.31 (b(elem!1, s(z))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[96, 43, 9166, 9165])).
% 2.14/2.31 tff(9168,plain,
% 2.14/2.31 ($false),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[5422, 9167, 9164, 2323, 8840])).
% 2.14/2.31 tff(9169,plain,((s(elem!1) = elem!1) | (~r(z, elem!1)) | r(s(elem!1), elem!1) | r(s(s(elem!1)), elem!1) | b(s(s(elem!1)), s(elem!1)) | b(elem!1, z) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.31 tff(9170,plain,
% 2.14/2.31 (b(s(s(elem!1)), s(elem!1))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[9169, 6, 374, 808, 193, 2, 2249])).
% 2.14/2.31 tff(9171,plain,
% 2.14/2.31 (b(s(s(elem!1)), elem!1)),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[47, 6, 91])).
% 2.14/2.31 tff(9172,plain,
% 2.14/2.31 ($false),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[6251, 306, 9171, 9170, 816, 815])).
% 2.14/2.31 tff(9173,plain,(r(s(s(elem!1)), elem!1) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (s(s(elem!1)) = elem!1) | (~r(z, elem!1)) | r(s(elem!1), elem!1) | (s(elem!1) = elem!1) | b(elem!1, z) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.31 tff(9174,plain,
% 2.14/2.31 (s(s(elem!1)) = elem!1),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[9173, 8839, 8818, 8809, 5330, 8734, 8808, 2, 3099])).
% 2.14/2.31 tff(9175,plain,
% 2.14/2.31 (elem!1 = s(s(elem!1))),
% 2.14/2.31 inference(symmetry,[status(thm)],[9174])).
% 2.14/2.31 tff(9176,plain,
% 2.14/2.31 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 2.14/2.31 inference(transitivity,[status(thm)],[8805, 9175])).
% 2.14/2.31 tff(9177,plain,
% 2.14/2.31 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(elem!1)))),
% 2.14/2.31 inference(monotonicity,[status(thm)],[9176])).
% 2.14/2.31 tff(9178,plain,
% 2.14/2.31 (s(s(s(s(s(z))))) = s(elem!1)),
% 2.14/2.31 inference(transitivity,[status(thm)],[2823, 9177, 66])).
% 2.14/2.31 tff(9179,plain,
% 2.14/2.31 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(elem!1))),
% 2.14/2.31 inference(monotonicity,[status(thm)],[9178])).
% 2.14/2.31 tff(9180,plain,
% 2.14/2.31 (s(s(s(s(z)))) = s(s(s(s(s(s(z))))))),
% 2.14/2.31 inference(transitivity,[status(thm)],[497, 9179, 135, 8806])).
% 2.14/2.31 tff(9181,plain,
% 2.14/2.31 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(s(s(z)))))))),
% 2.14/2.31 inference(monotonicity,[status(thm)],[9180])).
% 2.14/2.31 tff(9182,plain,
% 2.14/2.31 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(s(s(z)))))),
% 2.14/2.31 inference(symmetry,[status(thm)],[9181])).
% 2.14/2.31 tff(9183,plain,
% 2.14/2.31 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(s(z)))))))),
% 2.14/2.31 inference(symmetry,[status(thm)],[9177])).
% 2.14/2.31 tff(9184,plain,
% 2.14/2.31 (s(elem!1) = s(s(s(z)))),
% 2.14/2.31 inference(transitivity,[status(thm)],[67, 9183, 9182, 320])).
% 2.14/2.31 tff(9185,plain,
% 2.14/2.31 ($false),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[8814, 9184])).
% 2.14/2.31 tff(9186,plain,((z = elem!1) | b(elem!1, z) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | b(z, elem!1) | b(s(s(s(z))), s(z)) | (~b(s(s(s(z))), elem!1)) | r(s(s(s(z))), elem!1) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.31 tff(9187,plain,
% 2.14/2.31 (z = elem!1),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[9186, 4, 2, 1034, 1531, 5318, 9, 1967, 1484, 359])).
% 2.14/2.31 tff(9188,plain,
% 2.14/2.31 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[1511, 9187])).
% 2.14/2.31 tff(9189,plain,
% 2.14/2.31 (~(elem!1 = s(s(s(elem!1))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[1518, 9188])).
% 2.14/2.31 tff(9190,plain,
% 2.14/2.31 (r(s(z), z)),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[1524, 9187, 4])).
% 2.14/2.31 tff(9191,plain,
% 2.14/2.31 (s(s(s(elem!1))) = elem!1),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[2182, 9190, 114, 2, 359])).
% 2.14/2.31 tff(9192,plain,
% 2.14/2.31 ($false),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[2187, 9191, 9189])).
% 2.14/2.31 tff(9193,plain,((~r(s(z), elem!1)) | b(elem!1, z) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | b(z, elem!1) | b(s(s(s(z))), s(z)) | (~b(s(s(s(z))), elem!1)) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.14/2.31 tff(9194,plain,
% 2.14/2.31 (~r(s(z), elem!1)),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[9193, 8713, 2, 1034, 5320, 5318, 9, 5319, 1484])).
% 2.14/2.31 tff(9195,plain,
% 2.14/2.31 (~(s(z) = elem!1)),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[2235, 5319, 9])).
% 2.14/2.31 tff(9196,plain,
% 2.14/2.31 (~(elem!1 = s(z))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[3096, 9195])).
% 2.14/2.31 tff(9197,plain,
% 2.14/2.31 (b(s(z), elem!1)),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[1500, 43, 9194, 9195])).
% 2.14/2.31 tff(9198,plain,
% 2.14/2.31 (b(elem!1, s(s(s(z))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[2304, 8719, 8023])).
% 2.14/2.31 tff(9199,plain,
% 2.14/2.31 (~b(elem!1, s(z))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[8015, 5330, 5319, 2831, 206, 5320, 1034, 1484, 2170, 2, 87])).
% 2.14/2.31 tff(9200,plain,
% 2.14/2.31 (~(s(s(s(z))) = elem!1)),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[2204, 5612, 1629])).
% 2.14/2.31 tff(9201,plain,
% 2.14/2.31 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[7520, 1483, 359, 2831, 374, 1470])).
% 2.14/2.31 tff(9202,plain,
% 2.14/2.31 (r(s(elem!1), s(z))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[2639, 2621, 359])).
% 2.14/2.31 tff(9203,plain,
% 2.14/2.31 (s(s(s(elem!1))) = s(s(elem!1))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[2436, 176])).
% 2.14/2.31 tff(9204,plain,
% 2.14/2.31 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[5403, 9203])).
% 2.14/2.31 tff(9205,plain,
% 2.14/2.31 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[1144, 9204, 4269])).
% 2.14/2.31 tff(9206,plain,
% 2.14/2.31 (~b(s(z), z)),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[7480, 9205, 359, 374])).
% 2.14/2.31 tff(9207,plain,
% 2.14/2.31 (r(s(z), z)),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[221, 9206])).
% 2.14/2.31 tff(9208,plain,
% 2.14/2.31 (~r(s(elem!1), z)),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[2634, 9207, 9202])).
% 2.14/2.31 tff(9209,plain,
% 2.14/2.31 (b(s(elem!1), z)),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[2380, 9208])).
% 2.14/2.31 tff(9210,plain,
% 2.14/2.31 (s(s(s(elem!1))) = elem!1),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[2182, 9207, 206, 2, 359])).
% 2.14/2.31 tff(9211,plain,
% 2.14/2.31 (elem!1 = s(s(s(elem!1)))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[2187, 9210])).
% 2.14/2.31 tff(9212,plain,
% 2.14/2.31 (b(elem!1, z) <=> b(s(s(s(elem!1))), z)),
% 2.14/2.31 inference(monotonicity,[status(thm)],[1513])).
% 2.14/2.31 tff(9213,plain,
% 2.14/2.31 (b(s(s(s(elem!1))), z) <=> b(elem!1, z)),
% 2.14/2.31 inference(symmetry,[status(thm)],[9212])).
% 2.14/2.31 tff(9214,plain,
% 2.14/2.31 (b(elem!1, z)),
% 2.14/2.31 inference(modus_ponens,[status(thm)],[6445, 9213])).
% 2.14/2.31 tff(9215,plain,
% 2.14/2.31 ($false),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[2, 9214])).
% 2.14/2.31 tff(9216,plain,((~(elem!1 = s(s(s(elem!1))))) | b(elem!1, z) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.31 tff(9217,plain,
% 2.14/2.31 (~b(s(s(s(elem!1))), z)),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[9216, 9211, 2])).
% 2.14/2.31 tff(9218,plain,
% 2.14/2.31 (b(s(s(s(elem!1))), z) <=> b(s(elem!1), z)),
% 2.14/2.31 inference(monotonicity,[status(thm)],[136])).
% 2.14/2.31 tff(9219,plain,
% 2.14/2.31 ((~b(s(s(s(elem!1))), z)) <=> (~b(s(elem!1), z))),
% 2.14/2.31 inference(monotonicity,[status(thm)],[9218])).
% 2.14/2.31 tff(9220,assumption,(~b(s(s(s(elem!1))), z)), introduced(assumption)).
% 2.14/2.31 tff(9221,plain,
% 2.14/2.31 (~b(s(elem!1), z)),
% 2.14/2.31 inference(modus_ponens,[status(thm)],[9220, 9219])).
% 2.14/2.31 tff(9222,plain,
% 2.14/2.31 ($false),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[1199, 9221])).
% 2.14/2.31 tff(9223,plain,(b(s(s(s(elem!1))), z) | (~b(s(elem!1), z)) | (~(s(s(s(elem!1))) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.31 tff(9224,plain,
% 2.14/2.31 ($false),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[9223, 9217, 9209, 2431])).
% 2.14/2.31 tff(9225,plain,((~(s(elem!1) = elem!1)) | b(elem!1, z) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(z, elem!1)) | b(s(s(s(s(s(s(z)))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.14/2.31 tff(9226,plain,
% 2.14/2.31 (~(s(elem!1) = elem!1)),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[9225, 374, 206, 359, 2, 9201])).
% 2.14/2.31 tff(9227,plain,
% 2.14/2.31 (~(s(s(elem!1)) = s(elem!1))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[195, 9226])).
% 2.14/2.31 tff(9228,plain,
% 2.14/2.31 (b(s(elem!1), elem!1)),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[813, 808, 9226])).
% 2.14/2.31 tff(9229,plain,
% 2.14/2.31 (s(elem!1) = s(s(s(z)))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[8980, 9228, 206, 87, 8966, 1470, 1483, 5, 1531, 3099])).
% 2.14/2.31 tff(9230,plain,
% 2.14/2.31 (inj_0(s(elem!1)) = inj_0(s(s(s(z))))),
% 2.14/2.31 inference(monotonicity,[status(thm)],[2349])).
% 2.14/2.31 tff(9231,plain,
% 2.14/2.31 (elem!1 = s(s(z))),
% 2.14/2.31 inference(transitivity,[status(thm)],[1651, 9230, 102])).
% 2.14/2.31 tff(9232,plain,
% 2.14/2.31 (b(z, elem!1) <=> b(z, s(s(z)))),
% 2.14/2.31 inference(monotonicity,[status(thm)],[9231])).
% 2.14/2.31 tff(9233,plain,
% 2.14/2.31 (b(z, s(s(z))) <=> b(z, elem!1)),
% 2.14/2.31 inference(symmetry,[status(thm)],[9232])).
% 2.14/2.31 tff(9234,plain,
% 2.14/2.31 ((~b(z, s(s(z)))) <=> (~b(z, elem!1))),
% 2.14/2.31 inference(monotonicity,[status(thm)],[9233])).
% 2.14/2.31 tff(9235,plain,
% 2.14/2.31 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 2.14/2.31 inference(symmetry,[status(thm)],[9230])).
% 2.14/2.31 tff(9236,plain,
% 2.14/2.31 (s(s(z)) = elem!1),
% 2.14/2.31 inference(transitivity,[status(thm)],[103, 9235, 135])).
% 2.14/2.31 tff(9237,plain,
% 2.14/2.31 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(z))), elem!1)),
% 2.14/2.31 inference(monotonicity,[status(thm)],[9236])).
% 2.14/2.31 tff(9238,plain,
% 2.14/2.31 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(z)))),
% 2.14/2.31 inference(symmetry,[status(thm)],[9237])).
% 2.14/2.31 tff(9239,plain,
% 2.14/2.31 (b(s(s(s(z))), s(s(z)))),
% 2.14/2.31 inference(modus_ponens,[status(thm)],[1967, 9238])).
% 2.14/2.31 tff(9240,assumption,(~b(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 2.14/2.31 tff(9241,plain,
% 2.14/2.31 ($false),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[9240, 9239])).
% 2.14/2.31 tff(9242,plain,(b(s(s(s(z))), s(s(z))) | (~b(s(s(s(z))), elem!1)) | (~(s(elem!1) = s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.31 tff(9243,plain,
% 2.14/2.31 (b(s(s(s(z))), s(s(z)))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[9242, 2349, 1967])).
% 2.14/2.31 tff(9244,plain,
% 2.14/2.31 (b(s(s(z)), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 2.14/2.31 inference(monotonicity,[status(thm)],[9236])).
% 2.14/2.31 tff(9245,plain,
% 2.14/2.31 (b(elem!1, s(s(s(z)))) <=> b(s(s(z)), s(s(s(z))))),
% 2.14/2.31 inference(symmetry,[status(thm)],[9244])).
% 2.14/2.31 tff(9246,plain,
% 2.14/2.31 (b(s(s(z)), s(s(s(z))))),
% 2.14/2.31 inference(modus_ponens,[status(thm)],[1470, 9245])).
% 2.14/2.31 tff(9247,assumption,(b(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 2.14/2.31 tff(9248,plain,
% 2.14/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(9249,plain,
% 2.14/2.31 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(9250,plain,
% 2.14/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))))),
% 2.14/2.31 inference(monotonicity,[status(thm)],[9249])).
% 2.14/2.31 tff(9251,plain,
% 2.14/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.14/2.31 inference(transitivity,[status(thm)],[9250, 9248])).
% 2.14/2.31 tff(9252,plain,
% 2.14/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))),
% 2.14/2.31 inference(quant_inst,[status(thm)],[])).
% 2.14/2.31 tff(9253,plain,
% 2.14/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))),
% 2.14/2.31 inference(modus_ponens,[status(thm)],[9252, 9251])).
% 2.14/2.31 tff(9254,plain,
% 2.14/2.31 ($false),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[9253, 306, 2062, 1531, 2454, 9247])).
% 2.14/2.31 tff(9255,plain,((~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.31 tff(9256,plain,
% 2.14/2.31 (~b(z, s(s(z)))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[9255, 9246, 1531, 9243])).
% 2.14/2.31 tff(9257,plain,
% 2.14/2.31 (~b(z, elem!1)),
% 2.14/2.31 inference(modus_ponens,[status(thm)],[9256, 9234])).
% 2.14/2.31 tff(9258,plain,
% 2.14/2.31 (r(z, elem!1)),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[835, 9257, 2170])).
% 2.14/2.31 tff(9259,plain,
% 2.14/2.31 (~r(z, s(s(elem!1)))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[5837, 9258, 1730])).
% 2.14/2.31 tff(9260,plain,
% 2.14/2.31 (b(s(z), elem!1) <=> b(s(z), s(s(z)))),
% 2.14/2.31 inference(monotonicity,[status(thm)],[9231])).
% 2.14/2.31 tff(9261,plain,
% 2.14/2.31 (b(s(z), s(s(z)))),
% 2.14/2.31 inference(modus_ponens,[status(thm)],[2831, 9260])).
% 2.14/2.31 tff(9262,plain,
% 2.14/2.31 (s(s(elem!1)) = s(s(s(s(z))))),
% 2.14/2.31 inference(monotonicity,[status(thm)],[2349])).
% 2.14/2.31 tff(9263,plain,
% 2.14/2.31 ((s(s(elem!1)) = s(s(s(z)))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 2.14/2.31 inference(monotonicity,[status(thm)],[9262])).
% 2.14/2.31 tff(9264,plain,
% 2.14/2.31 ((~(s(s(elem!1)) = s(s(s(z))))) <=> (~(s(s(s(s(z)))) = s(s(s(z)))))),
% 2.14/2.31 inference(monotonicity,[status(thm)],[9263])).
% 2.14/2.31 tff(9265,plain,
% 2.14/2.31 ((s(s(elem!1)) = s(elem!1)) <=> (s(s(elem!1)) = s(s(s(z))))),
% 2.14/2.31 inference(monotonicity,[status(thm)],[2349])).
% 2.14/2.31 tff(9266,plain,
% 2.14/2.31 ((~(s(s(elem!1)) = s(elem!1))) <=> (~(s(s(elem!1)) = s(s(s(z)))))),
% 2.14/2.31 inference(monotonicity,[status(thm)],[9265])).
% 2.14/2.31 tff(9267,plain,
% 2.14/2.31 (~(s(s(elem!1)) = s(s(s(z))))),
% 2.14/2.31 inference(modus_ponens,[status(thm)],[403, 9266])).
% 2.14/2.31 tff(9268,plain,
% 2.14/2.31 (~(s(s(s(s(z)))) = s(s(s(z))))),
% 2.14/2.31 inference(modus_ponens,[status(thm)],[9267, 9264])).
% 2.14/2.31 tff(9269,plain,
% 2.14/2.31 (~b(s(z), s(s(s(z))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[2939, 2831, 1967, 1531, 1470])).
% 2.14/2.31 tff(9270,plain,
% 2.14/2.31 (r(s(z), s(s(s(z))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[3302, 9269])).
% 2.14/2.32 tff(9271,plain,
% 2.14/2.32 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.14/2.32 inference(symmetry,[status(thm)],[9262])).
% 2.14/2.32 tff(9272,plain,
% 2.14/2.32 (b(z, s(s(s(s(z))))) <=> b(z, s(s(elem!1)))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[9271])).
% 2.14/2.32 tff(9273,plain,
% 2.14/2.32 (b(z, s(s(elem!1))) <=> b(z, s(s(s(s(z)))))),
% 2.14/2.32 inference(symmetry,[status(thm)],[9272])).
% 2.14/2.32 tff(9274,plain,
% 2.14/2.32 (b(z, s(s(s(s(z)))))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[1198, 9273])).
% 2.14/2.32 tff(9275,plain,
% 2.14/2.32 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(elem!1)), elem!1)),
% 2.14/2.32 inference(monotonicity,[status(thm)],[9271, 9236])).
% 2.14/2.32 tff(9276,plain,
% 2.14/2.32 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(s(z)))), s(s(z)))),
% 2.14/2.32 inference(symmetry,[status(thm)],[9275])).
% 2.14/2.32 tff(9277,plain,
% 2.14/2.32 (r(s(s(s(s(z)))), s(s(z)))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[1730, 9276])).
% 2.14/2.32 tff(9278,plain,
% 2.14/2.32 (r(z, s(s(z))) <=> r(z, elem!1)),
% 2.14/2.32 inference(monotonicity,[status(thm)],[9236])).
% 2.14/2.32 tff(9279,plain,
% 2.14/2.32 (r(z, elem!1) <=> r(z, s(s(z)))),
% 2.14/2.32 inference(symmetry,[status(thm)],[9278])).
% 2.14/2.32 tff(9280,plain,
% 2.14/2.32 (r(z, s(s(z)))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[374, 9279])).
% 2.14/2.32 tff(9281,plain,
% 2.14/2.32 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(z)))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(9282,plain,
% 2.14/2.32 (((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(z)))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(9283,plain,
% 2.14/2.32 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(z))))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[9282])).
% 2.14/2.32 tff(9284,plain,
% 2.14/2.32 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(z)))))),
% 2.14/2.32 inference(transitivity,[status(thm)],[9283, 9281])).
% 2.14/2.32 tff(9285,plain,
% 2.14/2.32 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))),
% 2.14/2.32 inference(quant_inst,[status(thm)],[])).
% 2.14/2.32 tff(9286,plain,
% 2.14/2.32 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(z))))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[9285, 9284])).
% 2.14/2.32 tff(9287,plain,
% 2.14/2.32 ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(z))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[9286, 124])).
% 2.14/2.32 tff(9288,plain,
% 2.14/2.32 (~r(s(s(s(s(z)))), z)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[9287, 9280, 9277])).
% 2.14/2.32 tff(9289,plain,
% 2.14/2.32 (b(s(s(s(s(z)))), z)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[695, 9288])).
% 2.14/2.32 tff(9290,plain,
% 2.14/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(9291,plain,
% 2.14/2.32 (((~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(9292,plain,
% 2.14/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z))))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[9291])).
% 2.14/2.32 tff(9293,plain,
% 2.14/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))))),
% 2.14/2.32 inference(transitivity,[status(thm)],[9292, 9290])).
% 2.14/2.32 tff(9294,plain,
% 2.14/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.14/2.32 inference(quant_inst,[status(thm)],[])).
% 2.14/2.32 tff(9295,plain,
% 2.14/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z))))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[9294, 9293])).
% 2.14/2.32 tff(9296,plain,
% 2.14/2.32 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[9295, 306, 9289, 1531, 5097, 391])).
% 2.14/2.32 tff(9297,plain,
% 2.14/2.32 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[712, 9296, 342])).
% 2.14/2.32 tff(9298,plain,
% 2.14/2.32 (~r(s(z), s(s(s(s(z)))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[3585, 124, 1034, 9297])).
% 2.14/2.32 tff(9299,plain,
% 2.14/2.32 (b(s(z), s(s(s(s(z)))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[680, 43, 9298, 5134])).
% 2.14/2.32 tff(9300,plain,
% 2.14/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(9301,plain,
% 2.14/2.32 (((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z)))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(9302,plain,
% 2.14/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[9301])).
% 2.14/2.32 tff(9303,plain,
% 2.14/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.14/2.32 inference(transitivity,[status(thm)],[9302, 9300])).
% 2.14/2.32 tff(9304,plain,
% 2.14/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))),
% 2.14/2.32 inference(quant_inst,[status(thm)],[])).
% 2.14/2.32 tff(9305,plain,
% 2.14/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[9304, 9303])).
% 2.14/2.32 tff(9306,plain,
% 2.14/2.32 ($false),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[9305, 306, 9289, 9299, 391, 9274])).
% 2.14/2.32 tff(9307,plain,((~r(z, elem!1)) | (~r(s(z), s(s(s(z))))) | (~b(z, s(s(elem!1)))) | (~(s(elem!1) = s(s(s(z))))) | (s(s(s(s(z)))) = s(s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(z)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.32 tff(9308,plain,
% 2.14/2.32 (~b(z, s(s(elem!1)))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[9307, 9258, 9270, 2349, 9268, 1531, 9261, 1730, 359])).
% 2.14/2.32 tff(9309,plain,
% 2.14/2.32 ($false),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[460, 9308, 9259])).
% 2.14/2.32 tff(9310,plain,((~(s(elem!1) = s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(z))) | (z = elem!1) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (s(s(elem!1)) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.32 tff(9311,plain,
% 2.14/2.32 (~r(s(s(elem!1)), elem!1)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[9310, 9229, 359, 2831, 2170, 9227, 1967, 1470, 1531])).
% 2.14/2.32 tff(9312,plain,
% 2.14/2.32 (b(s(s(elem!1)), s(elem!1))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[9169, 9311, 374, 808, 9226, 2, 3099])).
% 2.14/2.32 tff(9313,plain,
% 2.14/2.32 (~(s(s(elem!1)) = elem!1)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[2356, 9229])).
% 2.14/2.32 tff(9314,plain,
% 2.14/2.32 (b(s(s(elem!1)), elem!1)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[47, 9313, 9311])).
% 2.14/2.32 tff(9315,plain,
% 2.14/2.32 (~(elem!1 = s(elem!1))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[364, 9226])).
% 2.14/2.32 tff(9316,plain,
% 2.14/2.32 (~b(elem!1, s(elem!1))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[9173, 9311, 9313, 9228, 374, 808, 9226, 2, 3099])).
% 2.14/2.32 tff(9317,plain,
% 2.14/2.32 (r(elem!1, s(elem!1))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[372, 9316, 9315])).
% 2.14/2.32 tff(9318,plain,
% 2.14/2.32 (~r(s(elem!1), z)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[287, 9317, 5612])).
% 2.14/2.32 tff(9319,plain,
% 2.14/2.32 (b(s(elem!1), z)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[2380, 9318])).
% 2.14/2.32 tff(9320,plain,
% 2.14/2.32 (~(elem!1 = s(s(elem!1)))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[186, 9313])).
% 2.14/2.32 tff(9321,plain,
% 2.14/2.32 (~b(elem!1, s(s(elem!1)))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[1024, 9314, 9228, 9312])).
% 2.14/2.32 tff(9322,plain,
% 2.14/2.32 (r(elem!1, s(s(elem!1)))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[516, 9321, 9320])).
% 2.14/2.32 tff(9323,plain,
% 2.14/2.32 (~r(z, s(s(elem!1)))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[978, 9322, 5612])).
% 2.14/2.32 tff(9324,plain,
% 2.14/2.32 (b(z, s(s(elem!1)))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[460, 9323])).
% 2.14/2.32 tff(9325,plain,
% 2.14/2.32 ($false),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[1228, 9324, 9319, 374, 9314, 9226, 9312])).
% 2.14/2.32 tff(9326,plain,(r(s(elem!1), elem!1) | (~r(z, elem!1)) | b(elem!1, z) | (~r(elem!1, s(z))) | (~b(s(z), elem!1)) | (z = elem!1) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (elem!1 = s(z)) | r(s(z), elem!1) | (s(s(s(z))) = elem!1) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.32 tff(9327,plain,
% 2.14/2.32 (r(s(elem!1), elem!1)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[9326, 5330, 2, 359, 2831, 2170, 5319, 9198, 5320, 206, 87, 8966, 9200, 9199])).
% 2.14/2.32 tff(9328,plain,
% 2.14/2.32 (~r(s(elem!1), s(z))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[2960, 9327, 359])).
% 2.14/2.32 tff(9329,plain,
% 2.14/2.32 (b(s(elem!1), s(z))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[2964, 9328, 3099])).
% 2.14/2.32 tff(9330,plain,
% 2.14/2.32 (~r(s(elem!1), z)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[416, 9327, 5330])).
% 2.14/2.32 tff(9331,plain,
% 2.14/2.32 (b(s(elem!1), z)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[2380, 9330])).
% 2.14/2.32 tff(9332,plain,
% 2.14/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(9333,plain,
% 2.14/2.32 (((~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z))) <=> ((~b(s(elem!1), z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(9334,plain,
% 2.14/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(elem!1), s(z)))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[9333])).
% 2.14/2.32 tff(9335,plain,
% 2.14/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))))),
% 2.14/2.32 inference(transitivity,[status(thm)],[9334, 9332])).
% 2.14/2.32 tff(9336,plain,
% 2.14/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)))),
% 2.14/2.32 inference(quant_inst,[status(thm)],[])).
% 2.14/2.32 tff(9337,plain,
% 2.14/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(elem!1), s(z)))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[9336, 9335])).
% 2.14/2.32 tff(9338,plain,
% 2.14/2.32 ($false),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[9337, 306, 9331, 2831, 9329, 9198, 8718])).
% 2.14/2.32 tff(9339,plain,((z = elem!1) | (~b(s(z), elem!1)) | (~r(elem!1, s(z))) | b(elem!1, z) | (~r(s(s(s(z))), s(z))) | (elem!1 = s(z)) | r(s(z), elem!1) | r(s(s(s(z))), z) | (~r(s(z), s(s(s(z))))) | r(s(s(s(z))), elem!1) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.14/2.32 tff(9340,plain,
% 2.14/2.32 (z = elem!1),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[9339, 9197, 8713, 2, 114, 9196, 9194, 1629, 1034, 1484, 5318])).
% 2.14/2.32 tff(9341,plain,
% 2.14/2.32 ((s(s(s(s(s(s(z)))))) = z) <=> (s(s(s(s(s(s(z)))))) = elem!1)),
% 2.14/2.32 inference(monotonicity,[status(thm)],[9340])).
% 2.14/2.32 tff(9342,plain,
% 2.14/2.32 ((~(s(s(s(s(s(s(z)))))) = z)) <=> (~(s(s(s(s(s(s(z)))))) = elem!1))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[9341])).
% 2.14/2.32 tff(9343,plain,
% 2.14/2.32 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[554, 9342])).
% 2.14/2.32 tff(9344,plain,
% 2.14/2.32 (r(s(s(elem!1)), z) <=> r(s(s(elem!1)), elem!1)),
% 2.14/2.32 inference(monotonicity,[status(thm)],[9340])).
% 2.14/2.32 tff(9345,plain,
% 2.14/2.32 (b(z, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[9340])).
% 2.14/2.32 tff(9346,plain,
% 2.14/2.32 (b(elem!1, s(s(s(elem!1)))) <=> b(z, s(s(s(elem!1))))),
% 2.14/2.32 inference(symmetry,[status(thm)],[9345])).
% 2.14/2.32 tff(9347,plain,
% 2.14/2.32 (s(z) = s(elem!1)),
% 2.14/2.32 inference(monotonicity,[status(thm)],[9340])).
% 2.14/2.32 tff(9348,plain,
% 2.14/2.32 (s(s(z)) = s(s(elem!1))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[9347])).
% 2.14/2.32 tff(9349,plain,
% 2.14/2.32 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[9348])).
% 2.14/2.32 tff(9350,plain,
% 2.14/2.32 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(s(elem!1))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[9349])).
% 2.14/2.32 tff(9351,plain,
% 2.14/2.32 (b(elem!1, s(s(s(z)))) <=> b(z, s(s(s(elem!1))))),
% 2.14/2.32 inference(transitivity,[status(thm)],[9350, 9346])).
% 2.14/2.32 tff(9352,plain,
% 2.14/2.32 (~r(elem!1, s(s(s(z))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[3293, 8713, 1034])).
% 2.14/2.32 tff(9353,plain,
% 2.14/2.32 (b(elem!1, s(s(s(z))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[2304, 9352, 8023])).
% 2.14/2.32 tff(9354,plain,
% 2.14/2.32 (b(z, s(s(s(elem!1))))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[9353, 9351])).
% 2.14/2.32 tff(9355,plain,
% 2.14/2.32 (b(s(s(s(elem!1))), z) <=> b(s(s(s(elem!1))), elem!1)),
% 2.14/2.32 inference(monotonicity,[status(thm)],[9340])).
% 2.14/2.32 tff(9356,plain,
% 2.14/2.32 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), z)),
% 2.14/2.32 inference(symmetry,[status(thm)],[9355])).
% 2.14/2.32 tff(9357,plain,
% 2.14/2.32 (elem!1 = z),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[1618, 9340])).
% 2.14/2.32 tff(9358,plain,
% 2.14/2.32 (~r(s(s(s(elem!1))), elem!1)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[1631, 9357, 1629])).
% 2.14/2.32 tff(9359,plain,
% 2.14/2.32 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[1511, 9340])).
% 2.14/2.32 tff(9360,plain,
% 2.14/2.32 (~(elem!1 = s(s(s(elem!1))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[1518, 9359])).
% 2.14/2.32 tff(9361,plain,
% 2.14/2.32 (~(s(s(s(elem!1))) = elem!1)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[2187, 9360])).
% 2.14/2.32 tff(9362,plain,
% 2.14/2.32 (b(s(s(s(elem!1))), elem!1)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[1636, 9361, 9358])).
% 2.14/2.32 tff(9363,plain,
% 2.14/2.32 (b(s(s(s(elem!1))), z)),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[9362, 9356])).
% 2.14/2.32 tff(9364,plain,
% 2.14/2.32 (b(s(elem!1), z) <=> b(s(elem!1), elem!1)),
% 2.14/2.32 inference(monotonicity,[status(thm)],[9340])).
% 2.14/2.32 tff(9365,plain,
% 2.14/2.32 (b(s(elem!1), elem!1) <=> b(s(elem!1), z)),
% 2.14/2.32 inference(symmetry,[status(thm)],[9364])).
% 2.14/2.32 tff(9366,plain,
% 2.14/2.32 (b(s(z), elem!1) <=> b(s(elem!1), elem!1)),
% 2.14/2.32 inference(monotonicity,[status(thm)],[9347])).
% 2.14/2.32 tff(9367,plain,
% 2.14/2.32 (b(s(z), elem!1) <=> b(s(elem!1), z)),
% 2.14/2.32 inference(transitivity,[status(thm)],[9366, 9365])).
% 2.14/2.32 tff(9368,plain,
% 2.14/2.32 (b(s(elem!1), z)),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[9197, 9367])).
% 2.14/2.32 tff(9369,plain,
% 2.14/2.32 (~(s(elem!1) = elem!1)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[2698, 9340])).
% 2.14/2.32 tff(9370,plain,
% 2.14/2.32 (~(s(s(elem!1)) = s(elem!1))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[195, 9369])).
% 2.14/2.32 tff(9371,plain,
% 2.14/2.32 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.14/2.32 inference(symmetry,[status(thm)],[9349])).
% 2.14/2.32 tff(9372,plain,
% 2.14/2.32 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(z))), s(elem!1))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[9371])).
% 2.14/2.32 tff(9373,plain,
% 2.14/2.32 (r(s(s(s(z))), s(elem!1)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 2.14/2.32 inference(symmetry,[status(thm)],[9372])).
% 2.14/2.32 tff(9374,plain,
% 2.14/2.32 (r(s(s(s(z))), s(z)) <=> r(s(s(s(z))), s(elem!1))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[9347])).
% 2.14/2.32 tff(9375,plain,
% 2.14/2.32 (r(s(s(s(z))), s(elem!1))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[114, 9374])).
% 2.14/2.32 tff(9376,plain,
% 2.14/2.32 (r(s(s(s(elem!1))), s(elem!1))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[9375, 9373])).
% 2.14/2.32 tff(9377,plain,
% 2.14/2.32 (s(elem!1) = s(z)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[2251, 9340])).
% 2.14/2.32 tff(9378,plain,
% 2.14/2.32 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[2724, 9377])).
% 2.14/2.32 tff(9379,plain,
% 2.14/2.32 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[152, 9378])).
% 2.14/2.32 tff(9380,plain,
% 2.14/2.32 (r(z, s(elem!1)) <=> r(elem!1, s(elem!1))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[9340])).
% 2.14/2.32 tff(9381,plain,
% 2.14/2.32 (r(elem!1, s(elem!1)) <=> r(z, s(elem!1))),
% 2.14/2.32 inference(symmetry,[status(thm)],[9380])).
% 2.14/2.32 tff(9382,plain,
% 2.14/2.32 (r(elem!1, s(z)) <=> r(elem!1, s(elem!1))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[9347])).
% 2.14/2.32 tff(9383,plain,
% 2.14/2.32 (r(elem!1, s(z)) <=> r(z, s(elem!1))),
% 2.14/2.32 inference(transitivity,[status(thm)],[9382, 9381])).
% 2.14/2.33 tff(9384,plain,
% 2.14/2.33 (r(z, s(elem!1))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[8713, 9383])).
% 2.14/2.33 tff(9385,plain,
% 2.14/2.33 (~r(s(s(elem!1)), s(elem!1))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[1600, 9354, 9384, 9379, 9376])).
% 2.14/2.33 tff(9386,plain,
% 2.14/2.33 (b(s(s(elem!1)), s(elem!1))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[994, 9385, 9370])).
% 2.14/2.33 tff(9387,plain,
% 2.14/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(9388,plain,
% 2.14/2.33 (((~b(s(s(s(elem!1))), z)) | (~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(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(9389,plain,
% 2.14/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1)))))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[9388])).
% 2.14/2.33 tff(9390,plain,
% 2.14/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.14/2.33 inference(transitivity,[status(thm)],[9389, 9387])).
% 2.14/2.33 tff(9391,plain,
% 2.14/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.14/2.33 inference(quant_inst,[status(thm)],[])).
% 2.14/2.33 tff(9392,plain,
% 2.14/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1)))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[9391, 9390])).
% 2.14/2.33 tff(9393,plain,
% 2.14/2.33 ($false),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[9392, 306, 818, 6445, 1199, 1005, 3968])).
% 2.14/2.33 tff(9394,plain,((~b(s(s(elem!1)), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.33 tff(9395,plain,
% 2.14/2.33 (~b(s(s(elem!1)), z)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[9394, 9386, 9368, 9363, 9354])).
% 2.14/2.33 tff(9396,plain,
% 2.14/2.33 (r(s(s(elem!1)), z)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[476, 9395])).
% 2.14/2.33 tff(9397,plain,
% 2.14/2.33 (r(s(s(elem!1)), elem!1)),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[9396, 9344])).
% 2.14/2.33 tff(9398,plain,
% 2.14/2.33 ((s(s(z)) = s(s(s(s(s(s(z))))))) <=> (s(s(elem!1)) = s(s(s(s(s(s(z)))))))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[9348])).
% 2.14/2.33 tff(9399,plain,
% 2.14/2.33 ((s(s(z)) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = s(s(elem!1)))),
% 2.14/2.33 inference(transitivity,[status(thm)],[9398, 3240])).
% 2.14/2.33 tff(9400,plain,
% 2.14/2.33 ((~(s(s(z)) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(s(s(s(s(z)))))) = s(s(elem!1))))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[9399])).
% 2.14/2.33 tff(9401,plain,
% 2.14/2.33 (~(s(s(s(s(s(s(z)))))) = s(s(elem!1)))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[2826, 9400])).
% 2.14/2.33 tff(9402,plain,
% 2.14/2.33 (b(elem!1, s(s(s(elem!1))))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[9353, 9350])).
% 2.14/2.33 tff(9403,plain,
% 2.14/2.33 (b(s(elem!1), elem!1)),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[9197, 9366])).
% 2.14/2.33 tff(9404,plain,
% 2.14/2.33 (s(elem!1) = s(z)),
% 2.14/2.33 inference(symmetry,[status(thm)],[9347])).
% 2.14/2.33 tff(9405,plain,
% 2.14/2.33 ((s(s(s(s(s(s(z)))))) = s(elem!1)) <=> (s(s(s(s(s(s(z)))))) = s(z))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[9404])).
% 2.14/2.33 tff(9406,plain,
% 2.14/2.33 ((s(s(s(s(s(s(z)))))) = s(z)) <=> (s(s(s(s(s(s(z)))))) = s(elem!1))),
% 2.14/2.33 inference(symmetry,[status(thm)],[9405])).
% 2.14/2.33 tff(9407,plain,
% 2.14/2.33 ((~(s(s(s(s(s(s(z)))))) = s(z))) <=> (~(s(s(s(s(s(s(z)))))) = s(elem!1)))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[9406])).
% 2.14/2.33 tff(9408,plain,
% 2.14/2.33 (~(s(s(s(s(s(s(z)))))) = s(elem!1))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[2844, 9407])).
% 2.14/2.33 tff(9409,plain,
% 2.14/2.33 (r(elem!1, s(elem!1))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[8713, 9382])).
% 2.14/2.33 tff(9410,plain,
% 2.14/2.33 (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[8458, 124, 1730, 2858])).
% 2.14/2.33 tff(9411,assumption,(~(s(s(s(s(s(s(z)))))) = s(s(elem!1)))), introduced(assumption)).
% 2.14/2.33 tff(9412,plain,
% 2.14/2.33 (b(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[3247, 43, 9411, 9410])).
% 2.14/2.33 tff(9413,plain,
% 2.14/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(9414,plain,
% 2.14/2.33 (((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(9415,plain,
% 2.14/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1)))))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[9414])).
% 2.14/2.33 tff(9416,plain,
% 2.14/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 2.14/2.33 inference(transitivity,[status(thm)],[9415, 9413])).
% 2.14/2.33 tff(9417,plain,
% 2.14/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))))),
% 2.14/2.33 inference(quant_inst,[status(thm)],[])).
% 2.14/2.33 tff(9418,plain,
% 2.14/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1)))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[9417, 9416])).
% 2.14/2.33 tff(9419,plain,
% 2.14/2.33 ($false),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[9418, 306, 1663, 1005, 816, 3875, 8502])).
% 2.14/2.33 tff(9420,plain,((~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.33 tff(9421,plain,
% 2.14/2.33 (~b(s(s(s(s(s(s(z)))))), s(elem!1))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[9420, 9412, 1005, 816, 1663])).
% 2.14/2.33 tff(9422,assumption,(~(s(s(s(s(s(s(z)))))) = s(elem!1))), introduced(assumption)).
% 2.14/2.33 tff(9423,plain,
% 2.14/2.33 (r(s(s(s(s(s(s(z)))))), s(elem!1))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[3220, 43, 9422, 9421])).
% 2.14/2.33 tff(9424,plain,
% 2.14/2.33 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(9425,plain,
% 2.14/2.33 (((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), elem!1))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(9426,plain,
% 2.14/2.33 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(elem!1)))))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[9425])).
% 2.14/2.33 tff(9427,plain,
% 2.14/2.33 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 2.14/2.33 inference(transitivity,[status(thm)],[9426, 9424])).
% 2.14/2.33 tff(9428,plain,
% 2.14/2.33 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))),
% 2.14/2.33 inference(quant_inst,[status(thm)],[])).
% 2.14/2.33 tff(9429,plain,
% 2.14/2.33 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(elem!1)))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[9428, 9427])).
% 2.14/2.33 tff(9430,plain,
% 2.14/2.33 ($false),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[9429, 124, 255, 2858, 9423])).
% 2.14/2.33 tff(9431,plain,((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(elem!1, s(elem!1))) | (s(s(s(s(s(s(z)))))) = s(elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (s(s(s(s(s(s(z)))))) = s(s(elem!1))) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.33 tff(9432,plain,
% 2.14/2.33 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[9431, 9409, 9408, 9386, 9403, 9402, 9401, 9397])).
% 2.14/2.33 tff(9433,plain,
% 2.14/2.33 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[1144, 9432, 9343])).
% 2.14/2.33 tff(9434,plain,
% 2.14/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(9435,plain,
% 2.14/2.33 (((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1)))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(9436,plain,
% 2.14/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1)))))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[9435])).
% 2.14/2.33 tff(9437,plain,
% 2.14/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 2.14/2.33 inference(transitivity,[status(thm)],[9436, 9434])).
% 2.14/2.33 tff(9438,plain,
% 2.14/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 2.14/2.33 inference(quant_inst,[status(thm)],[])).
% 2.14/2.33 tff(9439,plain,
% 2.14/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1)))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[9438, 9437])).
% 2.14/2.33 tff(9440,plain,
% 2.14/2.33 (~b(s(s(s(s(s(s(z)))))), s(elem!1))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[9439, 306, 9402, 9362, 9403, 9433])).
% 2.14/2.33 tff(9441,plain,
% 2.14/2.33 (r(s(s(s(s(s(s(z)))))), s(elem!1))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[3220, 43, 9408, 9440])).
% 2.14/2.33 tff(9442,plain,
% 2.14/2.33 (r(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))) <=> r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[9371])).
% 2.14/2.33 tff(9443,plain,
% 2.14/2.33 (r(s(s(s(s(s(s(z)))))), s(s(s(z)))) <=> r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))),
% 2.14/2.33 inference(symmetry,[status(thm)],[9442])).
% 2.14/2.33 tff(9444,plain,
% 2.14/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(9445,plain,
% 2.14/2.33 (((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(9446,plain,
% 2.14/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[9445])).
% 2.14/2.33 tff(9447,plain,
% 2.14/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 2.14/2.33 inference(transitivity,[status(thm)],[9446, 9444])).
% 2.14/2.33 tff(9448,plain,
% 2.14/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 2.14/2.33 inference(quant_inst,[status(thm)],[])).
% 2.14/2.33 tff(9449,plain,
% 2.14/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[9448, 9447])).
% 2.14/2.33 tff(9450,plain,
% 2.14/2.33 (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[9449, 306, 9402, 9362, 9433])).
% 2.14/2.33 tff(9451,plain,
% 2.14/2.33 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[2880, 9450, 9340])).
% 2.14/2.33 tff(9452,plain,
% 2.14/2.33 (r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[9451, 9443])).
% 2.14/2.33 tff(9453,plain,
% 2.14/2.33 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(9454,plain,
% 2.14/2.33 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 2.14/2.33 inference(quant_inst,[status(thm)],[])).
% 2.14/2.33 tff(9455,plain,
% 2.14/2.33 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[9454, 9453])).
% 2.14/2.33 tff(9456,plain,
% 2.14/2.33 ($false),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[9455, 124, 9376, 9452, 9441])).
% 2.14/2.33 tff(9457,plain,(r(s(s(s(z))), z) | b(elem!1, z) | (~r(s(z), s(s(s(z))))) | r(s(s(s(z))), elem!1) | b(z, elem!1) | b(s(s(s(z))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.33 tff(9458,plain,
% 2.14/2.33 (r(s(s(s(z))), z)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[9457, 5318, 1034, 1484, 2, 9])).
% 2.14/2.33 tff(9459,plain,
% 2.14/2.33 ((~b(s(s(s(z))), s(z))) <=> (~b(elem!1, s(z)))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[4547])).
% 2.14/2.33 tff(9460,plain,
% 2.14/2.33 (~b(elem!1, s(z))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[9, 9459])).
% 2.14/2.33 tff(9461,plain,
% 2.14/2.33 (r(elem!1, z)),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[205, 2200])).
% 2.14/2.33 tff(9462,plain,
% 2.14/2.33 ((s(s(s(z))) = z) <=> (elem!1 = z)),
% 2.14/2.33 inference(monotonicity,[status(thm)],[1430])).
% 2.14/2.33 tff(9463,plain,
% 2.14/2.33 ((s(s(s(z))) = z) <=> (z = elem!1)),
% 2.14/2.33 inference(transitivity,[status(thm)],[9462, 161])).
% 2.14/2.33 tff(9464,plain,
% 2.14/2.33 ((~(s(s(s(z))) = z)) <=> (~(z = elem!1))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[9463])).
% 2.14/2.33 tff(9465,plain,
% 2.14/2.33 (~(z = elem!1)),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[169, 9464])).
% 2.14/2.33 tff(9466,plain,
% 2.14/2.33 (r(z, elem!1)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[835, 9465, 5318])).
% 2.14/2.33 tff(9467,plain,
% 2.14/2.33 (r(s(z), s(s(s(z)))) <=> r(s(z), elem!1)),
% 2.14/2.33 inference(monotonicity,[status(thm)],[1430])).
% 2.14/2.33 tff(9468,plain,
% 2.14/2.33 (r(s(z), elem!1)),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[1034, 9467])).
% 2.14/2.33 tff(9469,plain,
% 2.14/2.33 (~r(s(s(elem!1)), elem!1)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[8838, 9468, 9466, 9461])).
% 2.14/2.33 tff(9470,plain,
% 2.14/2.33 ($false),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[1455, 9469, 1469, 9, 9460, 2])).
% 2.14/2.33 tff(9471,plain,((~(s(s(s(z))) = elem!1)) | b(s(s(s(z))), s(z)) | b(elem!1, z) | b(z, elem!1) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.33 tff(9472,plain,
% 2.14/2.33 (~(s(s(s(z))) = elem!1)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[9471, 5318, 2, 9, 1034, 9458])).
% 2.14/2.33 tff(9473,plain,
% 2.14/2.33 (b(s(s(s(z))), elem!1)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[1489, 9472, 1484])).
% 2.14/2.33 tff(9474,plain,
% 2.14/2.33 (~(s(z) = elem!1)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[2235, 9473, 9])).
% 2.14/2.33 tff(9475,plain,
% 2.14/2.33 (~(elem!1 = s(z))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[3096, 9474])).
% 2.14/2.33 tff(9476,plain,
% 2.14/2.33 (~r(s(z), z)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[211, 9458, 114])).
% 2.14/2.33 tff(9477,plain,
% 2.14/2.33 (b(s(z), z)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[221, 9476])).
% 2.14/2.33 tff(9478,plain,
% 2.14/2.33 (~(elem!1 = s(s(s(z))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[4555, 9472])).
% 2.14/2.33 tff(9479,plain,
% 2.14/2.33 (~r(elem!1, s(s(s(z))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[2312, 5612, 9458])).
% 2.14/2.33 tff(9480,plain,
% 2.14/2.33 (b(elem!1, s(s(s(z))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[2304, 9479, 9478])).
% 2.14/2.33 tff(9481,plain,
% 2.14/2.33 (b(s(s(s(z))), elem!1)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[1489, 1483, 1484])).
% 2.14/2.33 tff(9482,plain,
% 2.14/2.33 (~(s(z) = elem!1)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[2235, 9481, 9])).
% 2.14/2.33 tff(9483,plain,
% 2.14/2.33 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[7186, 4, 247, 374])).
% 2.14/2.33 tff(9484,plain,
% 2.14/2.33 (b(z, s(z))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[2263, 6808])).
% 2.14/2.33 tff(9485,plain,
% 2.14/2.33 (r(elem!1, s(z))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[96, 43, 5, 87])).
% 2.14/2.33 tff(9486,plain,
% 2.14/2.33 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[9225, 176, 114, 374, 2, 9485])).
% 2.14/2.33 tff(9487,plain,
% 2.14/2.33 ($false),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[7381, 9486, 5485, 9, 6, 246, 4, 247, 1483, 9484, 5, 2, 1034])).
% 2.14/2.33 tff(9488,plain,((~(s(elem!1) = elem!1)) | b(s(s(s(z))), s(z)) | r(s(s(elem!1)), elem!1) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~b(s(z), z)) | (s(s(s(z))) = elem!1) | b(elem!1, s(z)) | b(elem!1, z) | (~r(s(z), s(s(s(z))))) | (~r(z, elem!1)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.33 tff(9489,plain,
% 2.14/2.33 (~(s(elem!1) = elem!1)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[9488, 5, 6, 246, 4, 247, 1483, 9, 2, 1034, 374, 87])).
% 2.14/2.33 tff(9490,plain,
% 2.14/2.33 (r(s(elem!1), elem!1)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[813, 9489, 807])).
% 2.14/2.33 tff(9491,plain,
% 2.14/2.33 (~r(s(elem!1), s(z))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[2960, 9490, 9485])).
% 2.14/2.33 tff(9492,plain,
% 2.14/2.34 (b(s(elem!1), s(z))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[2964, 9491, 2249])).
% 2.14/2.34 tff(9493,plain,
% 2.14/2.34 (~r(s(elem!1), z)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[416, 9490, 374])).
% 2.14/2.34 tff(9494,plain,
% 2.14/2.34 (b(s(elem!1), z)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[2380, 9493])).
% 2.14/2.34 tff(9495,plain,
% 2.14/2.34 ($false),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[8068, 306, 9494, 9492, 247, 9484])).
% 2.14/2.34 tff(9496,plain,(b(elem!1, s(z)) | (~b(s(z), z)) | (s(elem!1) = s(z)) | (~r(z, elem!1)) | b(s(elem!1), elem!1) | r(s(s(elem!1)), elem!1) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (s(s(s(z))) = elem!1) | b(s(s(s(z))), s(z)) | b(elem!1, z) | (~r(s(z), s(s(s(z))))) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.34 tff(9497,plain,
% 2.14/2.34 (b(elem!1, s(z))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[9496, 4, 2249, 374, 807, 6, 246, 247, 1483, 9, 2, 1034, 8764])).
% 2.14/2.34 tff(9498,plain,
% 2.14/2.34 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[8030, 9497, 9483, 1034, 1470])).
% 2.14/2.34 tff(9499,plain,
% 2.14/2.34 (~b(s(elem!1), s(z))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[8068, 306, 7921, 247, 9484])).
% 2.14/2.34 tff(9500,plain,
% 2.14/2.34 (r(s(elem!1), s(z))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[2964, 9499, 2249])).
% 2.14/2.34 tff(9501,plain,
% 2.14/2.34 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(9502,plain,
% 2.14/2.34 (((~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z)))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(9503,plain,
% 2.14/2.34 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z)))))),
% 2.14/2.34 inference(monotonicity,[status(thm)],[9502])).
% 2.14/2.34 tff(9504,plain,
% 2.14/2.34 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))))),
% 2.14/2.34 inference(transitivity,[status(thm)],[9503, 9501])).
% 2.14/2.34 tff(9505,plain,
% 2.14/2.34 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))))),
% 2.14/2.34 inference(quant_inst,[status(thm)],[])).
% 2.14/2.34 tff(9506,plain,
% 2.14/2.34 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z)))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[9505, 9504])).
% 2.14/2.34 tff(9507,plain,
% 2.14/2.34 ($false),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[9506, 124, 802, 4, 9500])).
% 2.14/2.34 tff(9508,plain,((~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (s(elem!1) = s(z)) | (~b(s(z), z)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.34 tff(9509,plain,
% 2.14/2.34 (~r(s(elem!1), elem!1)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[9508, 4, 2249, 247, 374])).
% 2.14/2.34 tff(9510,plain,
% 2.14/2.34 (s(elem!1) = elem!1),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[813, 9509, 807])).
% 2.14/2.34 tff(9511,plain,
% 2.14/2.34 (s(s(s(elem!1))) = s(s(elem!1))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[2436, 9510])).
% 2.14/2.34 tff(9512,plain,
% 2.14/2.34 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[5403, 9511])).
% 2.14/2.34 tff(9513,plain,
% 2.14/2.34 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[1144, 9512, 9483])).
% 2.14/2.34 tff(9514,plain,
% 2.14/2.34 ($false),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[8103, 306, 1967, 9497, 247, 9513, 9498])).
% 2.14/2.34 tff(9515,plain,((~r(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), z)) | b(s(elem!1), elem!1) | (s(elem!1) = s(z)) | (~r(z, elem!1)) | (~r(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | r(s(s(elem!1)), elem!1) | (~r(elem!1, z)) | (s(s(s(z))) = elem!1) | b(s(s(s(z))), s(z)) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 2.14/2.34 tff(9516,plain,
% 2.14/2.34 (~r(s(z), elem!1)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[9515, 807, 247, 1967, 2249, 374, 1034, 1470, 6, 246, 1483, 9, 2])).
% 2.14/2.34 tff(9517,plain,
% 2.14/2.34 (b(s(z), elem!1)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[1500, 43, 9516, 8763])).
% 2.14/2.34 tff(9518,plain,
% 2.14/2.34 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[2974, 8764])).
% 2.14/2.34 tff(9519,plain,
% 2.14/2.34 (b(z, s(z))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[2263, 7475])).
% 2.14/2.34 tff(9520,plain,
% 2.14/2.34 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[7520, 359, 374, 2831, 1483, 1470])).
% 2.14/2.34 tff(9521,plain,
% 2.14/2.34 (~(s(elem!1) = elem!1)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[9225, 9520, 206, 374, 2, 359])).
% 2.14/2.34 tff(9522,plain,
% 2.14/2.34 (r(s(elem!1), elem!1)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[813, 9521, 807])).
% 2.14/2.34 tff(9523,plain,
% 2.14/2.34 (~r(s(elem!1), s(z))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[2960, 9522, 359])).
% 2.14/2.34 tff(9524,plain,
% 2.14/2.34 (b(s(elem!1), s(z))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[2964, 9523, 2249])).
% 2.14/2.34 tff(9525,plain,
% 2.14/2.34 (~r(s(elem!1), z)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[416, 9522, 374])).
% 2.14/2.34 tff(9526,plain,
% 2.14/2.34 (b(s(elem!1), z)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[2380, 9525])).
% 2.14/2.34 tff(9527,plain,
% 2.14/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(9528,plain,
% 2.14/2.34 (((~b(s(z), elem!1)) | (~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(z), elem!1)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(9529,plain,
% 2.14/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z)))))),
% 2.14/2.34 inference(monotonicity,[status(thm)],[9528])).
% 2.14/2.34 tff(9530,plain,
% 2.14/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))),
% 2.14/2.34 inference(transitivity,[status(thm)],[9529, 9527])).
% 2.14/2.34 tff(9531,plain,
% 2.14/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))),
% 2.14/2.34 inference(quant_inst,[status(thm)],[])).
% 2.14/2.34 tff(9532,plain,
% 2.14/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z)))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[9531, 9530])).
% 2.14/2.34 tff(9533,plain,
% 2.14/2.34 ($false),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[9532, 306, 9526, 2831, 9524, 247, 9519])).
% 2.14/2.34 tff(9534,plain,((~r(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (s(elem!1) = s(z)) | (~r(z, elem!1)) | b(s(elem!1), elem!1) | (~r(s(s(s(z))), s(z))) | b(elem!1, z) | (s(s(s(z))) = elem!1) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.34 tff(9535,plain,
% 2.14/2.34 (~r(elem!1, s(z))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[9534, 9517, 247, 2249, 374, 807, 114, 2, 1483, 1470])).
% 2.14/2.34 tff(9536,plain,
% 2.14/2.34 (b(elem!1, s(z))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[96, 43, 9535, 8764])).
% 2.14/2.34 tff(9537,plain,
% 2.14/2.34 (~b(s(s(elem!1)), elem!1)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[7970, 9536, 9518, 114, 1967, 9517])).
% 2.14/2.34 tff(9538,plain,
% 2.14/2.34 (s(s(elem!1)) = elem!1),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[47, 9537, 6])).
% 2.14/2.34 tff(9539,plain,
% 2.14/2.34 (elem!1 = s(s(elem!1))),
% 2.14/2.34 inference(symmetry,[status(thm)],[9538])).
% 2.14/2.34 tff(9540,plain,
% 2.14/2.34 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[5377, 9536, 1967, 9517, 1034])).
% 2.14/2.34 tff(9541,plain,
% 2.14/2.34 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[4284, 9538])).
% 2.14/2.34 tff(9542,plain,
% 2.14/2.34 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[1144, 9541, 9540])).
% 2.14/2.34 tff(9543,plain,
% 2.14/2.34 (~r(s(s(s(s(s(s(z)))))), z)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[5452, 9542, 374])).
% 2.14/2.34 tff(9544,plain,
% 2.14/2.34 (b(s(s(s(s(s(s(z)))))), z)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[4232, 9543])).
% 2.14/2.34 tff(9545,plain,
% 2.14/2.34 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[5377, 4346, 1967, 2831, 1034])).
% 2.14/2.34 tff(9546,plain,
% 2.14/2.34 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[5429, 808, 2831, 1967, 4346, 2249, 206])).
% 2.14/2.34 tff(9547,plain,
% 2.14/2.34 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[1144, 9546, 9545])).
% 2.14/2.34 tff(9548,plain,
% 2.14/2.34 (~r(z, s(s(s(s(s(s(z)))))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[5441, 124, 374, 9547])).
% 2.14/2.34 tff(9549,plain,
% 2.14/2.34 ((z = s(s(s(s(s(s(z))))))) | b(z, s(s(s(s(s(s(z)))))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[5445, 43, 9548])).
% 2.14/2.34 tff(9550,plain,
% 2.14/2.34 (b(z, s(s(s(s(s(s(z)))))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[9549, 5435])).
% 2.14/2.34 tff(9551,plain,
% 2.14/2.34 (~r(s(s(s(s(s(s(z)))))), z)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[5452, 9547, 374])).
% 2.14/2.34 tff(9552,plain,
% 2.14/2.34 (b(s(s(s(s(s(s(z)))))), z)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[4232, 9551])).
% 2.14/2.34 tff(9553,plain,
% 2.14/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(9554,plain,
% 2.14/2.34 (((~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z)))) <=> ((~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(9555,plain,
% 2.14/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z))))))))))),
% 2.14/2.34 inference(monotonicity,[status(thm)],[9554])).
% 2.14/2.34 tff(9556,plain,
% 2.14/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 2.14/2.34 inference(transitivity,[status(thm)],[9555, 9553])).
% 2.14/2.34 tff(9557,plain,
% 2.14/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 2.14/2.34 inference(quant_inst,[status(thm)],[])).
% 2.14/2.34 tff(9558,plain,
% 2.14/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z))))))))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[9557, 9556])).
% 2.14/2.34 tff(9559,plain,
% 2.14/2.34 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[9558, 306, 247, 9552, 9550])).
% 2.14/2.34 tff(9560,plain,
% 2.14/2.34 (r(s(s(s(s(s(s(z)))))), s(z))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[651, 43, 2844, 9559])).
% 2.14/2.34 tff(9561,plain,
% 2.14/2.34 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(9562,plain,
% 2.14/2.34 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 2.14/2.34 inference(quant_inst,[status(thm)],[])).
% 2.14/2.34 tff(9563,plain,
% 2.14/2.34 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[9562, 9561])).
% 2.14/2.34 tff(9564,plain,
% 2.14/2.34 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[9563, 124, 206, 9560])).
% 2.14/2.34 tff(9565,plain,
% 2.14/2.34 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[4603, 43, 9564, 4577])).
% 2.14/2.34 tff(9566,plain,
% 2.14/2.34 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[870, 124, 206, 9560])).
% 2.14/2.34 tff(9567,plain,
% 2.14/2.34 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[3207, 9566])).
% 2.14/2.34 tff(9568,plain,
% 2.14/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(9569,plain,
% 2.14/2.34 (((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z)))))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(9570,plain,
% 2.14/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))))),
% 2.14/2.34 inference(monotonicity,[status(thm)],[9569])).
% 2.14/2.34 tff(9571,plain,
% 2.14/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 2.14/2.34 inference(transitivity,[status(thm)],[9570, 9568])).
% 2.14/2.34 tff(9572,plain,
% 2.14/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z))))))),
% 2.14/2.34 inference(quant_inst,[status(thm)],[])).
% 2.14/2.34 tff(9573,plain,
% 2.14/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[9572, 9571])).
% 2.14/2.34 tff(9574,plain,
% 2.14/2.34 (~b(z, s(s(s(z))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[9573, 306, 1967, 9567, 9565, 9550])).
% 2.14/2.34 tff(9575,plain,
% 2.14/2.34 (r(z, s(s(s(z))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[2415, 43, 9574, 2405])).
% 2.14/2.34 tff(9576,plain,
% 2.14/2.34 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(9577,plain,
% 2.14/2.34 (((~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(9578,plain,
% 2.14/2.34 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z)))))))),
% 2.14/2.34 inference(monotonicity,[status(thm)],[9577])).
% 2.14/2.34 tff(9579,plain,
% 2.14/2.34 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 2.14/2.34 inference(transitivity,[status(thm)],[9578, 9576])).
% 2.14/2.34 tff(9580,plain,
% 2.14/2.34 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))))),
% 2.14/2.34 inference(quant_inst,[status(thm)],[])).
% 2.14/2.34 tff(9581,plain,
% 2.14/2.34 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z)))))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[9580, 9579])).
% 2.14/2.34 tff(9582,plain,
% 2.14/2.34 (~r(z, s(z))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[9581, 124, 1034, 9575])).
% 2.14/2.34 tff(9583,plain,
% 2.14/2.34 (b(z, s(z))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[2263, 9582])).
% 2.14/2.34 tff(9584,plain,
% 2.14/2.34 (s(elem!1) = elem!1),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[813, 808, 807])).
% 2.14/2.34 tff(9585,plain,
% 2.14/2.34 (~(s(s(z)) = elem!1)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[2398, 9584, 87])).
% 2.14/2.34 tff(9586,plain,
% 2.14/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(9587,plain,
% 2.14/2.35 (((~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))) <=> ((~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(9588,plain,
% 2.14/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[9587])).
% 2.14/2.35 tff(9589,plain,
% 2.14/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.14/2.35 inference(transitivity,[status(thm)],[9588, 9586])).
% 2.14/2.35 tff(9590,plain,
% 2.14/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.14/2.35 inference(quant_inst,[status(thm)],[])).
% 2.14/2.35 tff(9591,plain,
% 2.14/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[9590, 9589])).
% 2.14/2.35 tff(9592,plain,
% 2.14/2.35 (~b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[9591, 306, 1967, 4346, 2454, 1330])).
% 2.14/2.35 tff(9593,plain,
% 2.14/2.35 (r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[2829, 43, 2826, 9592])).
% 2.14/2.35 tff(9594,plain,
% 2.14/2.35 (~b(s(s(z)), elem!1)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[5544, 306, 1967, 4346, 1470, 2454])).
% 2.14/2.35 tff(9595,plain,
% 2.14/2.35 (r(s(s(z)), elem!1)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[2545, 9594, 2448])).
% 2.14/2.35 tff(9596,plain,
% 2.14/2.35 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), elem!1)))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(9597,plain,
% 2.14/2.35 (((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), elem!1)))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(9598,plain,
% 2.14/2.35 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), elem!1))))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[9597])).
% 2.14/2.35 tff(9599,plain,
% 2.14/2.35 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), elem!1)))),
% 2.14/2.35 inference(transitivity,[status(thm)],[9598, 9596])).
% 2.14/2.35 tff(9600,plain,
% 2.14/2.35 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.14/2.35 inference(quant_inst,[status(thm)],[])).
% 2.14/2.35 tff(9601,plain,
% 2.14/2.35 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), elem!1))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[9600, 9599])).
% 2.14/2.35 tff(9602,plain,
% 2.14/2.35 ($false),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[9601, 124, 2858, 9595, 9593])).
% 2.14/2.35 tff(9603,plain,((~b(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (s(s(z)) = elem!1) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.35 tff(9604,plain,
% 2.14/2.35 (~b(s(s(z)), s(s(s(z))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[9603, 9547, 9585, 1967, 4346, 9565, 1470])).
% 2.14/2.35 tff(9605,plain,
% 2.14/2.35 (r(s(s(z)), s(s(s(z))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[2514, 9604])).
% 2.14/2.35 tff(9606,plain,
% 2.14/2.35 (~r(s(s(z)), s(z))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[3833, 9605, 1034])).
% 2.14/2.35 tff(9607,plain,
% 2.14/2.35 (b(s(s(z)), s(z))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[2476, 9606])).
% 2.14/2.35 tff(9608,plain,
% 2.14/2.35 (~r(s(s(z)), z)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[2523, 9605, 9575])).
% 2.14/2.35 tff(9609,plain,
% 2.14/2.35 (b(s(s(z)), z)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[2531, 9608])).
% 2.14/2.35 tff(9610,plain,
% 2.14/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(9611,plain,
% 2.14/2.35 (((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(9612,plain,
% 2.14/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(s(z)), z)) | (~b(s(s(z)), s(z)))))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[9611])).
% 2.14/2.35 tff(9613,plain,
% 2.14/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 2.14/2.35 inference(transitivity,[status(thm)],[9612, 9610])).
% 2.14/2.35 tff(9614,plain,
% 2.14/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 2.14/2.35 inference(quant_inst,[status(thm)],[])).
% 2.14/2.35 tff(9615,plain,
% 2.14/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[9614, 9613])).
% 2.14/2.35 tff(9616,plain,
% 2.14/2.35 ($false),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[9615, 306, 2831, 4346, 9609, 9607, 9583])).
% 2.14/2.35 tff(9617,plain,(r(s(elem!1), elem!1) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~r(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~r(z, elem!1)) | (elem!1 = s(z)) | (s(elem!1) = s(z)) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.14/2.35 tff(9618,plain,
% 2.14/2.35 (r(s(elem!1), elem!1)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[9617, 9517, 9536, 1034, 1967, 1470, 114, 247, 374, 8764, 2249, 807])).
% 2.14/2.35 tff(9619,plain,
% 2.14/2.35 (~r(z, s(elem!1))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[7870, 124, 374, 9618])).
% 2.14/2.35 tff(9620,plain,
% 2.14/2.35 (b(z, s(elem!1))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[275, 9619])).
% 2.14/2.35 tff(9621,plain,
% 2.14/2.35 (~r(s(elem!1), z)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[416, 9618, 374])).
% 2.14/2.35 tff(9622,plain,
% 2.14/2.35 (b(s(elem!1), z)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[2380, 9621])).
% 2.14/2.35 tff(9623,plain,
% 2.14/2.35 (~b(s(s(s(s(s(s(z)))))), s(elem!1))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[7927, 306, 9622, 9620, 9544])).
% 2.14/2.35 tff(9624,plain,
% 2.14/2.35 (~r(s(s(s(s(s(s(z)))))), s(elem!1))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[3212, 124, 9618, 9542])).
% 2.14/2.35 tff(9625,plain,
% 2.14/2.35 ((s(s(s(s(s(s(z)))))) = s(elem!1)) | b(s(s(s(s(s(s(z)))))), s(elem!1))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[3220, 43, 9624])).
% 2.14/2.35 tff(9626,plain,
% 2.14/2.35 (s(s(s(s(s(s(z)))))) = s(elem!1)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[9625, 9623])).
% 2.14/2.35 tff(9627,plain,
% 2.14/2.35 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(elem!1))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[9626])).
% 2.14/2.35 tff(9628,plain,
% 2.14/2.35 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 2.14/2.35 inference(transitivity,[status(thm)],[2823, 9627, 135, 9539])).
% 2.14/2.35 tff(9629,plain,
% 2.14/2.35 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(elem!1)))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[9628])).
% 2.14/2.35 tff(9630,plain,
% 2.14/2.35 (s(s(s(s(z)))) = s(elem!1)),
% 2.14/2.35 inference(transitivity,[status(thm)],[497, 9629, 66])).
% 2.14/2.35 tff(9631,plain,
% 2.14/2.35 (inj_0(s(s(s(s(z))))) = inj_0(s(elem!1))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[9630])).
% 2.14/2.35 tff(9632,plain,
% 2.14/2.35 (s(s(s(z))) = elem!1),
% 2.14/2.35 inference(transitivity,[status(thm)],[321, 9631, 135])).
% 2.14/2.35 tff(9633,plain,
% 2.14/2.35 ($false),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[1483, 9632])).
% 2.14/2.35 tff(9634,plain,(b(s(elem!1), elem!1) | (s(s(s(z))) = elem!1) | (~r(z, elem!1)) | (~r(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), z)) | (s(elem!1) = s(z)) | r(s(s(elem!1)), elem!1) | b(elem!1, z) | (~r(elem!1, z)) | b(s(s(s(z))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.35 tff(9635,plain,
% 2.14/2.35 (b(s(elem!1), elem!1)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[9634, 6, 374, 1034, 9481, 1470, 247, 2249, 1483, 2, 246, 9])).
% 2.14/2.35 tff(9636,plain,
% 2.14/2.35 (~b(s(elem!1), s(s(s(z))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[2363, 306, 9635, 9481, 1470])).
% 2.14/2.35 tff(9637,plain,
% 2.14/2.35 (~(s(elem!1) = elem!1)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[2422, 9636, 1470])).
% 2.14/2.35 tff(9638,plain,
% 2.14/2.35 (r(elem!1, s(z))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[96, 43, 5, 5331])).
% 2.14/2.35 tff(9639,plain,
% 2.14/2.35 (~r(z, s(z))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[385, 9638, 374])).
% 2.14/2.35 tff(9640,plain,
% 2.14/2.35 (b(z, s(z))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[2263, 9639])).
% 2.14/2.35 tff(9641,plain,
% 2.14/2.35 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[7480, 9638, 374, 247])).
% 2.14/2.35 tff(9642,plain,
% 2.14/2.35 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[1144, 4918, 9641])).
% 2.14/2.35 tff(9643,plain,
% 2.14/2.35 (~b(s(z), elem!1)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[7520, 9642, 374, 9638, 1483, 1470])).
% 2.14/2.35 tff(9644,plain,
% 2.14/2.35 (r(s(z), elem!1)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[1500, 43, 9643, 3094])).
% 2.14/2.35 tff(9645,plain,
% 2.14/2.35 (s(s(z)) = elem!1),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[7381, 9644, 9, 6, 246, 5, 247, 1483, 9640, 9642, 2, 1034])).
% 2.14/2.35 tff(9646,plain,
% 2.14/2.35 (s(s(z)) = s(s(elem!1))),
% 2.14/2.35 inference(transitivity,[status(thm)],[9645, 1427])).
% 2.14/2.35 tff(9647,plain,
% 2.14/2.35 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[9646])).
% 2.14/2.35 tff(9648,plain,
% 2.14/2.35 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 2.14/2.35 inference(symmetry,[status(thm)],[9647])).
% 2.14/2.35 tff(9649,plain,
% 2.14/2.35 (s(elem!1) = s(z)),
% 2.14/2.35 inference(transitivity,[status(thm)],[67, 9648, 546])).
% 2.14/2.35 tff(9650,plain,
% 2.14/2.35 ($false),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[2249, 9649])).
% 2.14/2.35 tff(9651,plain,((~(s(s(elem!1)) = elem!1)) | (s(elem!1) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(elem!1)), elem!1) | (~r(elem!1, z)) | b(elem!1, s(z)) | (~b(s(z), z)) | (s(s(s(z))) = elem!1) | b(elem!1, z) | (~r(s(z), s(s(s(z))))) | (s(z) = elem!1) | (~r(z, elem!1)) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.35 tff(9652,plain,
% 2.14/2.35 (~(s(s(elem!1)) = elem!1)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[9651, 5, 9, 6, 246, 2249, 247, 1483, 2, 1034, 3094, 374, 1470])).
% 2.14/2.35 tff(9653,plain,
% 2.14/2.35 (b(s(s(elem!1)), s(elem!1))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[9169, 808, 374, 6, 193, 2, 2249])).
% 2.14/2.35 tff(9654,plain,
% 2.14/2.35 (~b(elem!1, s(s(elem!1)))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[1024, 92, 816, 9653])).
% 2.14/2.35 tff(9655,plain,
% 2.14/2.35 (r(elem!1, s(s(elem!1)))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[516, 9654, 187])).
% 2.14/2.35 tff(9656,plain,
% 2.14/2.35 (~r(z, s(s(elem!1)))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[978, 9655, 246])).
% 2.14/2.35 tff(9657,plain,
% 2.14/2.35 (~b(elem!1, s(elem!1))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[9173, 91, 6, 816, 374, 808, 193, 2, 2249])).
% 2.14/2.35 tff(9658,plain,
% 2.14/2.35 (r(elem!1, s(elem!1))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[372, 9657, 365])).
% 2.14/2.35 tff(9659,plain,
% 2.14/2.35 (~r(z, s(elem!1))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[265, 9658, 246])).
% 2.14/2.35 tff(9660,plain,
% 2.14/2.35 (b(z, s(elem!1))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[275, 9659])).
% 2.14/2.35 tff(9661,plain,
% 2.14/2.35 (~r(s(elem!1), z)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[287, 9658, 246])).
% 2.14/2.35 tff(9662,plain,
% 2.14/2.35 (b(s(elem!1), z)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[2380, 9661])).
% 2.14/2.35 tff(9663,plain,
% 2.14/2.35 (~b(z, s(s(elem!1)))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[1218, 9662, 9653, 9660])).
% 2.14/2.35 tff(9664,plain,
% 2.14/2.35 ($false),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[460, 9663, 9656])).
% 2.14/2.35 tff(9665,plain,((s(s(elem!1)) = elem!1) | (~r(elem!1, z)) | (~b(s(elem!1), elem!1)) | r(s(s(elem!1)), elem!1) | (~r(z, elem!1)) | r(s(elem!1), elem!1) | (s(elem!1) = elem!1) | b(elem!1, z) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.35 tff(9666,plain,
% 2.14/2.35 (r(s(elem!1), elem!1)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[9665, 9652, 816, 6, 374, 246, 193, 2, 2249])).
% 2.14/2.35 tff(9667,plain,
% 2.14/2.35 (~r(s(elem!1), s(z))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[2960, 9666, 9638])).
% 2.14/2.35 tff(9668,plain,
% 2.14/2.35 (b(s(elem!1), s(z))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[2964, 9667, 2249])).
% 2.14/2.35 tff(9669,plain,
% 2.14/2.35 (~r(s(elem!1), z)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[416, 9666, 374])).
% 2.14/2.35 tff(9670,plain,
% 2.14/2.35 (b(s(elem!1), z)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[2380, 9669])).
% 2.14/2.35 tff(9671,plain,
% 2.14/2.35 ($false),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[8068, 306, 9670, 9668, 247, 9640])).
% 2.14/2.35 tff(9672,plain,(b(elem!1, s(z)) | (~b(s(z), z)) | (s(elem!1) = s(z)) | (~r(z, elem!1)) | (~b(s(elem!1), elem!1)) | r(s(s(elem!1)), elem!1) | (~r(elem!1, z)) | (s(elem!1) = elem!1) | b(elem!1, z) | b(s(s(s(z))), s(z)) | (s(s(s(z))) = elem!1) | (~r(s(z), s(s(s(z))))) | (s(z) = elem!1) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.35 tff(9673,plain,
% 2.14/2.35 (b(elem!1, s(z))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[9672, 9635, 2249, 374, 247, 6, 246, 9637, 2, 9, 1483, 1034, 9482, 1470])).
% 2.14/2.35 tff(9674,plain,
% 2.14/2.35 (~b(s(elem!1), s(s(s(z))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[2363, 306, 816, 1967, 1470])).
% 2.14/2.35 tff(9675,plain,
% 2.14/2.35 (~(s(elem!1) = elem!1)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[2422, 9674, 1470])).
% 2.14/2.35 tff(9676,plain,
% 2.14/2.35 (s(s(elem!1)) = elem!1),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[9665, 808, 816, 6, 374, 246, 9675, 2, 2249])).
% 2.14/2.35 tff(9677,plain,
% 2.14/2.35 (~(s(elem!1) = s(s(s(z))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[2356, 9676])).
% 2.14/2.35 tff(9678,plain,
% 2.14/2.35 ((s(elem!1) = s(s(s(z)))) | r(s(elem!1), s(s(s(z))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[2367, 43, 9674])).
% 2.14/2.35 tff(9679,plain,
% 2.14/2.35 (r(s(elem!1), s(s(s(z))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[9678, 9677])).
% 2.14/2.35 tff(9680,plain,
% 2.14/2.35 (~r(s(elem!1), s(z))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[8076, 124, 1034, 9679])).
% 2.14/2.35 tff(9681,plain,
% 2.14/2.35 (b(s(elem!1), s(z))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[2964, 9680, 2249])).
% 2.14/2.35 tff(9682,plain,
% 2.14/2.35 (~b(s(z), elem!1)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[5422, 9681, 816, 4346])).
% 2.14/2.35 tff(9683,plain,
% 2.14/2.35 (r(s(z), elem!1)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[1500, 43, 9682, 3094])).
% 2.14/2.35 tff(9684,plain,
% 2.14/2.35 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[7186, 9683, 247, 374])).
% 2.14/2.35 tff(9685,plain,
% 2.14/2.35 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[8030, 9684, 4346, 1034, 1470])).
% 2.14/2.35 tff(9686,plain,
% 2.14/2.35 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[4284, 9676])).
% 2.14/2.35 tff(9687,plain,
% 2.14/2.35 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[1144, 9684, 9686])).
% 2.14/2.35 tff(9688,plain,
% 2.14/2.35 (b(s(s(elem!1)), s(elem!1))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[9169, 808, 374, 6, 9675, 2, 2249])).
% 2.14/2.35 tff(9689,plain,
% 2.14/2.35 (b(elem!1, s(elem!1))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[1005, 7435])).
% 2.14/2.35 tff(9690,plain,
% 2.14/2.35 ($false),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[367, 9689])).
% 2.14/2.35 tff(9691,plain,((~b(s(s(elem!1)), s(elem!1))) | b(elem!1, s(elem!1)) | (~(s(s(elem!1)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.35 tff(9692,plain,
% 2.14/2.35 (b(elem!1, s(elem!1))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[9691, 9676, 9688])).
% 2.14/2.35 tff(9693,plain,
% 2.14/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(9694,plain,
% 2.14/2.35 (((~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(9695,plain,
% 2.14/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), elem!1))))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[9694])).
% 2.14/2.35 tff(9696,plain,
% 2.14/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 2.14/2.35 inference(transitivity,[status(thm)],[9695, 9693])).
% 2.14/2.35 tff(9697,plain,
% 2.14/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 2.14/2.35 inference(quant_inst,[status(thm)],[])).
% 2.14/2.35 tff(9698,plain,
% 2.14/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), elem!1))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[9697, 9696])).
% 2.14/2.35 tff(9699,plain,
% 2.14/2.35 ($false),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[9698, 306, 9692, 1967, 9681, 9687, 9685])).
% 2.14/2.35 tff(9700,plain,(r(s(elem!1), elem!1) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~r(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), z)) | (~r(z, elem!1)) | (s(z) = elem!1) | (~b(s(elem!1), elem!1)) | (s(elem!1) = s(z)) | r(s(s(elem!1)), elem!1) | (~r(elem!1, z)) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 2.14/2.35 tff(9701,plain,
% 2.14/2.35 (r(s(elem!1), elem!1)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[9700, 9673, 9481, 1034, 1470, 247, 374, 9482, 9635, 2249, 6, 246, 2])).
% 2.14/2.35 tff(9702,plain,
% 2.14/2.35 (~r(s(z), elem!1)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[9508, 9701, 2249, 247, 374])).
% 2.14/2.35 tff(9703,plain,
% 2.14/2.35 (b(s(z), elem!1)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[1500, 43, 9702, 9482])).
% 2.14/2.35 tff(9704,plain,
% 2.14/2.35 (~(s(elem!1) = s(s(s(z))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[7863, 9701, 1484])).
% 2.14/2.35 tff(9705,plain,
% 2.14/2.35 ((s(elem!1) = s(s(s(z)))) | r(s(elem!1), s(s(s(z))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[2367, 43, 9636])).
% 2.14/2.35 tff(9706,plain,
% 2.14/2.35 (r(s(elem!1), s(s(s(z))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[9705, 9704])).
% 2.14/2.35 tff(9707,plain,
% 2.14/2.35 (~r(s(elem!1), s(z))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[8076, 124, 1034, 9706])).
% 2.14/2.35 tff(9708,plain,
% 2.14/2.35 (b(s(elem!1), s(z))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[2964, 9707, 2249])).
% 2.14/2.35 tff(9709,plain,
% 2.14/2.35 ($false),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[5422, 9708, 9703, 9635, 9673])).
% 2.14/2.35 tff(9710,plain,(r(s(s(elem!1)), elem!1) | (s(elem!1) = s(z)) | (~r(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~r(z, elem!1)) | r(s(s(s(z))), elem!1) | (~b(elem!1, s(s(s(z))))) | (~r(elem!1, z)) | b(elem!1, z) | b(s(s(s(z))), s(z)) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.14/2.35 tff(9711,plain,
% 2.14/2.35 (r(s(s(elem!1)), elem!1)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[9710, 3099, 1034, 9477, 5330, 1484, 9480, 5612, 2, 9, 9472])).
% 2.14/2.35 tff(9712,plain,
% 2.14/2.35 (~r(s(s(elem!1)), z)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[7786, 9711, 5612])).
% 2.14/2.35 tff(9713,plain,
% 2.14/2.35 (b(s(s(elem!1)), z)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[476, 9712])).
% 2.14/2.35 tff(9714,plain,
% 2.14/2.35 (~r(z, s(s(elem!1)))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[5837, 9711, 5330])).
% 2.14/2.35 tff(9715,plain,
% 2.14/2.35 (b(z, s(s(elem!1)))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[460, 9714])).
% 2.14/2.35 tff(9716,plain,
% 2.14/2.35 (~b(s(s(elem!1)), s(z))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[8836, 306, 9715, 9713, 9477])).
% 2.14/2.35 tff(9717,plain,
% 2.14/2.35 (r(s(s(elem!1)), s(z))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[3989, 9716])).
% 2.14/2.35 tff(9718,plain,
% 2.14/2.35 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(9719,plain,
% 2.14/2.35 (((~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(9720,plain,
% 2.14/2.35 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z)))))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[9719])).
% 2.14/2.35 tff(9721,plain,
% 2.14/2.35 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))))),
% 2.14/2.35 inference(transitivity,[status(thm)],[9720, 9718])).
% 2.14/2.35 tff(9722,plain,
% 2.14/2.35 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1)))),
% 2.14/2.35 inference(quant_inst,[status(thm)],[])).
% 2.14/2.35 tff(9723,plain,
% 2.14/2.35 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z)))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[9722, 9721])).
% 2.14/2.35 tff(9724,plain,
% 2.14/2.35 ($false),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[9723, 124, 1730, 359, 8821])).
% 2.14/2.35 tff(9725,plain,((~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.35 tff(9726,plain,
% 2.14/2.35 (~r(elem!1, s(z))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[9725, 9711, 9717])).
% 2.14/2.35 tff(9727,plain,
% 2.14/2.35 (b(elem!1, s(z))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[96, 43, 9726, 9475])).
% 2.14/2.35 tff(9728,plain,
% 2.14/2.35 (~r(s(z), elem!1)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[8838, 9711, 5330, 5612])).
% 2.14/2.35 tff(9729,plain,
% 2.14/2.35 (b(s(z), elem!1)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[1500, 43, 9728, 9474])).
% 2.14/2.35 tff(9730,plain,
% 2.14/2.35 (~r(s(s(elem!1)), s(elem!1))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[7985, 802, 1730])).
% 2.14/2.35 tff(9731,plain,
% 2.14/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(9732,plain,
% 2.14/2.35 (((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(9733,plain,
% 2.14/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1)))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[9732])).
% 2.14/2.36 tff(9734,plain,
% 2.14/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.14/2.36 inference(transitivity,[status(thm)],[9733, 9731])).
% 2.14/2.36 tff(9735,plain,
% 2.14/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.14/2.36 inference(quant_inst,[status(thm)],[])).
% 2.14/2.36 tff(9736,plain,
% 2.14/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1)))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[9735, 9734])).
% 2.14/2.36 tff(9737,plain,
% 2.14/2.36 (~b(s(s(elem!1)), s(elem!1))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[9736, 306, 7921, 6699, 3968])).
% 2.14/2.36 tff(9738,plain,
% 2.14/2.36 (s(s(elem!1)) = s(elem!1)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[994, 9737, 9730])).
% 2.14/2.36 tff(9739,plain,
% 2.14/2.36 (~b(s(s(elem!1)), s(z))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[8836, 306, 6699, 3968, 247])).
% 2.14/2.36 tff(9740,plain,
% 2.14/2.36 (r(s(s(elem!1)), s(z))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[3989, 9739])).
% 2.14/2.36 tff(9741,plain,
% 2.14/2.36 (~r(elem!1, s(z))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[9725, 1730, 9740])).
% 2.14/2.36 tff(9742,plain,
% 2.14/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(9743,plain,
% 2.14/2.36 (((~b(s(s(elem!1)), z)) | (~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(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(9744,plain,
% 2.14/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(z)))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[9743])).
% 2.14/2.36 tff(9745,plain,
% 2.14/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))),
% 2.14/2.36 inference(transitivity,[status(thm)],[9744, 9742])).
% 2.14/2.36 tff(9746,plain,
% 2.14/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))),
% 2.14/2.36 inference(quant_inst,[status(thm)],[])).
% 2.14/2.36 tff(9747,plain,
% 2.14/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(z)))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[9746, 9745])).
% 2.14/2.36 tff(9748,plain,
% 2.14/2.36 (~b(s(elem!1), s(z))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[9747, 306, 7921, 6699, 3968, 247])).
% 2.14/2.36 tff(9749,plain,
% 2.14/2.36 (~(elem!1 = s(elem!1))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[2615, 9748, 9741])).
% 2.14/2.36 tff(9750,plain,
% 2.14/2.36 (~(s(elem!1) = elem!1)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[2571, 9749])).
% 2.14/2.36 tff(9751,plain,
% 2.14/2.36 ($false),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[195, 9750, 9738])).
% 2.14/2.36 tff(9752,plain,((~r(s(elem!1), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.36 tff(9753,plain,
% 2.14/2.36 (~r(s(elem!1), elem!1)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[9752, 9713, 9477, 9711, 5330])).
% 2.14/2.36 tff(9754,plain,
% 2.14/2.36 (b(s(elem!1), elem!1)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[9617, 9753, 9729, 1034, 9473, 9480, 114, 9477, 5330, 9475, 3099, 9727])).
% 2.14/2.36 tff(9755,plain,
% 2.14/2.36 (~b(s(elem!1), s(z))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[5422, 9754, 9729, 9727])).
% 2.14/2.36 tff(9756,plain,
% 2.14/2.36 (r(s(elem!1), s(z))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[2964, 9755, 3099])).
% 2.14/2.36 tff(9757,plain,
% 2.14/2.36 (~r(s(elem!1), s(s(s(z))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[5427, 124, 114, 9756])).
% 2.14/2.36 tff(9758,plain,
% 2.14/2.36 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[5377, 9727, 9473, 9729, 1034])).
% 2.14/2.36 tff(9759,plain,
% 2.14/2.36 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[5429, 9753, 9729, 9473, 9727, 3099, 114])).
% 2.14/2.36 tff(9760,plain,
% 2.14/2.36 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[1144, 9759, 9758])).
% 2.14/2.36 tff(9761,plain,
% 2.14/2.36 (~r(s(s(s(s(s(s(z)))))), z)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[5452, 9760, 5330])).
% 2.14/2.36 tff(9762,plain,
% 2.14/2.36 (b(s(s(s(s(s(s(z)))))), z)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[4232, 9761])).
% 2.14/2.36 tff(9763,plain,
% 2.14/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(9764,plain,
% 2.14/2.36 (((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(9765,plain,
% 2.14/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1))))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[9764])).
% 2.14/2.36 tff(9766,plain,
% 2.14/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))))),
% 2.14/2.36 inference(transitivity,[status(thm)],[9765, 9763])).
% 2.14/2.36 tff(9767,plain,
% 2.14/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))))),
% 2.14/2.36 inference(quant_inst,[status(thm)],[])).
% 2.14/2.36 tff(9768,plain,
% 2.14/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1))))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[9767, 9766])).
% 2.14/2.36 tff(9769,plain,
% 2.14/2.36 (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[9768, 306, 9715, 9713, 9762])).
% 2.14/2.36 tff(9770,plain,
% 2.14/2.36 (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[8458, 124, 9711, 9760])).
% 2.14/2.36 tff(9771,plain,
% 2.14/2.36 ((s(s(s(s(s(s(z)))))) = s(s(elem!1))) | b(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[3247, 43, 9770])).
% 2.14/2.36 tff(9772,plain,
% 2.14/2.36 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[9771, 9769])).
% 2.14/2.36 tff(9773,plain,
% 2.14/2.36 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(elem!1)))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[9772])).
% 2.14/2.36 tff(9774,plain,
% 2.14/2.36 (s(s(s(s(s(z))))) = s(elem!1)),
% 2.14/2.36 inference(transitivity,[status(thm)],[2823, 9773, 66])).
% 2.14/2.36 tff(9775,plain,
% 2.14/2.36 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(elem!1))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[9774])).
% 2.14/2.36 tff(9776,plain,
% 2.14/2.36 (s(s(s(s(z)))) = elem!1),
% 2.14/2.36 inference(transitivity,[status(thm)],[497, 9775, 135])).
% 2.14/2.36 tff(9777,plain,
% 2.14/2.36 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(z)) = elem!1)),
% 2.14/2.36 inference(monotonicity,[status(thm)],[9776])).
% 2.14/2.36 tff(9778,plain,
% 2.14/2.36 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(z)) = elem!1))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[9777])).
% 2.14/2.36 tff(9779,plain,
% 2.14/2.36 (~(s(s(z)) = elem!1)),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[1612, 9778])).
% 2.14/2.36 tff(9780,plain,
% 2.14/2.36 (~(s(elem!1) = s(s(s(z))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[5384, 9779])).
% 2.14/2.36 tff(9781,plain,
% 2.14/2.36 (~b(s(elem!1), s(s(s(z))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[5412, 306, 9754, 9729, 9473, 9727])).
% 2.14/2.36 tff(9782,plain,
% 2.14/2.36 ((s(elem!1) = s(s(s(z)))) | r(s(elem!1), s(s(s(z))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[2367, 43, 9781])).
% 2.14/2.36 tff(9783,plain,
% 2.14/2.36 ($false),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[9782, 9780, 9757])).
% 2.14/2.36 tff(9784,plain,((z = elem!1) | (~r(s(z), s(s(s(z))))) | r(s(s(s(z))), elem!1) | b(elem!1, z) | b(s(s(s(z))), s(z)) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.14/2.36 tff(9785,plain,
% 2.14/2.36 (z = elem!1),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[9784, 5318, 1484, 2, 9, 1034])).
% 2.14/2.36 tff(9786,plain,
% 2.14/2.36 (r(s(s(s(z))), z) <=> r(s(s(s(z))), elem!1)),
% 2.14/2.36 inference(monotonicity,[status(thm)],[9785])).
% 2.14/2.36 tff(9787,plain,
% 2.14/2.36 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), z)),
% 2.14/2.36 inference(symmetry,[status(thm)],[9786])).
% 2.14/2.36 tff(9788,plain,
% 2.14/2.36 ((~r(s(s(s(z))), elem!1)) <=> (~r(s(s(s(z))), z))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[9787])).
% 2.14/2.36 tff(9789,plain,
% 2.14/2.36 (~r(s(s(s(z))), z)),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[1484, 9788])).
% 2.14/2.36 tff(9790,plain,
% 2.14/2.36 ($false),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[9458, 9789])).
% 2.14/2.36 tff(9791,plain,(b(z, elem!1) | r(s(s(s(z))), elem!1) | b(elem!1, z) | b(s(s(s(z))), s(z)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.36 tff(9792,plain,
% 2.14/2.36 (b(z, elem!1)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[9791, 1482, 2, 1034, 9])).
% 2.14/2.36 tff(9793,plain,
% 2.14/2.36 (~(s(s(s(z))) = elem!1)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[1472, 5317])).
% 2.14/2.36 tff(9794,plain,
% 2.14/2.36 (b(s(s(s(z))), elem!1)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[1489, 1482, 9793])).
% 2.14/2.36 tff(9795,plain,
% 2.14/2.36 (~b(s(s(s(z))), z)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[2228, 9794, 5317, 9792])).
% 2.14/2.36 tff(9796,plain,
% 2.14/2.36 (r(s(s(s(z))), z)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[2197, 9795])).
% 2.14/2.36 tff(9797,plain,
% 2.14/2.36 (~r(s(z), z)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[211, 9796, 114])).
% 2.14/2.36 tff(9798,plain,
% 2.14/2.36 (b(s(z), z)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[221, 9797])).
% 2.14/2.36 tff(9799,plain,
% 2.14/2.36 (~b(s(s(elem!1)), elem!1)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[3002, 9792, 5317, 2975, 9794])).
% 2.14/2.36 tff(9800,plain,
% 2.14/2.36 (s(s(elem!1)) = elem!1),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[47, 9799, 6])).
% 2.14/2.36 tff(9801,plain,
% 2.14/2.36 (elem!1 = s(s(elem!1))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[1174, 9800])).
% 2.14/2.36 tff(9802,plain,
% 2.14/2.36 (s(s(s(elem!1))) = s(elem!1)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[1168, 9801])).
% 2.14/2.36 tff(9803,plain,
% 2.14/2.36 (~(s(elem!1) = s(z))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[2724, 9802])).
% 2.14/2.36 tff(9804,plain,
% 2.14/2.36 (~(z = elem!1)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[2251, 9803])).
% 2.14/2.36 tff(9805,plain,
% 2.14/2.36 (~(elem!1 = z)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[2172, 9804])).
% 2.14/2.36 tff(9806,plain,
% 2.14/2.36 (r(elem!1, z)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[174, 9805, 2])).
% 2.14/2.36 tff(9807,assumption,(s(s(s(s(z)))) = elem!1), introduced(assumption)).
% 2.14/2.36 tff(9808,plain,
% 2.14/2.36 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.14/2.36 inference(transitivity,[status(thm)],[9807, 1427])).
% 2.14/2.36 tff(9809,plain,
% 2.14/2.36 (inj_0(s(s(s(s(z))))) = inj_0(s(s(elem!1)))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[9808])).
% 2.14/2.36 tff(9810,plain,
% 2.14/2.36 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(z)))))),
% 2.14/2.36 inference(symmetry,[status(thm)],[9809])).
% 2.14/2.36 tff(9811,plain,
% 2.14/2.36 (s(elem!1) = s(s(s(z)))),
% 2.14/2.36 inference(transitivity,[status(thm)],[67, 9810, 320])).
% 2.14/2.36 tff(9812,plain,
% 2.14/2.36 ($false),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[4282, 9811])).
% 2.14/2.36 tff(9813,plain,((~(s(s(s(s(z)))) = elem!1)) | (~(s(s(elem!1)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.36 tff(9814,plain,
% 2.14/2.36 (~(s(s(s(s(z)))) = elem!1)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[9813, 9800])).
% 2.14/2.36 tff(9815,assumption,(~(s(s(s(s(z)))) = elem!1)), introduced(assumption)).
% 2.14/2.36 tff(9816,plain,
% 2.14/2.36 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[4737, 397, 205])).
% 2.14/2.36 tff(9817,plain,
% 2.14/2.36 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[4471, 9816])).
% 2.14/2.36 tff(9818,plain,
% 2.14/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~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(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(9819,plain,
% 2.14/2.36 (((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(9820,plain,
% 2.14/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[9819])).
% 2.14/2.36 tff(9821,plain,
% 2.14/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.14/2.36 inference(transitivity,[status(thm)],[9820, 9818])).
% 2.14/2.36 tff(9822,plain,
% 2.14/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~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)))),
% 2.14/2.36 inference(quant_inst,[status(thm)],[])).
% 2.14/2.36 tff(9823,plain,
% 2.14/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[9822, 9821])).
% 2.14/2.36 tff(9824,plain,
% 2.14/2.36 (~b(s(s(s(s(z)))), elem!1)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[9823, 306, 1967, 1470, 9817])).
% 2.14/2.36 tff(9825,plain,
% 2.14/2.36 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(9826,plain,
% 2.14/2.36 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.14/2.36 inference(quant_inst,[status(thm)],[])).
% 2.14/2.36 tff(9827,plain,
% 2.14/2.36 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[9826, 9825])).
% 2.14/2.36 tff(9828,plain,
% 2.14/2.36 (~r(s(s(s(s(z)))), elem!1)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[9827, 124, 246, 397])).
% 2.14/2.36 tff(9829,plain,
% 2.14/2.36 (((~![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))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(9830,plain,
% 2.14/2.36 ((~![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))),
% 2.14/2.36 inference(quant_inst,[status(thm)],[])).
% 2.14/2.36 tff(9831,plain,
% 2.14/2.36 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1)),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[9830, 9829])).
% 2.14/2.36 tff(9832,plain,
% 2.14/2.36 ((s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[9831, 43])).
% 2.14/2.36 tff(9833,plain,
% 2.14/2.36 ($false),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[9832, 9828, 9824, 9815])).
% 2.14/2.36 tff(9834,plain,((~r(s(s(s(s(z)))), z)) | (s(s(s(s(z)))) = elem!1) | (~r(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.36 tff(9835,plain,
% 2.14/2.36 (~r(s(s(s(s(z)))), z)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[9834, 9814, 9806, 9794, 5317, 9796])).
% 2.14/2.36 tff(9836,plain,
% 2.14/2.36 (b(s(s(s(s(z)))), z)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[695, 9835])).
% 2.14/2.36 tff(9837,plain,
% 2.14/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(9838,plain,
% 2.14/2.36 (((~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(9839,plain,
% 2.14/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[9838])).
% 2.14/2.37 tff(9840,plain,
% 2.14/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)))),
% 2.14/2.37 inference(transitivity,[status(thm)],[9839, 9837])).
% 2.14/2.37 tff(9841,plain,
% 2.14/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 2.14/2.37 inference(quant_inst,[status(thm)],[])).
% 2.14/2.37 tff(9842,plain,
% 2.14/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[9841, 9840])).
% 2.14/2.37 tff(9843,plain,
% 2.14/2.37 (~b(s(s(s(s(z)))), s(z))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[9842, 306, 9792, 9836, 9798, 5317])).
% 2.14/2.37 tff(9844,plain,
% 2.14/2.37 (r(s(s(s(s(z)))), s(z))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[4490, 9843])).
% 2.14/2.37 tff(9845,plain,
% 2.14/2.37 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[707, 124, 114, 9844])).
% 2.14/2.37 tff(9846,plain,
% 2.14/2.37 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[4471, 9845])).
% 2.14/2.37 tff(9847,plain,
% 2.14/2.37 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(9848,plain,
% 2.14/2.37 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.14/2.37 inference(quant_inst,[status(thm)],[])).
% 2.14/2.37 tff(9849,plain,
% 2.14/2.37 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[9848, 9847])).
% 2.14/2.37 tff(9850,plain,
% 2.14/2.37 (~r(s(s(s(s(z)))), elem!1)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[9849, 124, 1474, 9844])).
% 2.14/2.37 tff(9851,plain,
% 2.14/2.37 (b(s(s(s(s(z)))), elem!1)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[9832, 9850, 9814])).
% 2.14/2.37 tff(9852,plain,
% 2.14/2.37 ($false),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[9823, 306, 9794, 5317, 9851, 9846])).
% 2.14/2.37 tff(9853,plain,(b(s(s(s(z))), s(z)) | b(elem!1, z) | r(s(s(elem!1)), elem!1) | (~r(s(z), s(s(s(z))))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.37 tff(9854,plain,
% 2.14/2.37 (b(s(s(s(z))), s(z))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[9853, 5, 6, 5008, 2])).
% 2.14/2.37 tff(9855,plain,
% 2.14/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(9856,plain,
% 2.14/2.37 (((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(9857,plain,
% 2.14/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z)))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[9856])).
% 2.14/2.37 tff(9858,plain,
% 2.14/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))))),
% 2.14/2.37 inference(transitivity,[status(thm)],[9857, 9855])).
% 2.14/2.37 tff(9859,plain,
% 2.14/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 2.14/2.37 inference(quant_inst,[status(thm)],[])).
% 2.14/2.37 tff(9860,plain,
% 2.14/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z)))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[9859, 9858])).
% 2.14/2.37 tff(9861,plain,
% 2.14/2.37 (~b(s(s(z)), s(z))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[9860, 306, 9854, 5316, 5310, 5010])).
% 2.14/2.37 tff(9862,plain,
% 2.14/2.37 (r(s(s(z)), s(z))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[2476, 9861])).
% 2.14/2.37 tff(9863,plain,
% 2.14/2.37 (~r(s(s(z)), s(s(s(z))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[3833, 9862, 5008])).
% 2.14/2.37 tff(9864,plain,
% 2.14/2.37 (b(s(s(z)), s(s(s(z))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[2514, 9863])).
% 2.14/2.37 tff(9865,plain,
% 2.14/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(9866,plain,
% 2.14/2.37 (((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(9867,plain,
% 2.14/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(z)))))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[9866])).
% 2.14/2.37 tff(9868,plain,
% 2.14/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 2.14/2.37 inference(transitivity,[status(thm)],[9867, 9865])).
% 2.14/2.37 tff(9869,plain,
% 2.14/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))),
% 2.14/2.37 inference(quant_inst,[status(thm)],[])).
% 2.14/2.37 tff(9870,plain,
% 2.14/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(z)))))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[9869, 9868])).
% 2.14/2.37 tff(9871,plain,
% 2.14/2.37 ($false),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[9870, 306, 9854, 5316, 5310, 5010, 9864])).
% 2.14/2.37 tff(9872,plain,(r(elem!1, z) | r(s(s(elem!1)), elem!1) | b(elem!1, s(z)) | r(z, elem!1) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 2.14/2.37 tff(9873,plain,
% 2.14/2.37 (r(elem!1, z)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[9872, 5, 6, 7, 2])).
% 2.14/2.37 tff(9874,plain,
% 2.14/2.37 (r(elem!1, z) <=> r(elem!1, elem!1)),
% 2.14/2.37 inference(monotonicity,[status(thm)],[1502])).
% 2.14/2.37 tff(9875,plain,
% 2.14/2.37 (r(elem!1, elem!1) <=> r(elem!1, z)),
% 2.14/2.37 inference(symmetry,[status(thm)],[9874])).
% 2.14/2.37 tff(9876,plain,
% 2.14/2.37 ((~r(elem!1, elem!1)) <=> (~r(elem!1, z))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[9875])).
% 2.14/2.37 tff(9877,plain,
% 2.14/2.37 (~r(elem!1, z)),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[4184, 9876])).
% 2.14/2.37 tff(9878,plain,
% 2.14/2.37 ($false),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[246, 9877])).
% 2.14/2.37 tff(9879,plain,((~(z = elem!1)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.37 tff(9880,plain,
% 2.14/2.37 (~(z = elem!1)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[9879, 9873])).
% 2.14/2.37 tff(9881,plain,
% 2.14/2.37 (b(z, elem!1)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[835, 9880, 7])).
% 2.14/2.37 tff(9882,plain,
% 2.14/2.37 (~(s(s(s(z))) = elem!1)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[1472, 5309])).
% 2.14/2.37 tff(9883,plain,
% 2.14/2.37 (b(s(z), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[85])).
% 2.14/2.37 tff(9884,plain,
% 2.14/2.37 (b(elem!1, s(s(s(z)))) <=> b(s(z), s(s(s(z))))),
% 2.14/2.37 inference(symmetry,[status(thm)],[9883])).
% 2.14/2.37 tff(9885,plain,
% 2.14/2.37 (b(s(z), s(s(s(z))))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[1470, 9884])).
% 2.14/2.37 tff(9886,plain,
% 2.14/2.37 ($false),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[3300, 9885])).
% 2.14/2.37 tff(9887,plain,((~(s(z) = elem!1)) | b(s(z), s(s(s(z)))) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.37 tff(9888,plain,
% 2.14/2.37 (~(s(z) = elem!1)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[9887, 5309, 5007])).
% 2.14/2.37 tff(9889,plain,
% 2.14/2.37 (~(elem!1 = s(z))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[3096, 9888])).
% 2.14/2.37 tff(9890,plain,
% 2.14/2.37 (r(elem!1, s(z))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[97, 9889])).
% 2.14/2.37 tff(9891,plain,
% 2.14/2.37 (~r(z, s(z))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[2273, 9890, 9873])).
% 2.14/2.37 tff(9892,plain,
% 2.14/2.37 (b(z, s(z))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[2263, 9891])).
% 2.14/2.37 tff(9893,plain,
% 2.14/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(z))))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(9894,plain,
% 2.14/2.37 (((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z)))) <=> ((~b(z, elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(z))))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(9895,plain,
% 2.14/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(z)))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[9894])).
% 2.14/2.37 tff(9896,plain,
% 2.14/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(z))))),
% 2.14/2.37 inference(transitivity,[status(thm)],[9895, 9893])).
% 2.14/2.37 tff(9897,plain,
% 2.14/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))),
% 2.14/2.37 inference(quant_inst,[status(thm)],[])).
% 2.14/2.37 tff(9898,plain,
% 2.14/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(z)))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[9897, 9896])).
% 2.14/2.37 tff(9899,plain,
% 2.14/2.37 ($false),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[9898, 306, 838, 2284, 2831, 1470, 485])).
% 2.14/2.37 tff(9900,plain,((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.37 tff(9901,plain,
% 2.14/2.37 (~b(s(z), elem!1)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[9900, 9881, 9854, 5309, 9892])).
% 2.14/2.37 tff(9902,plain,
% 2.14/2.37 (r(s(z), elem!1)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[1500, 43, 9901, 9888])).
% 2.14/2.37 tff(9903,plain,
% 2.14/2.37 (~r(s(s(s(z))), elem!1)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[3790, 9902, 5008])).
% 2.14/2.37 tff(9904,plain,
% 2.14/2.37 (b(s(s(s(z))), elem!1)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[1489, 9903, 9882])).
% 2.14/2.37 tff(9905,plain,
% 2.14/2.37 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[4243, 9904, 5309, 9854, 9881])).
% 2.14/2.37 tff(9906,plain,
% 2.14/2.37 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[4289, 9905, 5309, 6, 9889, 9904, 9881, 5])).
% 2.14/2.37 tff(9907,plain,
% 2.14/2.37 (b(s(s(s(s(s(s(z)))))), s(z))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[651, 43, 2844, 9906])).
% 2.14/2.37 tff(9908,plain,
% 2.14/2.37 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[2974, 9889])).
% 2.14/2.37 tff(9909,plain,
% 2.14/2.37 (~b(s(s(elem!1)), elem!1)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[3002, 9904, 5309, 9908, 9881])).
% 2.14/2.37 tff(9910,plain,
% 2.14/2.37 (s(s(elem!1)) = elem!1),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[47, 9909, 6])).
% 2.14/2.37 tff(9911,plain,
% 2.14/2.37 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[4284, 9910])).
% 2.14/2.37 tff(9912,plain,
% 2.14/2.37 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[1144, 9911, 9905])).
% 2.14/2.37 tff(9913,plain,
% 2.14/2.37 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(9914,plain,
% 2.14/2.37 (((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(z))))))))) <=> ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(9915,plain,
% 2.14/2.37 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), elem!1))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[9914])).
% 2.14/2.37 tff(9916,plain,
% 2.14/2.37 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))),
% 2.14/2.37 inference(transitivity,[status(thm)],[9915, 9913])).
% 2.14/2.37 tff(9917,plain,
% 2.14/2.37 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 2.14/2.37 inference(quant_inst,[status(thm)],[])).
% 2.14/2.37 tff(9918,plain,
% 2.14/2.37 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), elem!1))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[9917, 9916])).
% 2.14/2.37 tff(9919,plain,
% 2.14/2.37 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[9918, 124, 9902, 9912])).
% 2.14/2.37 tff(9920,plain,
% 2.14/2.37 (b(s(z), s(s(s(s(s(s(z)))))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[5358, 43, 5355, 9919])).
% 2.14/2.37 tff(9921,plain,
% 2.14/2.37 (~b(s(s(s(z))), z)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[2228, 9904, 5309, 9881])).
% 2.14/2.37 tff(9922,plain,
% 2.14/2.37 (r(s(s(s(z))), z)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[2197, 9921])).
% 2.14/2.37 tff(9923,plain,
% 2.14/2.37 (~r(s(z), z)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[1049, 9902, 9873])).
% 2.14/2.37 tff(9924,plain,
% 2.14/2.37 (b(s(z), z)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[221, 9923])).
% 2.14/2.37 tff(9925,plain,
% 2.14/2.37 (~b(s(s(s(s(s(s(z)))))), z)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[7183, 9907, 9924, 9892])).
% 2.14/2.37 tff(9926,plain,
% 2.14/2.37 (r(s(s(s(s(s(s(z)))))), z)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[4232, 9925])).
% 2.14/2.37 tff(9927,plain,
% 2.14/2.37 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[3203, 9926, 9922])).
% 2.14/2.37 tff(9928,plain,
% 2.14/2.37 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[3207, 9927])).
% 2.14/2.37 tff(9929,plain,
% 2.14/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(9930,plain,
% 2.14/2.37 (((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(9931,plain,
% 2.14/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(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(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[9930])).
% 2.14/2.37 tff(9932,plain,
% 2.14/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(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(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 2.14/2.37 inference(transitivity,[status(thm)],[9931, 9929])).
% 2.14/2.37 tff(9933,plain,
% 2.14/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(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(s(z)))))))))),
% 2.14/2.37 inference(quant_inst,[status(thm)],[])).
% 2.14/2.37 tff(9934,plain,
% 2.14/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[9933, 9932])).
% 2.14/2.37 tff(9935,plain,
% 2.14/2.37 ($false),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[9934, 306, 9854, 9928, 9920, 9907])).
% 2.14/2.37 tff(9936,plain,(b(elem!1, s(z)) | r(s(s(elem!1)), elem!1) | r(z, elem!1) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 2.14/2.37 tff(9937,plain,
% 2.14/2.37 (b(elem!1, s(z))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[9936, 7, 6, 2])).
% 2.14/2.37 tff(9938,plain,
% 2.14/2.37 (r(s(elem!1), s(s(s(z)))) <=> r(s(z), s(s(s(z))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[1621])).
% 2.14/2.37 tff(9939,plain,
% 2.14/2.37 (r(s(z), s(s(s(z)))) <=> r(s(elem!1), s(s(s(z))))),
% 2.14/2.37 inference(symmetry,[status(thm)],[9938])).
% 2.14/2.37 tff(9940,plain,
% 2.14/2.37 (r(s(elem!1), s(s(s(z))))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[1034, 9939])).
% 2.14/2.37 tff(9941,plain,
% 2.14/2.37 ((s(s(s(z))) = elem!1) <=> (s(s(s(z))) = z)),
% 2.14/2.37 inference(monotonicity,[status(thm)],[1620])).
% 2.14/2.37 tff(9942,plain,
% 2.14/2.37 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 2.14/2.37 inference(symmetry,[status(thm)],[9941])).
% 2.14/2.37 tff(9943,plain,
% 2.14/2.37 ((s(s(s(z))) = z) <=> (elem!1 = s(s(s(z))))),
% 2.14/2.37 inference(transitivity,[status(thm)],[9942, 6881])).
% 2.14/2.37 tff(9944,plain,
% 2.14/2.37 ((~(s(s(s(z))) = z)) <=> (~(elem!1 = s(s(s(z)))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[9943])).
% 2.14/2.37 tff(9945,plain,
% 2.14/2.37 (~(elem!1 = s(s(s(z))))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[169, 9944])).
% 2.14/2.37 tff(9946,plain,
% 2.14/2.37 (r(elem!1, s(s(s(z))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[2304, 9945, 3])).
% 2.14/2.37 tff(9947,plain,
% 2.14/2.37 (~r(s(elem!1), elem!1)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[7904, 9946, 9940])).
% 2.14/2.37 tff(9948,plain,
% 2.14/2.37 (b(s(elem!1), elem!1)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[813, 9947, 3333])).
% 2.14/2.37 tff(9949,plain,
% 2.14/2.37 (b(s(elem!1), z)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[2709, 9948, 3332])).
% 2.14/2.37 tff(9950,plain,
% 2.14/2.37 (b(s(z), elem!1)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[2718, 9949, 3332])).
% 2.14/2.37 tff(9951,plain,
% 2.14/2.37 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 2.14/2.37 inference(symmetry,[status(thm)],[4357])).
% 2.14/2.37 tff(9952,plain,
% 2.14/2.37 (~b(s(s(elem!1)), s(z))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[4380, 9950, 4346, 4362])).
% 2.14/2.37 tff(9953,plain,
% 2.14/2.37 (~b(s(s(z)), s(z))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[9952, 4366])).
% 2.14/2.37 tff(9954,plain,
% 2.14/2.37 (r(s(s(z)), s(z))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[2474, 43, 9953, 2470])).
% 2.14/2.37 tff(9955,plain,
% 2.14/2.37 (~r(s(s(z)), s(s(s(z))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[3833, 9954, 1034])).
% 2.14/2.37 tff(9956,plain,
% 2.14/2.37 (b(s(s(z)), s(s(s(z))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[2514, 9955])).
% 2.14/2.37 tff(9957,plain,
% 2.14/2.37 (b(s(s(elem!1)), s(s(s(z))))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[9956, 9951])).
% 2.14/2.37 tff(9958,plain,
% 2.14/2.37 (~b(s(s(s(z))), elem!1)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[7958, 9957, 4346, 4362, 9950])).
% 2.14/2.37 tff(9959,plain,
% 2.14/2.37 (~b(s(s(s(elem!1))), elem!1)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[2215, 9958, 3332])).
% 2.14/2.37 tff(9960,plain,
% 2.14/2.37 (r(s(s(s(elem!1))), elem!1)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[1636, 9959, 4365])).
% 2.14/2.37 tff(9961,plain,
% 2.14/2.37 (r(s(s(s(z))), z)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[1631, 9960, 1620])).
% 2.14/2.37 tff(9962,plain,
% 2.14/2.37 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(s(s(z))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[1623])).
% 2.14/2.38 tff(9963,plain,
% 2.14/2.38 (r(s(z), s(s(s(z)))) <=> r(s(z), s(s(s(elem!1))))),
% 2.14/2.38 inference(symmetry,[status(thm)],[9962])).
% 2.14/2.38 tff(9964,plain,
% 2.14/2.38 (r(s(z), s(s(s(elem!1))))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[1034, 9963])).
% 2.14/2.38 tff(9965,plain,
% 2.14/2.38 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(s(z))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[1623])).
% 2.14/2.38 tff(9966,plain,
% 2.14/2.38 (b(z, s(s(s(z)))) <=> b(z, s(s(s(elem!1))))),
% 2.14/2.38 inference(symmetry,[status(thm)],[9965])).
% 2.14/2.38 tff(9967,plain,
% 2.14/2.38 ((~b(z, s(s(s(z))))) <=> (~b(z, s(s(s(elem!1)))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[9966])).
% 2.14/2.38 tff(9968,plain,
% 2.14/2.38 (b(elem!1, s(s(s(z)))) <=> b(z, s(s(s(z))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[1620])).
% 2.14/2.38 tff(9969,plain,
% 2.14/2.38 ((~b(elem!1, s(s(s(z))))) <=> (~b(z, s(s(s(z)))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[9968])).
% 2.14/2.38 tff(9970,plain,
% 2.14/2.38 (~b(z, s(s(s(z))))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[3, 9969])).
% 2.14/2.38 tff(9971,plain,
% 2.14/2.38 (~b(z, s(s(s(elem!1))))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[9970, 9967])).
% 2.14/2.38 tff(9972,plain,
% 2.14/2.38 (r(z, s(s(s(elem!1))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[585, 9971])).
% 2.14/2.38 tff(9973,plain,
% 2.14/2.38 (~r(s(z), z)),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[4074, 9972, 9964])).
% 2.14/2.38 tff(9974,plain,
% 2.14/2.38 (b(s(z), z)),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[221, 9973])).
% 2.14/2.38 tff(9975,plain,
% 2.14/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(9976,plain,
% 2.14/2.38 (((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z))))) <=> ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(9977,plain,
% 2.14/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z))))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[9976])).
% 2.14/2.38 tff(9978,plain,
% 2.14/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))),
% 2.14/2.38 inference(transitivity,[status(thm)],[9977, 9975])).
% 2.14/2.38 tff(9979,plain,
% 2.14/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))),
% 2.14/2.38 inference(quant_inst,[status(thm)],[])).
% 2.14/2.38 tff(9980,plain,
% 2.14/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z))))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[9979, 9978])).
% 2.14/2.38 tff(9981,plain,
% 2.14/2.38 (~b(s(z), s(s(z)))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[9980, 306, 4536, 9974, 4347])).
% 2.14/2.38 tff(9982,plain,
% 2.14/2.38 (r(s(z), s(s(z)))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[4434, 9981])).
% 2.14/2.38 tff(9983,plain,
% 2.14/2.38 (r(s(elem!1), s(s(elem!1)))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[9982, 4418])).
% 2.14/2.38 tff(9984,plain,
% 2.14/2.38 (~b(s(s(s(s(elem!1)))), elem!1)),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[4458, 9983, 4414, 4362, 4363, 4400, 9948])).
% 2.14/2.38 tff(9985,plain,
% 2.14/2.38 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[1736, 9984, 4393])).
% 2.14/2.38 tff(9986,plain,
% 2.14/2.38 (r(s(s(s(s(z)))), z)),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[9985, 4386])).
% 2.14/2.38 tff(9987,plain,
% 2.14/2.38 ((s(s(s(s(elem!1)))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(z)))) = s(s(s(s(s(s(z)))))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[1704])).
% 2.14/2.38 tff(9988,plain,
% 2.14/2.38 ((s(s(s(s(elem!1)))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = s(s(s(s(z)))))),
% 2.14/2.38 inference(transitivity,[status(thm)],[9987, 4708])).
% 2.14/2.38 tff(9989,plain,
% 2.14/2.38 ((~(s(s(s(s(elem!1)))) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(s(s(s(s(z)))))) = s(s(s(s(z))))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[9988])).
% 2.14/2.38 tff(9990,plain,
% 2.14/2.38 (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[1719, 4400])).
% 2.14/2.38 tff(9991,plain,
% 2.14/2.38 (~(s(s(s(s(elem!1)))) = s(s(s(s(s(s(z)))))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[3709, 9990, 3332])).
% 2.14/2.38 tff(9992,plain,
% 2.14/2.38 (~(s(s(s(s(s(s(z)))))) = s(s(s(s(z)))))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[9991, 9989])).
% 2.14/2.38 tff(9993,assumption,(~(s(s(s(s(s(s(z)))))) = s(s(s(s(z)))))), introduced(assumption)).
% 2.14/2.38 tff(9994,plain,
% 2.14/2.38 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(9995,plain,
% 2.14/2.38 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.14/2.38 inference(quant_inst,[status(thm)],[])).
% 2.14/2.38 tff(9996,plain,
% 2.14/2.38 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[9995, 9994])).
% 2.14/2.38 tff(9997,plain,
% 2.14/2.38 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[9996, 124, 397, 3194])).
% 2.14/2.38 tff(9998,plain,
% 2.14/2.38 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[4725, 9997, 9993])).
% 2.14/2.38 tff(9999,plain,
% 2.14/2.38 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[1392, 124, 205, 3194])).
% 2.14/2.38 tff(10000,plain,
% 2.14/2.38 (b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[2880, 9999, 1502])).
% 2.14/2.38 tff(10001,plain,
% 2.14/2.38 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[2889, 10000, 1502])).
% 2.14/2.38 tff(10002,plain,
% 2.14/2.38 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[4464, 124, 205, 397])).
% 2.14/2.38 tff(10003,plain,
% 2.14/2.38 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[4471, 10002])).
% 2.14/2.38 tff(10004,plain,
% 2.14/2.38 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[4478, 124, 205, 397])).
% 2.14/2.38 tff(10005,plain,
% 2.14/2.38 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[4481, 10004])).
% 2.14/2.38 tff(10006,plain,
% 2.14/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(10007,plain,
% 2.14/2.38 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(10008,plain,
% 2.14/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[10007])).
% 2.14/2.38 tff(10009,plain,
% 2.14/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.14/2.38 inference(transitivity,[status(thm)],[10008, 10006])).
% 2.14/2.38 tff(10010,plain,
% 2.14/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 2.14/2.38 inference(quant_inst,[status(thm)],[])).
% 2.14/2.38 tff(10011,plain,
% 2.14/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[10010, 10009])).
% 2.14/2.38 tff(10012,plain,
% 2.14/2.38 ($false),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[10011, 306, 10005, 10003, 10001, 9998])).
% 2.14/2.38 tff(10013,plain,((~r(s(s(s(s(s(s(z)))))), z)) | (~(z = elem!1)) | (s(s(s(s(s(s(z)))))) = s(s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.38 tff(10014,plain,
% 2.14/2.38 (~r(s(s(s(s(s(s(z)))))), z)),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[10013, 3332, 9992, 9986, 9961])).
% 2.14/2.38 tff(10015,plain,
% 2.14/2.38 (b(s(s(s(s(s(s(z)))))), z)),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[4232, 10014])).
% 2.14/2.38 tff(10016,plain,
% 2.14/2.38 (b(elem!1, s(s(elem!1))) <=> b(z, s(s(elem!1)))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[1620])).
% 2.14/2.38 tff(10017,plain,
% 2.14/2.38 (b(elem!1, s(s(elem!1))) <=> b(z, s(s(z)))),
% 2.14/2.38 inference(transitivity,[status(thm)],[10016, 3511])).
% 2.14/2.38 tff(10018,plain,
% 2.14/2.38 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[4464, 124, 9961, 9986])).
% 2.14/2.38 tff(10019,plain,
% 2.14/2.38 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[4471, 10018])).
% 2.14/2.38 tff(10020,plain,
% 2.14/2.38 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[4478, 124, 9961, 9986])).
% 2.14/2.38 tff(10021,plain,
% 2.14/2.38 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[4481, 10020])).
% 2.14/2.38 tff(10022,plain,
% 2.14/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(10023,plain,
% 2.14/2.38 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(10024,plain,
% 2.14/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), 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(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[10023])).
% 2.14/2.38 tff(10025,plain,
% 2.14/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), 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(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.14/2.38 inference(transitivity,[status(thm)],[10024, 10022])).
% 2.14/2.38 tff(10026,plain,
% 2.14/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), 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(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.14/2.38 inference(quant_inst,[status(thm)],[])).
% 2.14/2.38 tff(10027,plain,
% 2.14/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[10026, 10025])).
% 2.14/2.38 tff(10028,plain,
% 2.14/2.38 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[10027, 306, 10021, 9956, 10019])).
% 2.14/2.38 tff(10029,plain,
% 2.14/2.38 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[3469, 10028, 1620])).
% 2.14/2.38 tff(10030,plain,
% 2.14/2.38 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[1302, 10029, 4400])).
% 2.14/2.38 tff(10031,plain,
% 2.14/2.38 (~r(elem!1, s(s(elem!1)))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[1297, 10030, 9985])).
% 2.14/2.38 tff(10032,plain,
% 2.14/2.38 (b(elem!1, s(s(elem!1)))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[516, 10031, 4360])).
% 2.14/2.38 tff(10033,plain,
% 2.14/2.38 (b(z, s(s(z)))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[10032, 10017])).
% 2.14/2.38 tff(10034,plain,
% 2.14/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(10035,plain,
% 2.14/2.38 (((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(10036,plain,
% 2.14/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[10035])).
% 2.14/2.38 tff(10037,plain,
% 2.14/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.14/2.38 inference(transitivity,[status(thm)],[10036, 10034])).
% 2.14/2.38 tff(10038,plain,
% 2.14/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.14/2.38 inference(quant_inst,[status(thm)],[])).
% 2.14/2.38 tff(10039,plain,
% 2.14/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[10038, 10037])).
% 2.14/2.38 tff(10040,plain,
% 2.14/2.38 (~b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[10039, 306, 10033, 4536, 10015])).
% 2.14/2.38 tff(10041,plain,
% 2.14/2.38 (r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[2829, 43, 2826, 10040])).
% 2.14/2.38 tff(10042,plain,
% 2.14/2.38 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[7183, 10015, 9974, 4347])).
% 2.14/2.38 tff(10043,plain,
% 2.14/2.38 (r(s(s(s(s(s(s(z)))))), s(z))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[651, 43, 2844, 10042])).
% 2.14/2.38 tff(10044,plain,
% 2.14/2.38 ($false),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[2853, 124, 9954, 10043, 10041])).
% 2.14/2.38 tff(10045,plain,((~(elem!1 = z)) | (~b(elem!1, s(z))) | (~r(s(z), s(s(s(z))))) | b(elem!1, s(s(s(z)))) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.14/2.38 tff(10046,plain,
% 2.14/2.38 (~(elem!1 = z)),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[10045, 3, 5008, 9937, 6])).
% 2.14/2.38 tff(10047,plain,
% 2.14/2.38 (~(z = elem!1)),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[1618, 10046])).
% 2.14/2.38 tff(10048,plain,
% 2.14/2.38 (b(z, elem!1)),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[835, 10047, 7])).
% 2.14/2.38 tff(10049,plain,
% 2.14/2.38 (b(elem!1, s(z)) <=> b(elem!1, elem!1)),
% 2.14/2.38 inference(monotonicity,[status(thm)],[85])).
% 2.14/2.38 tff(10050,plain,
% 2.14/2.38 (b(elem!1, elem!1) <=> b(elem!1, s(z))),
% 2.14/2.38 inference(symmetry,[status(thm)],[10049])).
% 2.14/2.38 tff(10051,plain,
% 2.14/2.38 ((~b(elem!1, elem!1)) <=> (~b(elem!1, s(z)))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[10050])).
% 2.14/2.38 tff(10052,plain,
% 2.14/2.38 (~b(elem!1, s(z))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[1468, 10051])).
% 2.14/2.38 tff(10053,plain,
% 2.14/2.38 ($false),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[4346, 10052])).
% 2.14/2.38 tff(10054,plain,((~(s(z) = elem!1)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.38 tff(10055,plain,
% 2.14/2.38 (~(s(z) = elem!1)),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[10054, 4346])).
% 2.14/2.38 tff(10056,plain,
% 2.14/2.38 (~(elem!1 = z)),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[10045, 3, 1034, 4346, 6])).
% 2.14/2.38 tff(10057,plain,
% 2.14/2.38 (r(elem!1, z)),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[174, 10056, 2])).
% 2.14/2.38 tff(10058,plain,
% 2.14/2.38 (~(elem!1 = s(z))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[4298, 247, 2])).
% 2.14/2.38 tff(10059,plain,
% 2.14/2.38 (~(s(z) = elem!1)),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[89, 10058])).
% 2.14/2.38 tff(10060,plain,
% 2.14/2.38 (r(s(z), elem!1)),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[4192, 10059])).
% 2.14/2.38 tff(10061,plain,
% 2.14/2.38 (~r(elem!1, s(s(s(z))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[3347, 10060, 1034])).
% 2.14/2.38 tff(10062,plain,
% 2.14/2.38 (elem!1 = s(s(s(z)))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[2304, 10061, 3])).
% 2.14/2.38 tff(10063,plain,
% 2.14/2.38 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[2974, 10058])).
% 2.14/2.39 tff(10064,plain,
% 2.14/2.39 ((s(s(elem!1)) = elem!1) <=> (s(s(elem!1)) = s(s(s(z))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[231])).
% 2.14/2.39 tff(10065,plain,
% 2.14/2.39 ((s(s(elem!1)) = elem!1) <=> (s(s(s(z))) = s(s(elem!1)))),
% 2.14/2.39 inference(transitivity,[status(thm)],[10064, 7095])).
% 2.14/2.39 tff(10066,plain,
% 2.14/2.39 (s(s(s(z))) = s(s(elem!1))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[1171, 10065])).
% 2.14/2.39 tff(10067,plain,
% 2.14/2.39 ($false),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[2976, 10066])).
% 2.14/2.39 tff(10068,plain,((~(s(s(elem!1)) = elem!1)) | (s(s(s(z))) = s(s(elem!1))) | (~(elem!1 = s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.39 tff(10069,plain,
% 2.14/2.39 (~(s(s(elem!1)) = elem!1)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[10068, 10063, 10062])).
% 2.14/2.39 tff(10070,plain,
% 2.14/2.39 (b(s(s(elem!1)), elem!1)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[47, 10069, 6])).
% 2.14/2.39 tff(10071,plain,
% 2.14/2.39 (~(elem!1 = s(s(elem!1)))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[186, 10069])).
% 2.14/2.39 tff(10072,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), z)))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(10073,plain,
% 2.14/2.39 (((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1))))) <=> ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), z)))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(10074,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), z))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[10073])).
% 2.14/2.39 tff(10075,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), z)))),
% 2.14/2.39 inference(transitivity,[status(thm)],[10074, 10072])).
% 2.14/2.39 tff(10076,plain,
% 2.14/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))),
% 2.14/2.39 inference(quant_inst,[status(thm)],[])).
% 2.14/2.39 tff(10077,plain,
% 2.14/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), z))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[10076, 10075])).
% 2.14/2.39 tff(10078,plain,
% 2.14/2.39 ($false),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[10077, 306, 838, 30, 1198, 4346, 247])).
% 2.14/2.39 tff(10079,plain,((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.39 tff(10080,plain,
% 2.14/2.39 (~b(z, s(s(elem!1)))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[10079, 10070, 4346, 838, 247])).
% 2.14/2.39 tff(10081,plain,
% 2.14/2.39 (r(z, s(s(elem!1)))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[460, 10080])).
% 2.14/2.39 tff(10082,plain,
% 2.14/2.39 (~r(elem!1, s(s(elem!1)))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[978, 10081, 10057])).
% 2.14/2.39 tff(10083,plain,
% 2.14/2.39 (b(elem!1, s(s(elem!1)))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[516, 10082, 10071])).
% 2.14/2.39 tff(10084,plain,
% 2.14/2.39 (~(z = elem!1)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[1618, 10056])).
% 2.14/2.39 tff(10085,plain,
% 2.14/2.39 (~(s(elem!1) = s(z))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[2689, 10084])).
% 2.14/2.39 tff(10086,plain,
% 2.14/2.39 (s(s(s(z))) = elem!1),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[4555, 10062])).
% 2.14/2.39 tff(10087,plain,
% 2.14/2.39 (~(s(s(s(elem!1))) = elem!1)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[4105, 10086, 10085])).
% 2.14/2.39 tff(10088,plain,
% 2.14/2.39 (~(s(s(elem!1)) = s(elem!1))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[1564, 10087])).
% 2.14/2.39 tff(10089,plain,
% 2.14/2.39 (s(elem!1) = s(s(s(s(z))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[10062])).
% 2.14/2.39 tff(10090,plain,
% 2.14/2.39 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[10089])).
% 2.14/2.39 tff(10091,plain,
% 2.14/2.39 (b(s(s(elem!1)), z) <=> b(s(s(s(s(s(z))))), z)),
% 2.14/2.39 inference(monotonicity,[status(thm)],[10090])).
% 2.14/2.39 tff(10092,plain,
% 2.14/2.39 (b(s(s(s(s(s(z))))), z) <=> b(s(s(elem!1)), z)),
% 2.14/2.39 inference(symmetry,[status(thm)],[10091])).
% 2.14/2.39 tff(10093,plain,
% 2.14/2.39 ((~b(s(s(s(s(s(z))))), z)) <=> (~b(s(s(elem!1)), z))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[10092])).
% 2.14/2.39 tff(10094,plain,
% 2.14/2.39 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 2.14/2.39 inference(symmetry,[status(thm)],[10090])).
% 2.14/2.39 tff(10095,plain,
% 2.14/2.39 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[10094])).
% 2.14/2.39 tff(10096,plain,
% 2.14/2.39 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.14/2.39 inference(symmetry,[status(thm)],[10095])).
% 2.14/2.39 tff(10097,plain,
% 2.14/2.39 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(s(s(z))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[10062])).
% 2.14/2.39 tff(10098,plain,
% 2.14/2.39 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.14/2.39 inference(transitivity,[status(thm)],[10097, 10096])).
% 2.14/2.39 tff(10099,plain,
% 2.14/2.39 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[10070, 10098])).
% 2.14/2.39 tff(10100,plain,
% 2.14/2.39 (b(z, s(s(s(z))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[842, 10062, 838])).
% 2.14/2.39 tff(10101,plain,
% 2.14/2.39 (~(s(s(s(z))) = elem!1)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[4551, 9, 4346])).
% 2.14/2.39 tff(10102,plain,
% 2.14/2.39 (~(elem!1 = s(s(s(z))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[4555, 10101])).
% 2.14/2.39 tff(10103,plain,
% 2.14/2.39 (r(elem!1, s(s(s(z))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[2304, 10102, 3])).
% 2.14/2.39 tff(10104,plain,
% 2.14/2.39 (~r(s(z), elem!1)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[3347, 10103, 1034])).
% 2.14/2.39 tff(10105,plain,
% 2.14/2.39 (b(s(z), elem!1)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[1500, 43, 10104, 90])).
% 2.14/2.39 tff(10106,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(10107,plain,
% 2.14/2.39 (((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z))) <=> ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(10108,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[10107])).
% 2.14/2.39 tff(10109,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)))),
% 2.14/2.39 inference(transitivity,[status(thm)],[10108, 10106])).
% 2.14/2.39 tff(10110,plain,
% 2.14/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))),
% 2.14/2.39 inference(quant_inst,[status(thm)],[])).
% 2.14/2.39 tff(10111,plain,
% 2.14/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[10110, 10109])).
% 2.14/2.39 tff(10112,plain,
% 2.14/2.39 (~b(s(z), z)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[10111, 306, 838, 2831, 4346])).
% 2.14/2.39 tff(10113,plain,
% 2.14/2.39 (r(s(z), z)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[221, 10112])).
% 2.14/2.39 tff(10114,plain,
% 2.14/2.39 (~r(s(s(s(z))), z)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[2312, 3313, 246])).
% 2.14/2.39 tff(10115,plain,
% 2.14/2.39 (b(s(s(s(z))), z)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[2197, 10114])).
% 2.14/2.39 tff(10116,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(10117,plain,
% 2.14/2.39 (((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(z, elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(10118,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[10117])).
% 2.14/2.39 tff(10119,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z)))),
% 2.14/2.39 inference(transitivity,[status(thm)],[10118, 10116])).
% 2.14/2.39 tff(10120,plain,
% 2.14/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.14/2.39 inference(quant_inst,[status(thm)],[])).
% 2.14/2.39 tff(10121,plain,
% 2.14/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), z))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[10120, 10119])).
% 2.14/2.39 tff(10122,plain,
% 2.14/2.39 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[10121, 306, 838, 4346, 942, 1531])).
% 2.14/2.39 tff(10123,plain,
% 2.14/2.39 ((s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z)))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[350, 43])).
% 2.14/2.39 tff(10124,plain,
% 2.14/2.39 (b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z)))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[10123, 4480])).
% 2.14/2.39 tff(10125,plain,
% 2.14/2.39 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[10124, 10122])).
% 2.14/2.39 tff(10126,assumption,(r(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 2.14/2.39 tff(10127,plain,
% 2.14/2.39 ($false),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[334, 124, 206, 2013, 10126])).
% 2.14/2.39 tff(10128,plain,((~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,[]))).
% 2.14/2.39 tff(10129,plain,
% 2.14/2.39 (~r(s(s(s(s(z)))), s(z))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[10128, 10125, 206])).
% 2.14/2.39 tff(10130,plain,
% 2.14/2.39 (b(s(s(s(s(z)))), s(z))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[4490, 10129])).
% 2.14/2.39 tff(10131,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(10132,plain,
% 2.14/2.39 (((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(10133,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[10132])).
% 2.14/2.39 tff(10134,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.14/2.39 inference(transitivity,[status(thm)],[10133, 10131])).
% 2.14/2.39 tff(10135,plain,
% 2.14/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.14/2.39 inference(quant_inst,[status(thm)],[])).
% 2.14/2.39 tff(10136,plain,
% 2.14/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[10135, 10134])).
% 2.14/2.39 tff(10137,plain,
% 2.14/2.39 (~b(s(s(s(s(z)))), elem!1)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[10136, 306, 2831, 4346, 10130])).
% 2.14/2.39 tff(10138,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(10139,plain,
% 2.14/2.39 (((~b(elem!1, s(z))) | (~b(z, 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)))))) <=> ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(10140,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[10139])).
% 2.14/2.39 tff(10141,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 2.14/2.39 inference(transitivity,[status(thm)],[10140, 10138])).
% 2.14/2.39 tff(10142,plain,
% 2.14/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, 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))))))),
% 2.14/2.39 inference(quant_inst,[status(thm)],[])).
% 2.14/2.39 tff(10143,plain,
% 2.14/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[10142, 10141])).
% 2.14/2.39 tff(10144,plain,
% 2.14/2.39 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[10143, 306, 838, 4346, 942, 1531])).
% 2.14/2.39 tff(10145,plain,
% 2.14/2.39 ((s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[421, 43])).
% 2.14/2.39 tff(10146,plain,
% 2.14/2.39 (b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[10145, 4470])).
% 2.14/2.39 tff(10147,plain,
% 2.14/2.39 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[10146, 10144])).
% 2.14/2.39 tff(10148,plain,
% 2.14/2.39 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(10149,plain,
% 2.14/2.39 (((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(10150,plain,
% 2.14/2.39 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[10149])).
% 2.14/2.39 tff(10151,plain,
% 2.14/2.39 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.14/2.39 inference(transitivity,[status(thm)],[10150, 10148])).
% 2.14/2.39 tff(10152,plain,
% 2.14/2.39 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.14/2.39 inference(quant_inst,[status(thm)],[])).
% 2.14/2.39 tff(10153,plain,
% 2.14/2.39 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[10152, 10151])).
% 2.14/2.39 tff(10154,plain,
% 2.14/2.39 (~r(s(s(s(s(z)))), elem!1)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[10153, 124, 3313, 10147])).
% 2.14/2.39 tff(10155,plain,
% 2.14/2.39 ($false),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[9832, 10154, 10137, 9815])).
% 2.14/2.39 tff(10156,plain,((~b(s(s(s(s(z)))), z)) | (s(s(s(s(z)))) = elem!1) | (~r(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.39 tff(10157,plain,
% 2.14/2.39 (~b(s(s(s(s(z)))), z)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[10156, 9815, 3313, 2831, 4346, 206, 838, 10115])).
% 2.14/2.39 tff(10158,plain,
% 2.14/2.39 (r(s(s(s(s(z)))), z)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[695, 10157])).
% 2.14/2.39 tff(10159,plain,
% 2.14/2.39 ($false),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[3408, 124, 204, 397, 10126])).
% 2.14/2.39 tff(10160,plain,((~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.39 tff(10161,plain,
% 2.14/2.39 (~r(s(s(s(s(z)))), s(z))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[10160, 10158, 10113])).
% 2.14/2.39 tff(10162,plain,
% 2.14/2.39 (b(s(s(s(s(z)))), s(z))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[4490, 10161])).
% 2.14/2.39 tff(10163,plain,
% 2.14/2.39 (~b(s(s(s(s(z)))), elem!1)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[10136, 306, 2831, 4346, 10162])).
% 2.14/2.39 tff(10164,plain,
% 2.14/2.39 (~r(s(s(s(s(z)))), elem!1)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[9827, 124, 246, 10158])).
% 2.14/2.39 tff(10165,plain,
% 2.14/2.39 ($false),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[9832, 10164, 10163, 9815])).
% 2.14/2.39 tff(10166,plain,((s(s(s(s(z)))) = elem!1) | (~r(elem!1, z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.39 tff(10167,plain,
% 2.14/2.39 (s(s(s(s(z)))) = elem!1),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[10166, 10105, 246, 4346, 10103, 114, 838])).
% 2.14/2.39 tff(10168,plain,
% 2.14/2.39 (s(s(s(s(s(z))))) = s(elem!1)),
% 2.14/2.39 inference(monotonicity,[status(thm)],[10167])).
% 2.14/2.39 tff(10169,plain,
% 2.14/2.39 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[10168])).
% 2.14/2.39 tff(10170,plain,
% 2.14/2.39 (b(s(s(s(s(s(s(z)))))), z) <=> b(s(s(elem!1)), z)),
% 2.14/2.39 inference(monotonicity,[status(thm)],[10169])).
% 2.14/2.39 tff(10171,plain,
% 2.14/2.39 (b(s(s(elem!1)), z) <=> b(s(s(s(s(s(s(z)))))), z)),
% 2.14/2.39 inference(symmetry,[status(thm)],[10170])).
% 2.14/2.39 tff(10172,plain,
% 2.14/2.39 ((~b(s(s(elem!1)), z)) <=> (~b(s(s(s(s(s(s(z)))))), z))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[10171])).
% 2.14/2.39 tff(10173,plain,
% 2.14/2.39 (~(s(s(elem!1)) = elem!1)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[9813, 10167])).
% 2.14/2.39 tff(10174,plain,
% 2.14/2.39 (b(s(s(elem!1)), elem!1)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[47, 10173, 6])).
% 2.14/2.39 tff(10175,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(10176,plain,
% 2.14/2.39 (((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z))) <=> ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))))),
% 2.14/2.40 inference(rewrite,[status(thm)],[])).
% 2.14/2.40 tff(10177,plain,
% 2.14/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z)))))),
% 2.14/2.40 inference(monotonicity,[status(thm)],[10176])).
% 2.14/2.40 tff(10178,plain,
% 2.14/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))))),
% 2.14/2.40 inference(transitivity,[status(thm)],[10177, 10175])).
% 2.14/2.40 tff(10179,plain,
% 2.14/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))),
% 2.14/2.40 inference(quant_inst,[status(thm)],[])).
% 2.14/2.40 tff(10180,plain,
% 2.14/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z)))),
% 2.14/2.40 inference(modus_ponens,[status(thm)],[10179, 10178])).
% 2.14/2.40 tff(10181,plain,
% 2.14/2.40 (~b(s(s(elem!1)), z)),
% 2.14/2.40 inference(unit_resolution,[status(thm)],[10180, 306, 838, 10174, 10105, 4346])).
% 2.14/2.40 tff(10182,plain,
% 2.14/2.40 (~b(s(s(s(s(s(s(z)))))), z)),
% 2.14/2.40 inference(modus_ponens,[status(thm)],[10181, 10172])).
% 2.14/2.40 tff(10183,plain,
% 2.14/2.40 (~b(s(z), z)),
% 2.14/2.40 inference(unit_resolution,[status(thm)],[10111, 306, 838, 10105, 4346])).
% 2.14/2.40 tff(10184,plain,
% 2.14/2.40 (r(s(z), z)),
% 2.14/2.40 inference(unit_resolution,[status(thm)],[221, 10183])).
% 2.14/2.40 tff(10185,plain,
% 2.14/2.40 (r(s(s(s(s(s(s(z)))))), s(z)) <=> r(s(s(elem!1)), s(z))),
% 2.14/2.40 inference(monotonicity,[status(thm)],[10169])).
% 2.14/2.40 tff(10186,plain,
% 2.14/2.40 (r(s(s(elem!1)), s(z)) <=> r(s(s(s(s(s(s(z)))))), s(z))),
% 2.14/2.40 inference(symmetry,[status(thm)],[10185])).
% 2.14/2.40 tff(10187,plain,
% 2.14/2.40 (~b(s(s(elem!1)), s(z))),
% 2.14/2.40 inference(unit_resolution,[status(thm)],[4380, 10174, 4346, 10105])).
% 2.14/2.40 tff(10188,plain,
% 2.14/2.40 (r(s(s(elem!1)), s(z))),
% 2.14/2.40 inference(unit_resolution,[status(thm)],[3989, 10187])).
% 2.14/2.40 tff(10189,plain,
% 2.14/2.40 (r(s(s(s(s(s(s(z)))))), s(z))),
% 2.14/2.40 inference(modus_ponens,[status(thm)],[10188, 10186])).
% 2.14/2.40 tff(10190,plain,
% 2.14/2.40 (~r(s(s(s(s(s(s(z)))))), z)),
% 2.14/2.40 inference(unit_resolution,[status(thm)],[4324, 10189, 10184])).
% 2.14/2.40 tff(10191,plain,
% 2.14/2.40 (b(s(s(s(s(s(s(z)))))), z)),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[4232, 10190])).
% 2.24/2.40 tff(10192,plain,
% 2.24/2.40 ($false),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[10191, 10182])).
% 2.24/2.40 tff(10193,plain,(b(s(s(s(z))), s(z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | r(s(s(elem!1)), elem!1) | (~r(elem!1, z)) | (~r(s(z), s(s(s(z))))) | b(elem!1, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.40 tff(10194,plain,
% 2.24/2.40 (b(s(s(s(z))), s(z))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[10193, 838, 4346, 6, 10057, 1034, 3])).
% 2.24/2.40 tff(10195,plain,
% 2.24/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(10196,plain,
% 2.24/2.40 (((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(10197,plain,
% 2.24/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z))))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[10196])).
% 2.24/2.40 tff(10198,plain,
% 2.24/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.24/2.40 inference(transitivity,[status(thm)],[10197, 10195])).
% 2.24/2.40 tff(10199,plain,
% 2.24/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.24/2.40 inference(quant_inst,[status(thm)],[])).
% 2.24/2.40 tff(10200,plain,
% 2.24/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[10199, 10198])).
% 2.24/2.40 tff(10201,plain,
% 2.24/2.40 (~b(s(s(s(s(s(z))))), z)),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[10200, 306, 10194, 10100, 247, 10099])).
% 2.24/2.40 tff(10202,plain,
% 2.24/2.40 (~b(s(s(elem!1)), z)),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[10201, 10093])).
% 2.24/2.40 tff(10203,plain,
% 2.24/2.40 (r(s(s(elem!1)), z)),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[476, 10202])).
% 2.24/2.40 tff(10204,plain,
% 2.24/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z)))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(10205,plain,
% 2.24/2.40 (((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z)))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(10206,plain,
% 2.24/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z))))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[10205])).
% 2.24/2.40 tff(10207,plain,
% 2.24/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z)))),
% 2.24/2.40 inference(transitivity,[status(thm)],[10206, 10204])).
% 2.24/2.40 tff(10208,plain,
% 2.24/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 2.24/2.40 inference(quant_inst,[status(thm)],[])).
% 2.24/2.40 tff(10209,plain,
% 2.24/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[10208, 10207])).
% 2.24/2.40 tff(10210,plain,
% 2.24/2.40 (~b(s(s(s(s(z)))), s(z))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[10209, 306, 2284, 942, 859, 247])).
% 2.24/2.40 tff(10211,plain,
% 2.24/2.40 (r(s(s(s(s(z)))), s(z))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[4490, 10210])).
% 2.24/2.40 tff(10212,plain,
% 2.24/2.40 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(s(s(z))))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[231])).
% 2.24/2.40 tff(10213,plain,
% 2.24/2.40 ((s(elem!1) = s(s(s(z)))) <=> (s(elem!1) = elem!1)),
% 2.24/2.40 inference(symmetry,[status(thm)],[10212])).
% 2.24/2.40 tff(10214,plain,
% 2.24/2.40 ((s(elem!1) = s(s(s(z)))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[234])).
% 2.24/2.40 tff(10215,plain,
% 2.24/2.40 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 2.24/2.40 inference(symmetry,[status(thm)],[10214])).
% 2.24/2.40 tff(10216,plain,
% 2.24/2.40 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(elem!1) = elem!1)),
% 2.24/2.40 inference(transitivity,[status(thm)],[10215, 10213])).
% 2.24/2.40 tff(10217,plain,
% 2.24/2.40 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(elem!1) = elem!1))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[10216])).
% 2.24/2.40 tff(10218,plain,
% 2.24/2.40 (~(s(elem!1) = elem!1)),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[4470, 10217])).
% 2.24/2.40 tff(10219,plain,
% 2.24/2.40 (r(s(z), s(elem!1)) <=> r(s(z), s(s(s(s(z)))))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[234])).
% 2.24/2.40 tff(10220,plain,
% 2.24/2.40 (r(s(z), s(s(s(s(z))))) <=> r(s(z), s(elem!1))),
% 2.24/2.40 inference(symmetry,[status(thm)],[10219])).
% 2.24/2.40 tff(10221,plain,
% 2.24/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z)))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(10222,plain,
% 2.24/2.40 (((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z)))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(10223,plain,
% 2.24/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z))))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[10222])).
% 2.24/2.40 tff(10224,plain,
% 2.24/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z)))),
% 2.24/2.40 inference(transitivity,[status(thm)],[10223, 10221])).
% 2.24/2.40 tff(10225,plain,
% 2.24/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 2.24/2.40 inference(quant_inst,[status(thm)],[])).
% 2.24/2.40 tff(10226,plain,
% 2.24/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[10225, 10224])).
% 2.24/2.40 tff(10227,plain,
% 2.24/2.40 (~b(s(z), s(s(s(s(z)))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[10226, 306, 2284, 942, 859, 247])).
% 2.24/2.40 tff(10228,plain,
% 2.24/2.40 (r(s(z), s(s(s(s(z)))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[5135, 10227])).
% 2.24/2.40 tff(10229,plain,
% 2.24/2.40 (r(s(z), s(elem!1))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[10228, 10220])).
% 2.24/2.40 tff(10230,plain,
% 2.24/2.40 (~r(s(s(elem!1)), s(elem!1))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[7618, 10229, 6, 4346, 2715])).
% 2.24/2.40 tff(10231,plain,
% 2.24/2.40 (b(s(s(elem!1)), s(elem!1))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[994, 10230, 403])).
% 2.24/2.40 tff(10232,plain,
% 2.24/2.40 (~b(s(elem!1), elem!1)),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[1024, 10231, 1003, 30])).
% 2.24/2.40 tff(10233,plain,
% 2.24/2.40 (r(s(elem!1), elem!1)),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[813, 10232, 10218])).
% 2.24/2.40 tff(10234,plain,
% 2.24/2.40 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[805, 10233, 231])).
% 2.24/2.40 tff(10235,plain,
% 2.24/2.40 ($false),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[1040, 124, 1034, 10234, 10211])).
% 2.24/2.40 tff(10236,plain,((~b(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(z))))) | (~(elem!1 = s(s(s(z))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (s(s(elem!1)) = s(elem!1)) | r(s(s(elem!1)), elem!1) | (~b(elem!1, s(z))) | b(s(z), elem!1) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.40 tff(10237,plain,
% 2.24/2.40 (~b(s(s(s(s(z)))), z)),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[10236, 10062, 1034, 10083, 10070, 10088, 6, 4346, 2715, 10194, 10100, 247])).
% 2.24/2.40 tff(10238,plain,
% 2.24/2.40 (r(s(s(s(s(z)))), z)),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[695, 10237])).
% 2.24/2.40 tff(10239,plain,
% 2.24/2.40 (r(s(elem!1), z)),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[411, 10238, 10062])).
% 2.24/2.40 tff(10240,plain,
% 2.24/2.40 (~r(s(s(elem!1)), s(elem!1))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[471, 10239, 10203])).
% 2.24/2.40 tff(10241,plain,
% 2.24/2.40 (b(s(s(elem!1)), s(elem!1))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[994, 10240, 10088])).
% 2.24/2.40 tff(10242,plain,
% 2.24/2.40 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(s(s(z))))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[10062])).
% 2.24/2.40 tff(10243,plain,
% 2.24/2.40 ((s(elem!1) = s(s(s(z)))) <=> (s(elem!1) = elem!1)),
% 2.24/2.40 inference(symmetry,[status(thm)],[10242])).
% 2.24/2.40 tff(10244,plain,
% 2.24/2.40 ((s(elem!1) = s(s(s(z)))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[10089])).
% 2.24/2.40 tff(10245,plain,
% 2.24/2.40 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 2.24/2.40 inference(symmetry,[status(thm)],[10244])).
% 2.24/2.40 tff(10246,plain,
% 2.24/2.40 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(elem!1) = elem!1)),
% 2.24/2.40 inference(transitivity,[status(thm)],[10245, 10243])).
% 2.24/2.40 tff(10247,plain,
% 2.24/2.40 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(elem!1) = elem!1))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[10246])).
% 2.24/2.40 tff(10248,plain,
% 2.24/2.40 (~(s(elem!1) = elem!1)),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[4470, 10247])).
% 2.24/2.40 tff(10249,plain,
% 2.24/2.40 (~b(s(s(s(z))), z)),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[1534, 10062, 2])).
% 2.24/2.40 tff(10250,plain,
% 2.24/2.40 (r(s(s(s(z))), z)),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[2197, 10249])).
% 2.24/2.40 tff(10251,plain,
% 2.24/2.40 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[4737, 10238, 10250])).
% 2.24/2.40 tff(10252,plain,
% 2.24/2.40 (~r(s(elem!1), elem!1)),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[805, 10251, 10062])).
% 2.24/2.40 tff(10253,plain,
% 2.24/2.40 (b(s(elem!1), elem!1)),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[813, 10252, 10248])).
% 2.24/2.40 tff(10254,plain,
% 2.24/2.40 ($false),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[1024, 10253, 10241, 10083, 10070])).
% 2.24/2.40 tff(10255,plain,((~b(s(z), z)) | (~r(s(z), s(s(s(z))))) | r(s(s(elem!1)), elem!1) | (~b(elem!1, s(z))) | b(s(z), elem!1) | (~b(z, elem!1)) | b(elem!1, z) | b(elem!1, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.40 tff(10256,plain,
% 2.24/2.40 (~b(s(z), z)),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[10255, 2715, 6, 4346, 1034, 838, 2, 3])).
% 2.24/2.40 tff(10257,plain,
% 2.24/2.40 (r(s(z), z)),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[221, 10256])).
% 2.24/2.40 tff(10258,plain,
% 2.24/2.40 (~r(s(z), elem!1)),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[1049, 10257, 10057])).
% 2.24/2.40 tff(10259,plain,
% 2.24/2.40 ($false),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[1500, 43, 2715, 10258, 10055])).
% 2.24/2.40 tff(10260,plain,(b(s(z), elem!1) | r(s(s(elem!1)), elem!1) | (~b(elem!1, s(z))) | (~r(s(z), s(s(s(z))))) | (~b(z, elem!1)) | b(elem!1, z) | b(elem!1, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.40 tff(10261,plain,
% 2.24/2.40 (b(s(z), elem!1)),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[10260, 10048, 9937, 5008, 6, 2, 3])).
% 2.24/2.40 tff(10262,plain,
% 2.24/2.40 (r(elem!1, z)),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[174, 10046, 2])).
% 2.24/2.40 tff(10263,plain,
% 2.24/2.40 (b(s(s(s(z))), s(z))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[10193, 10048, 9937, 6, 10262, 5008, 3])).
% 2.24/2.40 tff(10264,plain,
% 2.24/2.40 (~b(s(z), z)),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[10111, 306, 10048, 10261, 9937])).
% 2.24/2.40 tff(10265,plain,
% 2.24/2.40 (r(s(z), z)),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[221, 10264])).
% 2.24/2.40 tff(10266,plain,
% 2.24/2.40 (~(elem!1 = s(z))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[3096, 10055])).
% 2.24/2.40 tff(10267,plain,
% 2.24/2.40 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[2974, 10266])).
% 2.24/2.40 tff(10268,plain,
% 2.24/2.40 (~(elem!1 = s(s(s(z))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[10068, 1171, 10267])).
% 2.24/2.40 tff(10269,plain,
% 2.24/2.40 (r(elem!1, s(s(s(z))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[2304, 10268, 3])).
% 2.24/2.40 tff(10270,plain,
% 2.24/2.40 (~r(z, s(s(s(z))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[3392, 10269, 246])).
% 2.24/2.40 tff(10271,plain,
% 2.24/2.40 (b(z, s(s(s(z))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[2415, 43, 10270, 2405])).
% 2.24/2.40 tff(10272,plain,
% 2.24/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(10273,plain,
% 2.24/2.40 (((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(10274,plain,
% 2.24/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z)))))))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[10273])).
% 2.24/2.40 tff(10275,plain,
% 2.24/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))))),
% 2.24/2.41 inference(transitivity,[status(thm)],[10274, 10272])).
% 2.24/2.41 tff(10276,plain,
% 2.24/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 2.24/2.41 inference(quant_inst,[status(thm)],[])).
% 2.24/2.41 tff(10277,plain,
% 2.24/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z)))))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[10276, 10275])).
% 2.24/2.41 tff(10278,plain,
% 2.24/2.41 (~b(s(s(s(s(z)))), z)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[10277, 306, 2284, 2831, 859, 762])).
% 2.24/2.41 tff(10279,plain,
% 2.24/2.41 (r(s(s(s(s(z)))), z)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[695, 10278])).
% 2.24/2.41 tff(10280,plain,
% 2.24/2.41 (~r(s(s(s(s(z)))), s(z))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[10160, 10279, 204])).
% 2.24/2.41 tff(10281,plain,
% 2.24/2.41 (b(s(s(s(s(z)))), s(z))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[4490, 10280])).
% 2.24/2.41 tff(10282,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(10283,plain,
% 2.24/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), 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))))))),
% 2.24/2.41 inference(quant_inst,[status(thm)],[])).
% 2.24/2.41 tff(10284,plain,
% 2.24/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[10283, 10282])).
% 2.24/2.41 tff(10285,plain,
% 2.24/2.41 ($false),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[10284, 306, 2284, 2831, 4346, 762, 10281])).
% 2.24/2.41 tff(10286,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~r(s(z), z)) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.41 tff(10287,plain,
% 2.24/2.41 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[10286, 10271, 2831, 4346, 204, 2284])).
% 2.24/2.41 tff(10288,plain,
% 2.24/2.41 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[10146, 10287])).
% 2.24/2.41 tff(10289,plain,
% 2.24/2.41 (~r(s(s(s(s(z)))), s(z))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[1040, 124, 1034, 10288])).
% 2.24/2.41 tff(10290,plain,
% 2.24/2.41 (b(s(s(s(s(z)))), s(z))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[4490, 10289])).
% 2.24/2.41 tff(10291,plain,
% 2.24/2.41 (~(s(s(s(s(z)))) = elem!1)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[9813, 1171])).
% 2.24/2.41 tff(10292,plain,
% 2.24/2.41 (~r(s(s(s(s(z)))), elem!1)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[10153, 124, 10269, 10288])).
% 2.24/2.41 tff(10293,plain,
% 2.24/2.41 (b(s(s(s(s(z)))), elem!1)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[9832, 10292, 10291])).
% 2.24/2.41 tff(10294,plain,
% 2.24/2.41 ($false),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[10136, 306, 2831, 4346, 10293, 10290])).
% 2.24/2.41 tff(10295,plain,((~(s(s(elem!1)) = elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~r(elem!1, z)) | b(elem!1, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.41 tff(10296,plain,
% 2.24/2.41 (~(s(s(elem!1)) = elem!1)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[10295, 10261, 9937, 5008, 10265, 10263, 10262, 3])).
% 2.24/2.41 tff(10297,plain,
% 2.24/2.41 (b(s(s(elem!1)), elem!1)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[47, 10296, 6])).
% 2.24/2.41 tff(10298,plain,
% 2.24/2.41 (~b(s(s(elem!1)), s(z))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[4380, 10297, 9937, 10261])).
% 2.24/2.41 tff(10299,plain,
% 2.24/2.41 (r(s(s(elem!1)), s(z))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[3989, 10298])).
% 2.24/2.41 tff(10300,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(10301,plain,
% 2.24/2.41 (((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z)))) <=> ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(10302,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z)))))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[10301])).
% 2.24/2.41 tff(10303,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))))),
% 2.24/2.41 inference(transitivity,[status(thm)],[10302, 10300])).
% 2.24/2.41 tff(10304,plain,
% 2.24/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))),
% 2.24/2.41 inference(quant_inst,[status(thm)],[])).
% 2.24/2.41 tff(10305,plain,
% 2.24/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z)))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[10304, 10303])).
% 2.24/2.41 tff(10306,plain,
% 2.24/2.41 (~b(z, s(z))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[10305, 306, 10048, 10261, 9937])).
% 2.24/2.41 tff(10307,plain,
% 2.24/2.41 (r(z, s(z))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[2263, 10306])).
% 2.24/2.41 tff(10308,plain,
% 2.24/2.41 (~b(s(s(elem!1)), z)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[10180, 306, 10048, 10297, 10261, 9937])).
% 2.24/2.41 tff(10309,plain,
% 2.24/2.41 (r(s(s(elem!1)), z)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[476, 10308])).
% 2.24/2.41 tff(10310,plain,
% 2.24/2.41 ($false),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[4657, 124, 10309, 10307, 10299])).
% 2.24/2.41 tff(10311,plain,(b(elem!1, s(s(s(z)))) | r(s(s(elem!1)), elem!1) | b(elem!1, z) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.24/2.41 tff(10312,plain,
% 2.24/2.41 (b(elem!1, s(s(s(z))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[10311, 7, 2, 6])).
% 2.24/2.41 tff(10313,plain,
% 2.24/2.41 (~(s(s(s(z))) = elem!1)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[1472, 10312])).
% 2.24/2.41 tff(10314,plain,
% 2.24/2.41 (~(s(z) = elem!1)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[10054, 9937])).
% 2.24/2.41 tff(10315,plain,
% 2.24/2.41 (r(s(z), elem!1)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[1500, 43, 2715, 10314])).
% 2.24/2.41 tff(10316,plain,
% 2.24/2.41 (~r(s(s(s(z))), elem!1)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[3790, 10315, 5008])).
% 2.24/2.41 tff(10317,plain,
% 2.24/2.41 (b(s(s(s(z))), elem!1)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[1489, 10316, 10313])).
% 2.24/2.41 tff(10318,plain,
% 2.24/2.41 (~(elem!1 = s(z))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[3096, 10314])).
% 2.24/2.41 tff(10319,plain,
% 2.24/2.41 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[2974, 10318])).
% 2.24/2.41 tff(10320,plain,
% 2.24/2.41 (r(s(s(z)), s(z)) <=> r(s(s(elem!1)), s(z))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[1780])).
% 2.24/2.41 tff(10321,plain,
% 2.24/2.41 (r(s(s(elem!1)), s(z)) <=> r(s(s(z)), s(z))),
% 2.24/2.41 inference(symmetry,[status(thm)],[10320])).
% 2.24/2.41 tff(10322,plain,
% 2.24/2.41 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(elem!1)), s(z))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[1621])).
% 2.24/2.41 tff(10323,plain,
% 2.24/2.41 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(z)), s(z))),
% 2.24/2.41 inference(transitivity,[status(thm)],[10322, 10321])).
% 2.24/2.41 tff(10324,plain,
% 2.24/2.41 (b(elem!1, s(s(s(elem!1)))) <=> b(z, s(s(s(elem!1))))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[1620])).
% 2.24/2.41 tff(10325,plain,
% 2.24/2.41 (b(z, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 2.24/2.41 inference(symmetry,[status(thm)],[10324])).
% 2.24/2.41 tff(10326,plain,
% 2.24/2.41 (b(z, s(s(s(z)))) <=> b(elem!1, s(s(s(elem!1))))),
% 2.24/2.41 inference(transitivity,[status(thm)],[9966, 10325])).
% 2.24/2.41 tff(10327,plain,
% 2.24/2.41 (b(z, s(s(s(z))))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[1470, 9968])).
% 2.24/2.41 tff(10328,plain,
% 2.24/2.41 (b(elem!1, s(s(s(elem!1))))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[10327, 10326])).
% 2.24/2.41 tff(10329,plain,
% 2.24/2.41 (~b(s(elem!1), z)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[2718, 3332, 2715])).
% 2.24/2.41 tff(10330,plain,
% 2.24/2.41 (~b(s(elem!1), elem!1)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[2709, 10329, 3332])).
% 2.24/2.41 tff(10331,plain,
% 2.24/2.41 (r(s(elem!1), elem!1)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[813, 10330, 3333])).
% 2.24/2.41 tff(10332,plain,
% 2.24/2.41 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(z))), s(z))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[1623, 1621])).
% 2.24/2.41 tff(10333,plain,
% 2.24/2.41 (b(s(s(s(z))), s(z)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 2.24/2.41 inference(symmetry,[status(thm)],[10332])).
% 2.24/2.41 tff(10334,plain,
% 2.24/2.41 (b(s(s(s(z))), elem!1)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[1489, 1484, 4198])).
% 2.24/2.41 tff(10335,plain,
% 2.24/2.41 (~b(z, elem!1)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[3002, 4362, 1470, 2976, 10334])).
% 2.24/2.41 tff(10336,plain,
% 2.24/2.41 (b(s(s(s(z))), s(z))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[9791, 10335, 2, 1034, 1484])).
% 2.24/2.41 tff(10337,plain,
% 2.24/2.41 (b(s(s(s(elem!1))), s(elem!1))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[10336, 10333])).
% 2.24/2.41 tff(10338,plain,
% 2.24/2.41 (~b(s(s(elem!1)), s(elem!1))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[3280, 10337, 3332, 10331, 4362, 10328, 4353, 3334])).
% 2.24/2.41 tff(10339,plain,
% 2.24/2.41 (r(s(s(elem!1)), s(elem!1))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[994, 10338, 3334])).
% 2.24/2.41 tff(10340,plain,
% 2.24/2.41 (r(s(s(z)), s(z))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[10339, 10323])).
% 2.24/2.41 tff(10341,plain,
% 2.24/2.41 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), z)),
% 2.24/2.41 inference(monotonicity,[status(thm)],[1620])).
% 2.24/2.41 tff(10342,plain,
% 2.24/2.41 (b(s(s(s(z))), z)),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[10334, 10341])).
% 2.24/2.41 tff(10343,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(10344,plain,
% 2.24/2.41 (((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(10345,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[10344])).
% 2.24/2.41 tff(10346,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.24/2.41 inference(transitivity,[status(thm)],[10345, 10343])).
% 2.24/2.41 tff(10347,plain,
% 2.24/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 2.24/2.41 inference(quant_inst,[status(thm)],[])).
% 2.24/2.41 tff(10348,plain,
% 2.24/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[10347, 10346])).
% 2.24/2.41 tff(10349,plain,
% 2.24/2.41 (~b(s(s(z)), s(s(s(z))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[10348, 306, 10336, 4536, 10342, 10327])).
% 2.24/2.41 tff(10350,plain,
% 2.24/2.41 (r(s(s(z)), s(s(s(z))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[2514, 10349])).
% 2.24/2.41 tff(10351,plain,
% 2.24/2.41 (~r(s(s(z)), s(z))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[3833, 10350, 1034])).
% 2.24/2.41 tff(10352,plain,
% 2.24/2.41 ($false),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[10351, 10340])).
% 2.24/2.41 tff(10353,plain,((~(elem!1 = z)) | (~r(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | b(elem!1, z) | r(s(s(s(z))), elem!1) | (s(s(s(z))) = s(s(elem!1))) | r(s(s(elem!1)), elem!1) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.24/2.41 tff(10354,plain,
% 2.24/2.41 (~(elem!1 = z)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[10353, 10316, 10312, 2, 5008, 10319, 6, 2715])).
% 2.24/2.41 tff(10355,plain,
% 2.24/2.41 (~(z = elem!1)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[1618, 10354])).
% 2.24/2.41 tff(10356,plain,
% 2.24/2.41 (b(z, elem!1)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[835, 10355, 7])).
% 2.24/2.41 tff(10357,plain,
% 2.24/2.41 (~b(z, s(s(s(z))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[2411, 306, 10356, 10317, 10312])).
% 2.24/2.41 tff(10358,plain,
% 2.24/2.41 (r(z, s(s(s(z))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[2415, 43, 10357, 2405])).
% 2.24/2.41 tff(10359,plain,
% 2.24/2.41 (~r(z, s(z))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[9581, 124, 5008, 10358])).
% 2.24/2.41 tff(10360,plain,
% 2.24/2.41 (b(z, s(z))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[2263, 10359])).
% 2.24/2.41 tff(10361,plain,
% 2.24/2.41 (r(elem!1, z)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[174, 10354, 2])).
% 2.24/2.41 tff(10362,plain,
% 2.24/2.41 (~r(s(z), z)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[1049, 10361, 10315])).
% 2.24/2.41 tff(10363,plain,
% 2.24/2.41 (b(s(z), z)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[221, 10362])).
% 2.24/2.41 tff(10364,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), z)))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(10365,plain,
% 2.24/2.41 (((~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1))) <=> ((~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), z)))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(10366,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), z))))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[10365])).
% 2.24/2.41 tff(10367,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), z)))),
% 2.24/2.41 inference(transitivity,[status(thm)],[10366, 10364])).
% 2.24/2.41 tff(10368,plain,
% 2.24/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))),
% 2.24/2.41 inference(quant_inst,[status(thm)],[])).
% 2.24/2.41 tff(10369,plain,
% 2.24/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), z))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[10368, 10367])).
% 2.24/2.41 tff(10370,plain,
% 2.24/2.41 ($false),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[10369, 306, 10356, 9937, 10363, 10360])).
% 2.24/2.41 tff(10371,plain,(b(s(z), elem!1) | r(z, elem!1) | b(elem!1, z) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.24/2.41 tff(10372,plain,
% 2.24/2.41 (b(s(z), elem!1)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[10371, 7, 2, 6])).
% 2.24/2.41 tff(10373,plain,
% 2.24/2.41 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(z)))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[1623, 1622])).
% 2.24/2.41 tff(10374,plain,
% 2.24/2.41 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[159, 4354])).
% 2.24/2.41 tff(10375,plain,
% 2.24/2.41 (r(s(s(elem!1)), s(z)) <=> r(s(s(elem!1)), s(elem!1))),
% 2.24/2.41 inference(symmetry,[status(thm)],[10322])).
% 2.24/2.41 tff(10376,plain,
% 2.24/2.41 (~b(s(s(elem!1)), s(z))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[4380, 4362, 4346, 2831])).
% 2.24/2.41 tff(10377,plain,
% 2.24/2.41 (r(s(s(elem!1)), s(z))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[3989, 10376])).
% 2.24/2.41 tff(10378,plain,
% 2.24/2.41 (r(s(s(elem!1)), s(elem!1))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[10377, 10375])).
% 2.24/2.41 tff(10379,plain,
% 2.24/2.41 (b(s(elem!1), elem!1) <=> b(s(elem!1), z)),
% 2.24/2.41 inference(monotonicity,[status(thm)],[1620])).
% 2.24/2.41 tff(10380,plain,
% 2.24/2.41 (b(s(elem!1), z) <=> b(s(elem!1), elem!1)),
% 2.24/2.41 inference(symmetry,[status(thm)],[10379])).
% 2.24/2.41 tff(10381,plain,
% 2.24/2.41 (b(s(elem!1), z) <=> b(s(z), z)),
% 2.24/2.41 inference(monotonicity,[status(thm)],[1621])).
% 2.24/2.41 tff(10382,plain,
% 2.24/2.41 (b(s(z), z) <=> b(s(elem!1), z)),
% 2.24/2.41 inference(symmetry,[status(thm)],[10381])).
% 2.24/2.41 tff(10383,plain,
% 2.24/2.41 (b(s(z), z) <=> b(s(elem!1), elem!1)),
% 2.24/2.41 inference(transitivity,[status(thm)],[10382, 10380])).
% 2.24/2.41 tff(10384,plain,
% 2.24/2.41 (b(s(z), elem!1) <=> b(s(z), z)),
% 2.24/2.41 inference(monotonicity,[status(thm)],[1620])).
% 2.24/2.41 tff(10385,plain,
% 2.24/2.41 (b(s(z), z)),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[2831, 10384])).
% 2.24/2.41 tff(10386,plain,
% 2.24/2.41 (b(s(elem!1), elem!1)),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[10385, 10383])).
% 2.24/2.41 tff(10387,plain,
% 2.24/2.41 (b(z, s(s(s(elem!1))))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[10327, 9966])).
% 2.24/2.41 tff(10388,plain,
% 2.24/2.41 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[826, 10387, 4413, 10386, 4414])).
% 2.24/2.41 tff(10389,plain,
% 2.24/2.41 (r(s(s(s(elem!1))), s(elem!1))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[664, 10388, 4353])).
% 2.24/2.41 tff(10390,plain,
% 2.24/2.41 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[659, 10389, 10378])).
% 2.24/2.41 tff(10391,plain,
% 2.24/2.41 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[610, 10390, 10374])).
% 2.24/2.41 tff(10392,plain,
% 2.24/2.41 (b(s(s(s(z))), s(s(z)))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[10391, 10373])).
% 2.24/2.41 tff(10393,plain,
% 2.24/2.41 (r(s(s(z)), s(z))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[10377, 10321])).
% 2.24/2.41 tff(10394,plain,
% 2.24/2.41 (~r(s(s(z)), s(s(s(z))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[3833, 10393, 1034])).
% 2.24/2.41 tff(10395,plain,
% 2.24/2.41 (b(s(s(z)), s(s(s(z))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[2514, 10394])).
% 2.24/2.41 tff(10396,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(10397,plain,
% 2.24/2.41 (((~b(s(s(z)), z)) | (~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(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(10398,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[10397])).
% 2.24/2.41 tff(10399,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.24/2.41 inference(transitivity,[status(thm)],[10398, 10396])).
% 2.24/2.41 tff(10400,plain,
% 2.24/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))),
% 2.24/2.41 inference(quant_inst,[status(thm)],[])).
% 2.24/2.41 tff(10401,plain,
% 2.24/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[10400, 10399])).
% 2.24/2.41 tff(10402,plain,
% 2.24/2.41 ($false),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[10401, 306, 4536, 10327, 10395, 10392])).
% 2.24/2.41 tff(10403,plain,((~(elem!1 = z)) | (~r(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.24/2.41 tff(10404,plain,
% 2.24/2.41 (~(elem!1 = z)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[10403, 5008, 10312, 10372, 9937, 6])).
% 2.24/2.41 tff(10405,plain,
% 2.24/2.41 (~(z = elem!1)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[1618, 10404])).
% 2.24/2.41 tff(10406,plain,
% 2.24/2.41 (b(z, elem!1)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[835, 10405, 7])).
% 2.24/2.41 tff(10407,plain,
% 2.24/2.41 (~b(s(z), z)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[10111, 306, 10406, 10372, 9937])).
% 2.24/2.41 tff(10408,plain,
% 2.24/2.41 (r(s(z), z)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[221, 10407])).
% 2.24/2.41 tff(10409,plain,
% 2.24/2.41 (~b(z, s(z))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[10305, 306, 10406, 10372, 9937])).
% 2.24/2.41 tff(10410,plain,
% 2.24/2.41 (r(z, s(z))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[2263, 10409])).
% 2.24/2.41 tff(10411,plain,
% 2.24/2.41 (~r(z, s(s(s(z))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[5572, 124, 206, 2265])).
% 2.24/2.42 tff(10412,plain,
% 2.24/2.42 (b(z, s(s(s(z))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[2415, 43, 10411, 2405])).
% 2.24/2.42 tff(10413,plain,
% 2.24/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(10414,plain,
% 2.24/2.42 (((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, elem!1))) <=> ((~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(10415,plain,
% 2.24/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z)))))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[10414])).
% 2.24/2.42 tff(10416,plain,
% 2.24/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 2.24/2.42 inference(transitivity,[status(thm)],[10415, 10413])).
% 2.24/2.42 tff(10417,plain,
% 2.24/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, elem!1)))),
% 2.24/2.42 inference(quant_inst,[status(thm)],[])).
% 2.24/2.42 tff(10418,plain,
% 2.24/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z)))))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[10417, 10416])).
% 2.24/2.42 tff(10419,plain,
% 2.24/2.42 ($false),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[10418, 306, 838, 7717, 10412, 1470])).
% 2.24/2.42 tff(10420,plain,((~r(s(s(s(z))), s(z))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~r(z, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.42 tff(10421,plain,
% 2.24/2.42 (~r(s(s(s(z))), s(z))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[10420, 10406, 10312, 10410, 10408])).
% 2.24/2.42 tff(10422,plain,
% 2.24/2.42 (b(s(s(s(z))), s(z))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[113, 10421])).
% 2.24/2.42 tff(10423,plain,
% 2.24/2.42 ($false),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[7747, 306, 10422, 10372, 9937, 10312])).
% 2.24/2.42 tff(10424,plain,(r(z, elem!1) | r(s(s(elem!1)), elem!1) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 2.24/2.42 tff(10425,plain,
% 2.24/2.42 (r(z, elem!1)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[10424, 6, 2])).
% 2.24/2.42 tff(10426,plain,
% 2.24/2.42 (~r(s(z), s(s(s(z))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[5308, 3, 5, 2, 6])).
% 2.24/2.42 tff(10427,plain,
% 2.24/2.42 (b(s(z), s(s(s(z))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[3302, 10426])).
% 2.24/2.42 tff(10428,plain,
% 2.24/2.42 ((~b(elem!1, s(s(s(z))))) <=> (~b(s(z), s(s(s(z)))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[9884])).
% 2.24/2.42 tff(10429,plain,
% 2.24/2.42 (~b(s(z), s(s(s(z))))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[3, 10428])).
% 2.24/2.42 tff(10430,plain,
% 2.24/2.42 ($false),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[8, 10429])).
% 2.24/2.42 tff(10431,plain,((~(s(z) = elem!1)) | (~b(s(z), s(s(s(z))))) | b(elem!1, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.42 tff(10432,plain,
% 2.24/2.42 (~(s(z) = elem!1)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[10431, 10427, 3])).
% 2.24/2.42 tff(10433,plain,
% 2.24/2.42 (~(elem!1 = s(z))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[3096, 10432])).
% 2.24/2.42 tff(10434,plain,
% 2.24/2.42 (r(elem!1, s(z))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[97, 10433])).
% 2.24/2.42 tff(10435,plain,
% 2.24/2.42 (~r(z, s(z))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[385, 10434, 10425])).
% 2.24/2.42 tff(10436,plain,
% 2.24/2.42 (b(z, s(z))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[2263, 10435])).
% 2.24/2.42 tff(10437,plain,
% 2.24/2.42 (r(z, elem!1) <=> r(z, z)),
% 2.24/2.42 inference(monotonicity,[status(thm)],[1620])).
% 2.24/2.42 tff(10438,plain,
% 2.24/2.42 (r(z, z) <=> r(z, elem!1)),
% 2.24/2.42 inference(symmetry,[status(thm)],[10437])).
% 2.24/2.42 tff(10439,plain,
% 2.24/2.42 ((~r(z, z)) <=> (~r(z, elem!1))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[10438])).
% 2.24/2.42 tff(10440,plain,
% 2.24/2.42 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, z)) | (~r(z, elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, z)) | (~r(z, elem!1)))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(10441,plain,
% 2.24/2.42 (((~r(z, elem!1)) | (~r(z, elem!1)) | (~r(z, z))) <=> ((~r(z, z)) | (~r(z, elem!1)))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(10442,plain,
% 2.24/2.42 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, elem!1)) | (~r(z, z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, z)) | (~r(z, elem!1))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[10441])).
% 2.24/2.42 tff(10443,plain,
% 2.24/2.42 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, elem!1)) | (~r(z, z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, z)) | (~r(z, elem!1)))),
% 2.24/2.42 inference(transitivity,[status(thm)],[10442, 10440])).
% 2.24/2.42 tff(10444,plain,
% 2.24/2.42 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, elem!1)) | (~r(z, z)))),
% 2.24/2.42 inference(quant_inst,[status(thm)],[])).
% 2.24/2.42 tff(10445,plain,
% 2.24/2.42 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, z)) | (~r(z, elem!1))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[10444, 10443])).
% 2.24/2.42 tff(10446,plain,
% 2.24/2.42 (~r(z, z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[10445, 124, 374])).
% 2.24/2.42 tff(10447,plain,
% 2.24/2.42 (~r(z, elem!1)),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[10446, 10439])).
% 2.24/2.42 tff(10448,plain,
% 2.24/2.42 ($false),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[374, 10447])).
% 2.24/2.42 tff(10449,plain,((~(elem!1 = z)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.42 tff(10450,plain,
% 2.24/2.42 (~(elem!1 = z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[10449, 10425])).
% 2.24/2.42 tff(10451,plain,
% 2.24/2.42 (r(elem!1, z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[174, 10450, 2])).
% 2.24/2.42 tff(10452,plain,
% 2.24/2.42 (~r(z, s(s(s(z))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[3392, 5018, 10451])).
% 2.24/2.42 tff(10453,plain,
% 2.24/2.42 (b(z, s(s(s(z))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[2415, 43, 10452, 2405])).
% 2.24/2.42 tff(10454,plain,
% 2.24/2.42 (((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(10455,plain,
% 2.24/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z)))))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[10454])).
% 2.24/2.42 tff(10456,plain,
% 2.24/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))),
% 2.24/2.42 inference(transitivity,[status(thm)],[10455, 2293])).
% 2.24/2.42 tff(10457,plain,
% 2.24/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))))),
% 2.24/2.42 inference(quant_inst,[status(thm)],[])).
% 2.24/2.42 tff(10458,plain,
% 2.24/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z)))))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[10457, 10456])).
% 2.24/2.42 tff(10459,plain,
% 2.24/2.42 ($false),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[10458, 306, 2283, 10427, 10453, 10436])).
% 2.24/2.42 tff(10460,plain,(b(elem!1, s(s(s(z)))) | b(elem!1, s(z)) | r(s(s(elem!1)), elem!1) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 2.24/2.42 tff(10461,plain,
% 2.24/2.42 (r(s(s(elem!1)), elem!1)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[10460, 2, 5, 3])).
% 2.24/2.42 tff(10462,plain,
% 2.24/2.42 (r(elem!1, s(s(s(z)))) <=> r(z, s(s(s(z))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[3063])).
% 2.24/2.42 tff(10463,plain,
% 2.24/2.42 (~b(s(elem!1), z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[2718, 3064, 2715])).
% 2.24/2.42 tff(10464,plain,
% 2.24/2.42 (~b(s(elem!1), elem!1)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[2709, 10463, 3064])).
% 2.24/2.42 tff(10465,plain,
% 2.24/2.42 (b(s(z), z) <=> b(s(z), elem!1)),
% 2.24/2.42 inference(monotonicity,[status(thm)],[1502])).
% 2.24/2.42 tff(10466,plain,
% 2.24/2.42 (b(s(z), elem!1) <=> b(s(z), z)),
% 2.24/2.42 inference(symmetry,[status(thm)],[10465])).
% 2.24/2.42 tff(10467,plain,
% 2.24/2.42 (b(s(elem!1), elem!1) <=> b(s(z), elem!1)),
% 2.24/2.42 inference(symmetry,[status(thm)],[2712])).
% 2.24/2.42 tff(10468,plain,
% 2.24/2.42 (b(s(elem!1), elem!1) <=> b(s(z), z)),
% 2.24/2.42 inference(transitivity,[status(thm)],[10467, 10466])).
% 2.24/2.42 tff(10469,plain,
% 2.24/2.42 ((~b(s(elem!1), elem!1)) <=> (~b(s(z), z))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[10468])).
% 2.24/2.42 tff(10470,plain,
% 2.24/2.42 (~b(s(z), z)),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[807, 10469])).
% 2.24/2.42 tff(10471,plain,
% 2.24/2.42 ($false),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[247, 10470])).
% 2.24/2.42 tff(10472,plain,(b(s(elem!1), elem!1) | (~b(s(z), z)) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.42 tff(10473,plain,
% 2.24/2.42 (~b(s(z), z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[10472, 10464, 3064])).
% 2.24/2.42 tff(10474,plain,
% 2.24/2.42 (r(s(z), z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[221, 10473])).
% 2.24/2.42 tff(10475,plain,
% 2.24/2.42 (~(s(z) = elem!1)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[3089, 10474, 3062])).
% 2.24/2.42 tff(10476,plain,
% 2.24/2.42 (~(elem!1 = s(z))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[3096, 10475])).
% 2.24/2.42 tff(10477,plain,
% 2.24/2.42 (r(elem!1, s(z))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[97, 10476])).
% 2.24/2.42 tff(10478,plain,
% 2.24/2.42 (r(s(z), elem!1)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[4192, 10475])).
% 2.24/2.42 tff(10479,plain,
% 2.24/2.42 (~r(s(s(s(z))), s(z))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[2189, 10478, 2, 3064, 10477])).
% 2.24/2.42 tff(10480,plain,
% 2.24/2.42 (b(s(s(s(z))), s(z))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[113, 10479])).
% 2.24/2.42 tff(10481,plain,
% 2.24/2.42 (~(elem!1 = s(s(s(z))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[5016, 10480, 5])).
% 2.24/2.42 tff(10482,plain,
% 2.24/2.42 (r(elem!1, s(s(s(z))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[2304, 10481, 3])).
% 2.24/2.42 tff(10483,plain,
% 2.24/2.42 (r(z, s(s(s(z))))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[10482, 10462])).
% 2.24/2.42 tff(10484,plain,
% 2.24/2.42 (r(s(s(elem!1)), z) <=> r(s(s(z)), z)),
% 2.24/2.42 inference(monotonicity,[status(thm)],[5311])).
% 2.24/2.42 tff(10485,plain,
% 2.24/2.42 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), z)),
% 2.24/2.42 inference(monotonicity,[status(thm)],[3063])).
% 2.24/2.42 tff(10486,plain,
% 2.24/2.42 (r(s(s(elem!1)), z)),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[10461, 10485])).
% 2.24/2.42 tff(10487,plain,
% 2.24/2.42 (r(s(s(z)), z)),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[10486, 10484])).
% 2.24/2.42 tff(10488,plain,
% 2.24/2.42 (~r(s(s(z)), s(s(s(z))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[2523, 10487, 10483])).
% 2.24/2.42 tff(10489,plain,
% 2.24/2.42 (b(s(s(z)), s(s(s(z))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[2514, 10488])).
% 2.24/2.42 tff(10490,plain,
% 2.24/2.42 (~r(s(z), s(s(z)))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[8168, 124, 10474, 10487])).
% 2.24/2.42 tff(10491,plain,
% 2.24/2.42 (b(s(z), s(s(z)))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[4434, 10490])).
% 2.24/2.42 tff(10492,plain,
% 2.24/2.42 (~r(s(z), s(s(s(z))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[3293, 10482, 10477])).
% 2.24/2.42 tff(10493,plain,
% 2.24/2.42 (b(s(z), s(s(s(z))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[3302, 10492])).
% 2.24/2.42 tff(10494,plain,
% 2.24/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(10495,plain,
% 2.24/2.42 (((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(10496,plain,
% 2.24/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(z)), s(s(s(z))))) | (~b(s(z), s(s(z))))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[10495])).
% 2.24/2.42 tff(10497,plain,
% 2.24/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 2.24/2.42 inference(transitivity,[status(thm)],[10496, 10494])).
% 2.24/2.42 tff(10498,plain,
% 2.24/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 2.24/2.42 inference(quant_inst,[status(thm)],[])).
% 2.24/2.42 tff(10499,plain,
% 2.24/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z))))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[10498, 10497])).
% 2.24/2.42 tff(10500,plain,
% 2.24/2.42 ($false),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[10499, 306, 10480, 10493, 10491, 10489])).
% 2.24/2.42 tff(10501,plain,(r(elem!1, z) | b(elem!1, s(s(s(z)))) | b(elem!1, s(z)) | b(elem!1, z) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.24/2.42 tff(10502,plain,
% 2.24/2.42 (r(elem!1, z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[10501, 2715, 5, 2, 3])).
% 2.24/2.42 tff(10503,plain,
% 2.24/2.42 (~(s(elem!1) = elem!1)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[2654, 204, 246, 5])).
% 2.24/2.42 tff(10504,plain,
% 2.24/2.42 (~(elem!1 = s(elem!1))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[364, 10503])).
% 2.24/2.42 tff(10505,plain,
% 2.24/2.42 (s(z) = elem!1),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[4192, 2237])).
% 2.24/2.42 tff(10506,plain,
% 2.24/2.42 (s(s(z)) = s(elem!1)),
% 2.24/2.42 inference(monotonicity,[status(thm)],[10505])).
% 2.24/2.42 tff(10507,plain,
% 2.24/2.42 (s(s(s(z))) = s(s(elem!1))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[10506])).
% 2.24/2.42 tff(10508,plain,
% 2.24/2.42 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(s(elem!1)))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[10507])).
% 2.24/2.42 tff(10509,plain,
% 2.24/2.42 (r(s(z), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[10505])).
% 2.24/2.42 tff(10510,plain,
% 2.24/2.42 (~b(s(z), s(s(s(z))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[10431, 10505, 3])).
% 2.24/2.42 tff(10511,plain,
% 2.24/2.42 (r(s(z), s(s(s(z))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[3302, 10510])).
% 2.24/2.42 tff(10512,plain,
% 2.24/2.42 (r(elem!1, s(s(s(z))))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[10511, 10509])).
% 2.24/2.42 tff(10513,plain,
% 2.24/2.42 (r(elem!1, s(s(elem!1)))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[10512, 10508])).
% 2.24/2.42 tff(10514,plain,
% 2.24/2.42 (~(s(s(elem!1)) = s(elem!1))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[195, 10503])).
% 2.24/2.42 tff(10515,plain,
% 2.24/2.42 (~r(z, s(s(elem!1)))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[978, 10513, 246])).
% 2.24/2.42 tff(10516,plain,
% 2.24/2.42 (b(z, s(s(elem!1)))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[460, 10515])).
% 2.24/2.42 tff(10517,plain,
% 2.24/2.42 (~r(elem!1, s(elem!1))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[5054, 10516, 246, 10514, 10513])).
% 2.24/2.42 tff(10518,plain,
% 2.24/2.42 (b(elem!1, s(elem!1))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[372, 10517, 10504])).
% 2.24/2.42 tff(10519,plain,
% 2.24/2.42 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[10507])).
% 2.24/2.42 tff(10520,plain,
% 2.24/2.42 ((s(s(z)) = s(s(s(s(z))))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[10506, 10519])).
% 2.24/2.42 tff(10521,plain,
% 2.24/2.42 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 2.24/2.42 inference(transitivity,[status(thm)],[10520, 1573])).
% 2.24/2.42 tff(10522,plain,
% 2.24/2.42 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[10521])).
% 2.24/2.42 tff(10523,plain,
% 2.24/2.42 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[1612, 10522])).
% 2.24/2.42 tff(10524,plain,
% 2.24/2.42 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[1284, 10523])).
% 2.24/2.42 tff(10525,plain,
% 2.24/2.42 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[10519])).
% 2.24/2.42 tff(10526,plain,
% 2.24/2.42 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[10525, 10506])).
% 2.24/2.42 tff(10527,plain,
% 2.24/2.42 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(s(s(elem!1)))) = s(elem!1)))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[10526])).
% 2.24/2.42 tff(10528,plain,
% 2.24/2.42 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[6464, 10527])).
% 2.24/2.42 tff(10529,plain,
% 2.24/2.42 (elem!1 = s(z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[89, 10505])).
% 2.24/2.42 tff(10530,plain,
% 2.24/2.42 (~(s(s(s(s(elem!1)))) = elem!1)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[6321, 10529])).
% 2.24/2.42 tff(10531,plain,
% 2.24/2.42 (~(z = elem!1)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[9879, 246])).
% 2.24/2.42 tff(10532,plain,
% 2.24/2.42 (s(s(s(s(s(s(z)))))) = s(s(s(s(s(elem!1)))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[8871])).
% 2.24/2.42 tff(10533,plain,
% 2.24/2.42 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(s(z))))))),
% 2.24/2.42 inference(symmetry,[status(thm)],[10532])).
% 2.24/2.42 tff(10534,plain,
% 2.24/2.42 ((s(s(s(s(s(elem!1))))) = elem!1) <=> (s(s(s(s(s(s(z)))))) = elem!1)),
% 2.24/2.42 inference(monotonicity,[status(thm)],[10533])).
% 2.24/2.42 tff(10535,plain,
% 2.24/2.42 ((s(s(s(s(s(s(z)))))) = elem!1) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 2.24/2.42 inference(symmetry,[status(thm)],[10534])).
% 2.24/2.42 tff(10536,plain,
% 2.24/2.42 ((~(s(s(s(s(s(s(z)))))) = elem!1)) <=> (~(s(s(s(s(s(elem!1))))) = elem!1))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[10535])).
% 2.24/2.42 tff(10537,plain,
% 2.24/2.42 (elem!1 = s(z)),
% 2.24/2.42 inference(symmetry,[status(thm)],[85])).
% 2.24/2.42 tff(10538,plain,
% 2.24/2.42 ((s(s(s(s(s(s(z)))))) = elem!1) <=> (s(s(s(s(s(s(z)))))) = s(z))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[10537])).
% 2.24/2.42 tff(10539,plain,
% 2.24/2.42 ((s(s(s(s(s(s(z)))))) = s(z)) <=> (s(s(s(s(s(s(z)))))) = elem!1)),
% 2.24/2.42 inference(symmetry,[status(thm)],[10538])).
% 2.24/2.42 tff(10540,plain,
% 2.24/2.42 ((~(s(s(s(s(s(s(z)))))) = s(z))) <=> (~(s(s(s(s(s(s(z)))))) = elem!1))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[10539])).
% 2.24/2.42 tff(10541,plain,
% 2.24/2.42 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[2844, 10540])).
% 2.24/2.42 tff(10542,plain,
% 2.24/2.42 (~(s(s(s(s(s(elem!1))))) = elem!1)),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[10541, 10536])).
% 2.24/2.42 tff(10543,plain,
% 2.24/2.42 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[10533])).
% 2.24/2.42 tff(10544,plain,
% 2.24/2.42 (b(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.24/2.42 inference(symmetry,[status(thm)],[10543])).
% 2.24/2.42 tff(10545,plain,
% 2.24/2.42 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[8851])).
% 2.24/2.42 tff(10546,plain,
% 2.24/2.42 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 2.24/2.42 inference(symmetry,[status(thm)],[8851])).
% 2.24/2.42 tff(10547,plain,
% 2.24/2.42 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[10533, 10546])).
% 2.24/2.42 tff(10548,plain,
% 2.24/2.42 ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) <=> (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[10547])).
% 2.24/2.42 tff(10549,plain,
% 2.24/2.42 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[8851, 8850])).
% 2.24/2.42 tff(10550,plain,
% 2.24/2.42 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 2.24/2.42 inference(transitivity,[status(thm)],[10549, 154])).
% 2.24/2.42 tff(10551,plain,
% 2.24/2.42 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[10550])).
% 2.24/2.42 tff(10552,plain,
% 2.24/2.42 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[4470, 10551])).
% 2.24/2.42 tff(10553,plain,
% 2.24/2.42 (~r(elem!1, s(elem!1))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[5054, 1160, 246, 392, 970])).
% 2.24/2.42 tff(10554,plain,
% 2.24/2.42 (b(elem!1, s(elem!1))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[372, 10553, 365])).
% 2.24/2.42 tff(10555,plain,
% 2.24/2.42 (b(s(s(elem!1)), s(elem!1))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[994, 9730, 403])).
% 2.24/2.42 tff(10556,plain,
% 2.24/2.42 (((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(10557,plain,
% 2.24/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1)))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[10556])).
% 2.24/2.42 tff(10558,plain,
% 2.24/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.24/2.42 inference(transitivity,[status(thm)],[10557, 9731])).
% 2.24/2.42 tff(10559,plain,
% 2.24/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.24/2.42 inference(quant_inst,[status(thm)],[])).
% 2.24/2.42 tff(10560,plain,
% 2.24/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1)))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[10559, 10558])).
% 2.24/2.42 tff(10561,plain,
% 2.24/2.42 ($false),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[10560, 306, 7921, 10555, 1198, 3968])).
% 2.24/2.42 tff(10562,plain,((~r(s(elem!1), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (s(s(elem!1)) = s(elem!1)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.42 tff(10563,plain,
% 2.24/2.42 (~r(s(elem!1), elem!1)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[10562, 374, 7788, 392, 1160, 1730])).
% 2.24/2.42 tff(10564,plain,
% 2.24/2.42 (b(s(elem!1), elem!1)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[813, 10563, 193])).
% 2.24/2.42 tff(10565,plain,
% 2.24/2.42 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[7090, 10563, 8857, 10531])).
% 2.24/2.42 tff(10566,plain,
% 2.24/2.42 (~r(s(s(s(elem!1))), elem!1)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[7780, 10565, 1730])).
% 2.24/2.42 tff(10567,plain,
% 2.24/2.42 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[7812, 10566, 1730, 10552, 246, 365, 8863, 10564])).
% 2.24/2.42 tff(10568,plain,
% 2.24/2.42 (r(s(s(s(elem!1))), s(elem!1))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[664, 10567, 8855])).
% 2.24/2.42 tff(10569,plain,
% 2.24/2.42 (~r(s(s(elem!1)), s(elem!1))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[659, 10568, 10565])).
% 2.24/2.42 tff(10570,plain,
% 2.24/2.42 (b(s(s(elem!1)), s(elem!1))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[994, 10569, 392])).
% 2.24/2.42 tff(10571,plain,
% 2.24/2.42 (~b(z, s(elem!1))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[6476, 10570, 1160, 10564, 10554])).
% 2.24/2.42 tff(10572,plain,
% 2.24/2.42 (r(z, s(elem!1))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[275, 10571])).
% 2.24/2.42 tff(10573,plain,
% 2.24/2.42 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(10574,plain,
% 2.24/2.42 (((~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(10575,plain,
% 2.24/2.42 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1)))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[10574])).
% 2.24/2.42 tff(10576,plain,
% 2.24/2.42 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))))),
% 2.24/2.42 inference(transitivity,[status(thm)],[10575, 10573])).
% 2.24/2.42 tff(10577,plain,
% 2.24/2.42 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z)))),
% 2.24/2.42 inference(quant_inst,[status(thm)],[])).
% 2.24/2.42 tff(10578,plain,
% 2.24/2.42 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1)))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[10577, 10576])).
% 2.24/2.42 tff(10579,plain,
% 2.24/2.42 (~r(s(s(s(elem!1))), z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[10578, 124, 10568, 10572])).
% 2.24/2.42 tff(10580,plain,
% 2.24/2.42 (b(s(s(s(elem!1))), z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[3033, 43, 579, 10579])).
% 2.24/2.42 tff(10581,plain,
% 2.24/2.42 (~r(z, s(s(s(elem!1))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[5741, 10572, 10568])).
% 2.24/2.42 tff(10582,plain,
% 2.24/2.42 (b(z, s(s(s(elem!1))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[585, 10581])).
% 2.24/2.42 tff(10583,plain,
% 2.24/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(10584,plain,
% 2.24/2.43 (((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(10585,plain,
% 2.24/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[10584])).
% 2.24/2.43 tff(10586,plain,
% 2.24/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.24/2.43 inference(transitivity,[status(thm)],[10585, 10583])).
% 2.24/2.43 tff(10587,plain,
% 2.24/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.24/2.43 inference(quant_inst,[status(thm)],[])).
% 2.24/2.43 tff(10588,plain,
% 2.24/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[10587, 10586])).
% 2.24/2.43 tff(10589,plain,
% 2.24/2.43 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[10588, 306, 10582, 10580, 7788])).
% 2.24/2.43 tff(10590,plain,
% 2.24/2.43 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[891, 10589, 10552])).
% 2.24/2.43 tff(10591,plain,
% 2.24/2.43 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[8849, 8851])).
% 2.24/2.43 tff(10592,plain,
% 2.24/2.43 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[8849, 8851])).
% 2.24/2.43 tff(10593,plain,
% 2.24/2.43 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 2.24/2.43 inference(symmetry,[status(thm)],[10592])).
% 2.24/2.43 tff(10594,plain,
% 2.24/2.43 ((~b(s(elem!1), s(s(s(elem!1))))) <=> (~b(s(s(z)), s(s(s(s(z))))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[10593])).
% 2.24/2.43 tff(10595,plain,
% 2.24/2.43 (b(s(s(s(elem!1))), elem!1)),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[1636, 10566, 8863])).
% 2.24/2.43 tff(10596,plain,
% 2.24/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(10597,plain,
% 2.24/2.43 (((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(10598,plain,
% 2.24/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1)))))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[10597])).
% 2.24/2.43 tff(10599,plain,
% 2.24/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 2.24/2.43 inference(transitivity,[status(thm)],[10598, 10596])).
% 2.24/2.43 tff(10600,plain,
% 2.24/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 2.24/2.43 inference(quant_inst,[status(thm)],[])).
% 2.24/2.43 tff(10601,plain,
% 2.24/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1)))))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[10600, 10599])).
% 2.24/2.43 tff(10602,plain,
% 2.24/2.43 (~b(s(elem!1), s(s(s(elem!1))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[10601, 306, 10595, 10564, 10554])).
% 2.24/2.43 tff(10603,plain,
% 2.24/2.43 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[10602, 10594])).
% 2.24/2.43 tff(10604,plain,
% 2.24/2.43 (r(s(s(z)), s(s(s(s(z)))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[4510, 10603])).
% 2.24/2.43 tff(10605,plain,
% 2.24/2.43 (r(s(elem!1), s(s(s(elem!1))))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[10604, 10591])).
% 2.24/2.43 tff(10606,plain,
% 2.24/2.43 (~r(s(elem!1), s(s(elem!1)))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[2109, 124, 10590, 10605])).
% 2.24/2.43 tff(10607,plain,
% 2.24/2.43 (b(s(elem!1), s(s(elem!1)))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[1684, 43, 10606, 8841])).
% 2.24/2.43 tff(10608,plain,
% 2.24/2.43 ((s(s(s(s(s(elem!1))))) = s(elem!1)) <=> (s(s(s(s(s(s(z)))))) = s(elem!1))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[10533])).
% 2.24/2.43 tff(10609,plain,
% 2.24/2.43 ((s(s(s(s(s(s(z)))))) = s(elem!1)) <=> (s(s(s(s(s(elem!1))))) = s(elem!1))),
% 2.24/2.43 inference(symmetry,[status(thm)],[10608])).
% 2.24/2.43 tff(10610,plain,
% 2.24/2.43 ((~(s(s(s(s(s(s(z)))))) = s(elem!1))) <=> (~(s(s(s(s(s(elem!1))))) = s(elem!1)))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[10609])).
% 2.24/2.43 tff(10611,plain,
% 2.24/2.43 ((s(s(z)) = s(s(s(s(s(s(z))))))) <=> (s(elem!1) = s(s(s(s(s(s(z)))))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[8849])).
% 2.24/2.43 tff(10612,plain,
% 2.24/2.43 ((s(s(z)) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = s(elem!1))),
% 2.24/2.43 inference(transitivity,[status(thm)],[10611, 3849])).
% 2.24/2.43 tff(10613,plain,
% 2.24/2.43 ((~(s(s(z)) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(s(s(s(s(z)))))) = s(elem!1)))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[10612])).
% 2.24/2.43 tff(10614,plain,
% 2.24/2.43 (~(s(s(s(s(s(s(z)))))) = s(elem!1))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[2826, 10613])).
% 2.24/2.43 tff(10615,plain,
% 2.24/2.43 (~(s(s(s(s(s(elem!1))))) = s(elem!1))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[10614, 10610])).
% 2.24/2.43 tff(10616,assumption,(r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))), introduced(assumption)).
% 2.24/2.43 tff(10617,plain,
% 2.24/2.43 ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[1886, 124, 3439])).
% 2.24/2.43 tff(10618,plain,
% 2.24/2.43 (~r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[10617, 10616])).
% 2.24/2.43 tff(10619,plain,
% 2.24/2.43 ((s(s(s(s(s(elem!1))))) = s(elem!1)) | b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[1840, 43, 10618])).
% 2.24/2.43 tff(10620,plain,
% 2.24/2.43 (b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[10619, 10615])).
% 2.24/2.43 tff(10621,plain,
% 2.24/2.43 ((s(s(elem!1)) = s(s(s(s(s(elem!1)))))) <=> (s(s(elem!1)) = s(s(s(s(s(s(z)))))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[10533])).
% 2.24/2.43 tff(10622,plain,
% 2.24/2.43 ((s(s(elem!1)) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(s(z)))))) = s(s(elem!1)))),
% 2.24/2.43 inference(transitivity,[status(thm)],[10621, 3240])).
% 2.24/2.43 tff(10623,plain,
% 2.24/2.43 ((s(s(s(s(s(s(z)))))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(s(s(elem!1))))))),
% 2.24/2.43 inference(symmetry,[status(thm)],[10622])).
% 2.24/2.43 tff(10624,plain,
% 2.24/2.43 ((~(s(s(s(s(s(s(z)))))) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = s(s(s(s(s(elem!1)))))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[10623])).
% 2.24/2.43 tff(10625,plain,
% 2.24/2.43 (s(s(elem!1)) = s(s(s(z)))),
% 2.24/2.43 inference(symmetry,[status(thm)],[8850])).
% 2.24/2.43 tff(10626,plain,
% 2.24/2.43 ((s(s(s(s(s(s(z)))))) = s(s(elem!1))) <=> (s(s(s(s(s(s(z)))))) = s(s(s(z))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[10625])).
% 2.24/2.43 tff(10627,plain,
% 2.24/2.43 ((s(s(s(s(s(s(z)))))) = s(s(elem!1))) <=> (s(s(s(z))) = s(s(s(s(s(s(z)))))))),
% 2.24/2.43 inference(transitivity,[status(thm)],[10626, 1122])).
% 2.24/2.43 tff(10628,plain,
% 2.24/2.43 ((s(s(s(z))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = s(s(elem!1)))),
% 2.24/2.43 inference(symmetry,[status(thm)],[10627])).
% 2.24/2.43 tff(10629,plain,
% 2.24/2.43 ((~(s(s(s(z))) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(s(s(s(s(z)))))) = s(s(elem!1))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[10628])).
% 2.24/2.43 tff(10630,plain,
% 2.24/2.43 (~(s(s(s(s(s(s(z)))))) = s(s(elem!1)))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[556, 10629])).
% 2.24/2.43 tff(10631,plain,
% 2.24/2.43 (~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[10630, 10624])).
% 2.24/2.43 tff(10632,plain,
% 2.24/2.43 (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[10631, 1810])).
% 2.24/2.43 tff(10633,plain,
% 2.24/2.43 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(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))))))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(10634,plain,
% 2.24/2.43 (((~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))))))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(10635,plain,
% 2.24/2.43 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(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)))))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[10634])).
% 2.24/2.43 tff(10636,plain,
% 2.24/2.43 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(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))))))),
% 2.24/2.43 inference(transitivity,[status(thm)],[10635, 10633])).
% 2.24/2.43 tff(10637,plain,
% 2.24/2.43 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.24/2.43 inference(quant_inst,[status(thm)],[])).
% 2.24/2.43 tff(10638,plain,
% 2.24/2.43 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[10637, 10636])).
% 2.24/2.43 tff(10639,plain,
% 2.24/2.43 ((~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)))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[10638, 124, 878])).
% 2.24/2.43 tff(10640,plain,
% 2.24/2.43 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[10639, 10616])).
% 2.24/2.43 tff(10641,plain,
% 2.24/2.43 ((s(s(s(s(s(elem!1))))) = s(s(elem!1))) | b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[1831, 43, 10640])).
% 2.24/2.43 tff(10642,plain,
% 2.24/2.43 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[10641, 10632])).
% 2.24/2.43 tff(10643,plain,
% 2.24/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), 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))))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(10644,plain,
% 2.24/2.43 (((~b(s(elem!1), elem!1)) | (~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), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), 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))))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(10645,plain,
% 2.24/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), 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)))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[10644])).
% 2.24/2.43 tff(10646,plain,
% 2.24/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), 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))))),
% 2.24/2.43 inference(transitivity,[status(thm)],[10645, 10643])).
% 2.24/2.43 tff(10647,plain,
% 2.24/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~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))))),
% 2.24/2.43 inference(quant_inst,[status(thm)],[])).
% 2.24/2.43 tff(10648,plain,
% 2.24/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[10647, 10646])).
% 2.24/2.43 tff(10649,plain,
% 2.24/2.43 ($false),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[10648, 306, 1005, 816, 1690, 10642, 10620])).
% 2.24/2.43 tff(10650,plain,((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~(s(z) = elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.43 tff(10651,plain,
% 2.24/2.43 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[10650, 10570, 10564, 10607, 85, 10605, 10590])).
% 2.24/2.43 tff(10652,plain,
% 2.24/2.43 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[10651, 10548])).
% 2.24/2.43 tff(10653,plain,
% 2.24/2.43 ((~(s(s(s(s(z)))) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(s(s(s(s(z)))))) = s(s(s(s(z))))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[4708])).
% 2.24/2.43 tff(10654,assumption,(s(s(s(s(z)))) = s(s(s(s(s(s(z))))))), introduced(assumption)).
% 2.24/2.43 tff(10655,plain,
% 2.24/2.43 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(s(s(z)))))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[10654])).
% 2.24/2.43 tff(10656,plain,
% 2.24/2.43 (s(s(s(z))) = s(s(s(s(s(z)))))),
% 2.24/2.43 inference(transitivity,[status(thm)],[321, 10655, 540])).
% 2.24/2.43 tff(10657,plain,
% 2.24/2.43 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(s(z))))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[10656])).
% 2.24/2.43 tff(10658,plain,
% 2.24/2.43 (s(s(z)) = s(s(s(s(s(s(z))))))),
% 2.24/2.43 inference(transitivity,[status(thm)],[103, 10657, 496, 10654])).
% 2.24/2.43 tff(10659,plain,
% 2.24/2.43 ($false),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[2826, 10658])).
% 2.24/2.43 tff(10660,plain,(~(s(s(s(s(z)))) = s(s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.43 tff(10661,plain,
% 2.24/2.43 (~(s(s(s(s(s(s(z)))))) = s(s(s(s(z)))))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[10660, 10653])).
% 2.24/2.43 tff(10662,plain,
% 2.24/2.43 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[4725, 10661])).
% 2.24/2.43 tff(10663,plain,
% 2.24/2.43 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[10662, 10652])).
% 2.24/2.43 tff(10664,plain,
% 2.24/2.43 (b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[10663, 10545])).
% 2.24/2.43 tff(10665,plain,
% 2.24/2.43 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[10664, 10544])).
% 2.24/2.43 tff(10666,plain,
% 2.24/2.43 (~r(elem!1, s(s(s(elem!1))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[1256, 124, 970, 10565])).
% 2.24/2.43 tff(10667,plain,
% 2.24/2.43 (b(elem!1, s(s(s(elem!1))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[3284, 10666, 8848])).
% 2.24/2.43 tff(10668,plain,
% 2.24/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~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))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(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))))), elem!1)))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(10669,plain,
% 2.24/2.43 (((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~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(elem!1, s(s(s(elem!1))))) | (~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))))), elem!1)))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(10670,plain,
% 2.24/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(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))))), elem!1))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[10669])).
% 2.24/2.43 tff(10671,plain,
% 2.24/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(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))))), elem!1)))),
% 2.24/2.43 inference(transitivity,[status(thm)],[10670, 10668])).
% 2.24/2.43 tff(10672,plain,
% 2.24/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~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)))),
% 2.24/2.43 inference(quant_inst,[status(thm)],[])).
% 2.24/2.43 tff(10673,plain,
% 2.24/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~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))))), elem!1))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[10672, 10671])).
% 2.24/2.43 tff(10674,plain,
% 2.24/2.43 ((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[10673, 306, 10667, 10582, 10580])).
% 2.24/2.43 tff(10675,plain,
% 2.24/2.43 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[10674, 10665])).
% 2.24/2.43 tff(10676,plain,
% 2.24/2.43 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[1855, 10675, 10542])).
% 2.24/2.43 tff(10677,plain,
% 2.24/2.43 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), z)))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(10678,plain,
% 2.24/2.43 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), z)))),
% 2.24/2.43 inference(quant_inst,[status(thm)],[])).
% 2.24/2.43 tff(10679,plain,
% 2.24/2.43 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), z))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[10678, 10677])).
% 2.24/2.43 tff(10680,plain,
% 2.24/2.43 (~r(s(s(s(s(s(elem!1))))), z)),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[10679, 124, 374, 10676])).
% 2.24/2.43 tff(10681,plain,
% 2.24/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(10682,plain,
% 2.24/2.43 (((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(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)))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(10683,plain,
% 2.24/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), z))))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[10682])).
% 2.24/2.44 tff(10684,plain,
% 2.24/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 2.24/2.44 inference(transitivity,[status(thm)],[10683, 10681])).
% 2.24/2.44 tff(10685,plain,
% 2.24/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~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)))),
% 2.24/2.44 inference(quant_inst,[status(thm)],[])).
% 2.24/2.44 tff(10686,plain,
% 2.24/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(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))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[10685, 10684])).
% 2.24/2.44 tff(10687,plain,
% 2.24/2.44 ((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), z))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[10686, 306, 10582, 10580])).
% 2.24/2.44 tff(10688,plain,
% 2.24/2.44 (~b(s(s(s(s(s(elem!1))))), z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[10687, 10665])).
% 2.24/2.44 tff(10689,plain,
% 2.24/2.44 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = z) | b(s(s(s(s(s(elem!1))))), z) | r(s(s(s(s(s(elem!1))))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = z) | b(s(s(s(s(s(elem!1))))), z) | r(s(s(s(s(s(elem!1))))), z))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(10690,plain,
% 2.24/2.44 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = z) | b(s(s(s(s(s(elem!1))))), z) | r(s(s(s(s(s(elem!1))))), z))),
% 2.24/2.44 inference(quant_inst,[status(thm)],[])).
% 2.24/2.44 tff(10691,plain,
% 2.24/2.44 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = z) | b(s(s(s(s(s(elem!1))))), z) | r(s(s(s(s(s(elem!1))))), z)),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[10690, 10689])).
% 2.24/2.44 tff(10692,plain,
% 2.24/2.44 ($false),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[10691, 43, 1822, 10688, 10680])).
% 2.24/2.44 tff(10693,plain,((~r(z, elem!1)) | (~(s(z) = elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, z)) | (s(elem!1) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.24/2.44 tff(10694,plain,
% 2.24/2.44 (~r(z, elem!1)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[10693, 10505, 10513, 1730, 246, 10503])).
% 2.24/2.44 tff(10695,plain,
% 2.24/2.44 (b(z, elem!1)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[835, 10694, 10531])).
% 2.24/2.44 tff(10696,plain,
% 2.24/2.44 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 2.24/2.44 inference(symmetry,[status(thm)],[10519])).
% 2.24/2.44 tff(10697,plain,
% 2.24/2.44 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 2.24/2.44 inference(monotonicity,[status(thm)],[10696])).
% 2.24/2.44 tff(10698,plain,
% 2.24/2.44 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 2.24/2.44 inference(symmetry,[status(thm)],[10697])).
% 2.24/2.44 tff(10699,plain,
% 2.24/2.44 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(z)))), elem!1)),
% 2.24/2.44 inference(monotonicity,[status(thm)],[10505])).
% 2.24/2.44 tff(10700,plain,
% 2.24/2.44 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(elem!1))), elem!1)),
% 2.24/2.44 inference(transitivity,[status(thm)],[10699, 10698])).
% 2.24/2.44 tff(10701,plain,
% 2.24/2.44 (b(z, s(s(s(z)))) <=> b(z, s(s(elem!1)))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[10507])).
% 2.24/2.44 tff(10702,plain,
% 2.24/2.44 (b(z, s(s(elem!1))) <=> b(z, s(s(s(z))))),
% 2.24/2.44 inference(symmetry,[status(thm)],[10701])).
% 2.24/2.44 tff(10703,plain,
% 2.24/2.44 (b(z, s(s(s(z))))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[10516, 10702])).
% 2.24/2.44 tff(10704,plain,
% 2.24/2.44 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[8851, 8850])).
% 2.24/2.44 tff(10705,plain,
% 2.24/2.44 (~r(s(s(s(s(z)))), z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[10160, 10126, 204])).
% 2.24/2.44 tff(10706,plain,
% 2.24/2.44 (b(s(s(s(s(z)))), z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[695, 10705])).
% 2.24/2.44 tff(10707,plain,
% 2.24/2.44 (r(s(s(s(z))), s(z)) <=> r(s(s(s(z))), elem!1)),
% 2.24/2.44 inference(monotonicity,[status(thm)],[85])).
% 2.24/2.44 tff(10708,plain,
% 2.24/2.44 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(z))),
% 2.24/2.44 inference(symmetry,[status(thm)],[10707])).
% 2.24/2.44 tff(10709,plain,
% 2.24/2.44 (r(s(s(s(z))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 2.24/2.44 inference(monotonicity,[status(thm)],[8850])).
% 2.24/2.44 tff(10710,plain,
% 2.24/2.44 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(z))), elem!1)),
% 2.24/2.44 inference(symmetry,[status(thm)],[10709])).
% 2.24/2.44 tff(10711,plain,
% 2.24/2.44 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(z))), s(z))),
% 2.24/2.44 inference(transitivity,[status(thm)],[10710, 10708])).
% 2.24/2.44 tff(10712,plain,
% 2.24/2.44 (r(s(s(s(z))), s(z))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[1730, 10711])).
% 2.24/2.44 tff(10713,plain,
% 2.24/2.44 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[10128, 10126, 10712])).
% 2.24/2.44 tff(10714,plain,
% 2.24/2.44 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[4481, 10713])).
% 2.24/2.44 tff(10715,plain,
% 2.24/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(10716,plain,
% 2.24/2.44 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(10717,plain,
% 2.24/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(z)))), z)) | (~b(z, s(s(s(z)))))))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[10716])).
% 2.24/2.44 tff(10718,plain,
% 2.24/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(z)))), z)) | (~b(z, s(s(s(z))))))),
% 2.24/2.44 inference(transitivity,[status(thm)],[10717, 10715])).
% 2.24/2.44 tff(10719,plain,
% 2.24/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 2.24/2.44 inference(quant_inst,[status(thm)],[])).
% 2.24/2.44 tff(10720,plain,
% 2.24/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z)))))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[10719, 10718])).
% 2.24/2.44 tff(10721,plain,
% 2.24/2.44 ($false),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[10720, 306, 393, 942, 859, 762])).
% 2.24/2.44 tff(10722,plain,((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.44 tff(10723,plain,
% 2.24/2.44 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[10722, 10714, 859, 10706])).
% 2.24/2.44 tff(10724,plain,
% 2.24/2.44 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[10146, 10723])).
% 2.24/2.44 tff(10725,plain,
% 2.24/2.44 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[10724, 10704])).
% 2.24/2.44 tff(10726,plain,
% 2.24/2.44 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(z)))), elem!1)),
% 2.24/2.44 inference(monotonicity,[status(thm)],[10546])).
% 2.24/2.44 tff(10727,plain,
% 2.24/2.44 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 2.24/2.44 inference(symmetry,[status(thm)],[10726])).
% 2.24/2.44 tff(10728,plain,
% 2.24/2.44 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(s(z)))), elem!1)),
% 2.24/2.44 inference(monotonicity,[status(thm)],[85])).
% 2.24/2.44 tff(10729,plain,
% 2.24/2.44 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(elem!1))), elem!1)),
% 2.24/2.44 inference(transitivity,[status(thm)],[10728, 10727])).
% 2.24/2.44 tff(10730,plain,
% 2.24/2.44 (r(s(s(s(elem!1))), elem!1)),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[10126, 10729])).
% 2.24/2.44 tff(10731,plain,
% 2.24/2.44 ($false),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[7778, 124, 1730, 10730, 10725])).
% 2.24/2.44 tff(10732,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), elem!1)) | (~(s(z) = elem!1)) | (~b(z, s(s(s(z))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.44 tff(10733,plain,
% 2.24/2.44 (~r(s(s(s(s(z)))), s(z))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[10732, 10505, 1730, 10703, 204])).
% 2.24/2.44 tff(10734,plain,
% 2.24/2.44 (b(s(s(s(s(z)))), s(z))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[4490, 10733])).
% 2.24/2.44 tff(10735,plain,
% 2.24/2.44 (b(s(s(s(elem!1))), elem!1)),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[10734, 10700])).
% 2.24/2.44 tff(10736,plain,
% 2.24/2.44 ((s(z) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[10505])).
% 2.24/2.44 tff(10737,plain,
% 2.24/2.44 ((~(s(z) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[10736])).
% 2.24/2.44 tff(10738,plain,
% 2.24/2.44 (~(elem!1 = s(s(s(elem!1))))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[645, 10737])).
% 2.24/2.44 tff(10739,plain,
% 2.24/2.44 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[10519, 10507])).
% 2.24/2.44 tff(10740,plain,
% 2.24/2.44 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 2.24/2.44 inference(transitivity,[status(thm)],[10739, 154])).
% 2.24/2.44 tff(10741,plain,
% 2.24/2.44 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[10740])).
% 2.24/2.44 tff(10742,plain,
% 2.24/2.44 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[4470, 10741])).
% 2.24/2.44 tff(10743,plain,
% 2.24/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(10744,plain,
% 2.24/2.44 (((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(10745,plain,
% 2.24/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[10744])).
% 2.24/2.44 tff(10746,plain,
% 2.24/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.24/2.44 inference(transitivity,[status(thm)],[10745, 10743])).
% 2.24/2.44 tff(10747,plain,
% 2.24/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.24/2.44 inference(quant_inst,[status(thm)],[])).
% 2.24/2.44 tff(10748,plain,
% 2.24/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[10747, 10746])).
% 2.24/2.44 tff(10749,plain,
% 2.24/2.44 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[10748, 306, 838, 6445, 3968, 815])).
% 2.24/2.44 tff(10750,plain,
% 2.24/2.44 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[891, 10749, 157])).
% 2.24/2.44 tff(10751,plain,
% 2.24/2.44 (~r(elem!1, s(s(s(elem!1))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[5766, 10750, 1730])).
% 2.24/2.44 tff(10752,plain,
% 2.24/2.44 (b(elem!1, s(s(s(elem!1))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[3284, 10751, 1653])).
% 2.24/2.44 tff(10753,plain,
% 2.24/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(10754,plain,
% 2.24/2.44 (((~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(10755,plain,
% 2.24/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1))))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[10754])).
% 2.24/2.44 tff(10756,plain,
% 2.24/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.24/2.44 inference(transitivity,[status(thm)],[10755, 10753])).
% 2.24/2.44 tff(10757,plain,
% 2.24/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(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)))),
% 2.24/2.44 inference(quant_inst,[status(thm)],[])).
% 2.24/2.44 tff(10758,plain,
% 2.24/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[10757, 10756])).
% 2.24/2.44 tff(10759,plain,
% 2.24/2.44 ($false),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[10758, 306, 838, 10752, 6445, 1664])).
% 2.24/2.44 tff(10760,plain,((~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (elem!1 = s(s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.44 tff(10761,plain,
% 2.24/2.44 (~b(s(s(s(elem!1))), z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[10760, 10695, 10735, 10738, 1730, 10742, 7788, 10518])).
% 2.24/2.44 tff(10762,plain,
% 2.24/2.44 (r(s(s(s(elem!1))), z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[3033, 43, 579, 10761])).
% 2.24/2.44 tff(10763,plain,
% 2.24/2.44 (~r(elem!1, s(s(s(elem!1))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[851, 10762, 246])).
% 2.24/2.44 tff(10764,plain,
% 2.24/2.44 (b(elem!1, s(s(s(elem!1))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[3284, 10763, 10738])).
% 2.24/2.44 tff(10765,plain,
% 2.24/2.44 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[3437, 10742])).
% 2.24/2.44 tff(10766,plain,
% 2.24/2.44 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[1776, 306, 1663, 1664, 2076])).
% 2.24/2.44 tff(10767,plain,
% 2.24/2.44 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[1958, 43, 3476, 10766])).
% 2.24/2.44 tff(10768,plain,
% 2.24/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(10769,plain,
% 2.24/2.44 (((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(10770,plain,
% 2.24/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1))))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[10769])).
% 2.24/2.44 tff(10771,plain,
% 2.24/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.24/2.45 inference(transitivity,[status(thm)],[10770, 10768])).
% 2.24/2.45 tff(10772,plain,
% 2.24/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.24/2.45 inference(quant_inst,[status(thm)],[])).
% 2.24/2.45 tff(10773,plain,
% 2.24/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[10772, 10771])).
% 2.24/2.45 tff(10774,plain,
% 2.24/2.45 (~b(s(s(s(s(elem!1)))), z)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[10773, 306, 838, 1663, 1664, 2076])).
% 2.24/2.45 tff(10775,plain,
% 2.24/2.45 (r(s(s(s(s(elem!1)))), z)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[5723, 10774])).
% 2.24/2.45 tff(10776,plain,
% 2.24/2.45 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(10777,plain,
% 2.24/2.45 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.24/2.45 inference(quant_inst,[status(thm)],[])).
% 2.24/2.45 tff(10778,plain,
% 2.24/2.45 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[10777, 10776])).
% 2.24/2.45 tff(10779,plain,
% 2.24/2.45 ($false),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[10778, 124, 3021, 10775, 10767])).
% 2.24/2.45 tff(10780,plain,((~b(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), z)) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.45 tff(10781,plain,
% 2.24/2.45 (~b(s(s(s(s(elem!1)))), elem!1)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[10780, 10762, 10765, 10764, 10735, 10695])).
% 2.24/2.45 tff(10782,plain,
% 2.24/2.45 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[1736, 10781, 10530])).
% 2.24/2.45 tff(10783,plain,
% 2.24/2.45 ((s(elem!1) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 2.24/2.45 inference(commutativity,[status(thm)],[])).
% 2.24/2.45 tff(10784,plain,
% 2.24/2.45 ((s(s(s(s(elem!1)))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(elem!1)))))),
% 2.24/2.45 inference(symmetry,[status(thm)],[10783])).
% 2.24/2.45 tff(10785,plain,
% 2.24/2.45 ((~(s(s(s(s(elem!1)))) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(s(elem!1))))))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[10784])).
% 2.24/2.45 tff(10786,plain,
% 2.24/2.45 (~(s(elem!1) = s(s(s(s(elem!1)))))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[1516, 10785])).
% 2.24/2.45 tff(10787,plain,
% 2.24/2.45 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[1989, 10786])).
% 2.24/2.45 tff(10788,plain,
% 2.24/2.45 (~r(s(elem!1), s(s(elem!1)))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[1680, 124, 802, 1730])).
% 2.24/2.45 tff(10789,plain,
% 2.24/2.45 ((s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1)))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[1684, 43, 10788])).
% 2.24/2.45 tff(10790,plain,
% 2.24/2.45 (b(s(elem!1), s(s(elem!1)))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[10789, 1659])).
% 2.24/2.45 tff(10791,plain,
% 2.24/2.45 (~r(s(s(elem!1)), s(elem!1))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[7985, 1730, 802])).
% 2.24/2.45 tff(10792,plain,
% 2.24/2.45 (b(s(s(elem!1)), s(elem!1))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[994, 10791, 403])).
% 2.24/2.45 tff(10793,plain,
% 2.24/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(10794,plain,
% 2.24/2.45 (((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(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(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(10795,plain,
% 2.24/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(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(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[10794])).
% 2.24/2.45 tff(10796,plain,
% 2.24/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(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(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 2.24/2.45 inference(transitivity,[status(thm)],[10795, 10793])).
% 2.24/2.45 tff(10797,plain,
% 2.24/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(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(elem!1)))))))),
% 2.24/2.45 inference(quant_inst,[status(thm)],[])).
% 2.24/2.45 tff(10798,plain,
% 2.24/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[10797, 10796])).
% 2.24/2.45 tff(10799,plain,
% 2.24/2.45 ($false),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[10798, 306, 10792, 1973, 10790, 10787])).
% 2.24/2.45 tff(10800,plain,((s(s(s(s(elem!1)))) = s(elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (s(s(elem!1)) = s(elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.45 tff(10801,plain,
% 2.24/2.45 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[10800, 1289, 403, 802, 1516, 1730])).
% 2.24/2.45 tff(10802,plain,
% 2.24/2.45 ($false),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[1302, 10801, 4889, 1717])).
% 2.24/2.45 tff(10803,plain,((~r(s(s(s(s(elem!1)))), elem!1)) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (s(s(elem!1)) = s(elem!1)) | (~r(s(elem!1), elem!1)) | (s(s(s(s(elem!1)))) = s(elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.45 tff(10804,plain,
% 2.24/2.45 (~r(s(elem!1), elem!1)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[10803, 10782, 1730, 10514, 10528, 10513, 10524])).
% 2.24/2.45 tff(10805,plain,
% 2.24/2.45 (b(s(elem!1), elem!1)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[813, 10804, 10503])).
% 2.24/2.45 tff(10806,plain,
% 2.24/2.45 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 2.24/2.45 inference(monotonicity,[status(thm)],[10505])).
% 2.24/2.45 tff(10807,plain,
% 2.24/2.45 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = elem!1))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[10806])).
% 2.24/2.45 tff(10808,plain,
% 2.24/2.45 (~(s(s(elem!1)) = elem!1)),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[80, 10807])).
% 2.24/2.45 tff(10809,plain,
% 2.24/2.45 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[7090, 10804, 10808, 10531])).
% 2.24/2.45 tff(10810,plain,
% 2.24/2.45 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(z)))), elem!1)),
% 2.24/2.45 inference(monotonicity,[status(thm)],[10696])).
% 2.24/2.45 tff(10811,plain,
% 2.24/2.45 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 2.24/2.45 inference(symmetry,[status(thm)],[10810])).
% 2.24/2.45 tff(10812,plain,
% 2.24/2.45 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(s(z)))), elem!1)),
% 2.24/2.45 inference(monotonicity,[status(thm)],[10505])).
% 2.24/2.45 tff(10813,plain,
% 2.24/2.45 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(elem!1))), elem!1)),
% 2.24/2.45 inference(transitivity,[status(thm)],[10812, 10811])).
% 2.24/2.45 tff(10814,plain,
% 2.24/2.45 ((~r(s(s(s(s(z)))), s(z))) <=> (~r(s(s(s(elem!1))), elem!1))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[10813])).
% 2.24/2.45 tff(10815,plain,
% 2.24/2.45 (~r(s(s(s(elem!1))), elem!1)),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[10733, 10814])).
% 2.24/2.45 tff(10816,plain,
% 2.24/2.45 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 2.24/2.45 inference(transitivity,[status(thm)],[10736, 1555])).
% 2.24/2.45 tff(10817,plain,
% 2.24/2.45 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[10816])).
% 2.24/2.45 tff(10818,plain,
% 2.24/2.45 (~(s(s(s(elem!1))) = elem!1)),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[645, 10817])).
% 2.24/2.45 tff(10819,plain,
% 2.24/2.45 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[7812, 10805, 1730, 10742, 246, 10504, 10818, 10815])).
% 2.24/2.45 tff(10820,plain,
% 2.24/2.45 (r(s(s(s(elem!1))), s(elem!1))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[664, 10819, 10523])).
% 2.24/2.45 tff(10821,plain,
% 2.24/2.45 (~r(s(s(elem!1)), s(elem!1))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[659, 10820, 10809])).
% 2.24/2.45 tff(10822,plain,
% 2.24/2.45 (b(s(s(elem!1)), s(elem!1))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[994, 10821, 10514])).
% 2.24/2.45 tff(10823,plain,
% 2.24/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(10824,plain,
% 2.24/2.45 (((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(10825,plain,
% 2.24/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1))))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[10824])).
% 2.24/2.45 tff(10826,plain,
% 2.24/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.24/2.45 inference(transitivity,[status(thm)],[10825, 10823])).
% 2.24/2.45 tff(10827,plain,
% 2.24/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))),
% 2.24/2.45 inference(quant_inst,[status(thm)],[])).
% 2.24/2.45 tff(10828,plain,
% 2.24/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[10827, 10826])).
% 2.24/2.45 tff(10829,plain,
% 2.24/2.45 (~b(z, s(s(s(elem!1))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[10828, 306, 10695, 10764, 10735])).
% 2.24/2.45 tff(10830,plain,
% 2.24/2.45 (r(z, s(s(s(elem!1))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[585, 10829])).
% 2.24/2.45 tff(10831,plain,
% 2.24/2.45 (~r(z, s(elem!1))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[5741, 10820, 10830])).
% 2.24/2.45 tff(10832,plain,
% 2.24/2.45 (b(z, s(elem!1))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[275, 10831])).
% 2.24/2.45 tff(10833,plain,
% 2.24/2.45 ($false),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[6476, 10832, 10822, 10516, 10805, 10518])).
% 2.24/2.45 tff(10834,plain,((~r(s(z), z)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, z)) | b(elem!1, s(s(s(z)))) | b(s(z), elem!1) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.45 tff(10835,plain,
% 2.24/2.45 (~r(s(z), z)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[10834, 10502, 10461, 3, 2715, 5])).
% 2.24/2.45 tff(10836,plain,
% 2.24/2.45 (b(s(z), z)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[221, 10835])).
% 2.24/2.45 tff(10837,plain,
% 2.24/2.45 (~(elem!1 = s(z))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[4298, 10836, 2])).
% 2.24/2.45 tff(10838,plain,
% 2.24/2.45 (r(elem!1, s(z))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[97, 10837])).
% 2.24/2.45 tff(10839,plain,
% 2.24/2.45 (~b(s(s(s(z))), z)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[4943, 8, 3, 247, 246, 2])).
% 2.24/2.45 tff(10840,plain,
% 2.24/2.45 (r(s(s(s(z))), z)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[2197, 10839])).
% 2.24/2.45 tff(10841,plain,
% 2.24/2.45 (~r(elem!1, s(s(s(z))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[2312, 10840, 246])).
% 2.24/2.45 tff(10842,plain,
% 2.24/2.45 (elem!1 = s(s(s(z)))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[2304, 10841, 3])).
% 2.24/2.45 tff(10843,plain,
% 2.24/2.45 (b(s(z), elem!1) <=> b(s(z), s(s(s(z))))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[10842])).
% 2.24/2.45 tff(10844,plain,
% 2.24/2.45 (b(s(z), s(s(s(z)))) <=> b(s(z), elem!1)),
% 2.24/2.45 inference(symmetry,[status(thm)],[10843])).
% 2.24/2.45 tff(10845,plain,
% 2.24/2.45 (b(s(z), elem!1)),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[8, 10844])).
% 2.24/2.45 tff(10846,plain,
% 2.24/2.45 ($false),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[2715, 10845])).
% 2.24/2.45 tff(10847,plain,((~b(s(z), s(s(s(z))))) | b(s(z), elem!1) | b(elem!1, s(s(s(z)))) | (~r(elem!1, z)) | (~b(s(z), z)) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 2.24/2.45 tff(10848,plain,
% 2.24/2.45 (~b(s(z), s(s(s(z))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[10847, 2715, 3, 10502, 10836, 2])).
% 2.24/2.45 tff(10849,plain,
% 2.24/2.45 (r(s(z), s(s(s(z))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[3302, 10848])).
% 2.24/2.45 tff(10850,plain,
% 2.24/2.45 (~r(elem!1, s(s(s(z))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[3293, 10849, 10838])).
% 2.24/2.45 tff(10851,plain,
% 2.24/2.45 (elem!1 = s(s(s(z)))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[2304, 10850, 3])).
% 2.24/2.45 tff(10852,plain,
% 2.24/2.45 (s(elem!1) = s(s(s(s(z))))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[10851])).
% 2.24/2.45 tff(10853,plain,
% 2.24/2.45 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[10852])).
% 2.24/2.45 tff(10854,plain,
% 2.24/2.45 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 2.24/2.45 inference(symmetry,[status(thm)],[10853])).
% 2.24/2.45 tff(10855,plain,
% 2.24/2.45 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[10854])).
% 2.24/2.45 tff(10856,plain,
% 2.24/2.45 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(s(s(z))))), s(z))),
% 2.24/2.45 inference(symmetry,[status(thm)],[10855])).
% 2.24/2.45 tff(10857,plain,
% 2.24/2.45 (~r(s(s(elem!1)), s(z))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[9725, 10838, 10461])).
% 2.24/2.45 tff(10858,plain,
% 2.24/2.45 (b(s(s(elem!1)), s(z))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[3989, 10857])).
% 2.24/2.45 tff(10859,plain,
% 2.24/2.45 (b(s(s(s(s(s(z))))), s(z))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[10858, 10856])).
% 2.24/2.45 tff(10860,plain,
% 2.24/2.45 (b(s(s(elem!1)), z) <=> b(s(s(s(s(s(z))))), z)),
% 2.24/2.45 inference(monotonicity,[status(thm)],[10853])).
% 2.24/2.45 tff(10861,plain,
% 2.24/2.45 (~r(s(s(elem!1)), z)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[7786, 10502, 10461])).
% 2.24/2.45 tff(10862,plain,
% 2.24/2.45 (b(s(s(elem!1)), z)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[476, 10861])).
% 2.24/2.45 tff(10863,plain,
% 2.24/2.45 (b(s(s(s(s(s(z))))), z)),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[10862, 10860])).
% 2.24/2.45 tff(10864,plain,
% 2.24/2.45 (~(z = elem!1)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[9879, 10502])).
% 2.24/2.45 tff(10865,plain,
% 2.24/2.45 (~(s(z) = elem!1)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[89, 10837])).
% 2.24/2.45 tff(10866,plain,
% 2.24/2.45 (r(s(z), elem!1)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[4192, 10865])).
% 2.24/2.45 tff(10867,plain,
% 2.24/2.45 (~r(z, elem!1)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[8838, 10866, 10461, 10502])).
% 2.24/2.45 tff(10868,plain,
% 2.24/2.45 (b(z, elem!1)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[835, 10867, 10864])).
% 2.24/2.45 tff(10869,plain,
% 2.24/2.45 (b(z, s(s(s(z))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[842, 10851, 10868])).
% 2.24/2.45 tff(10870,plain,
% 2.24/2.45 (~r(z, s(z))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[2273, 10838, 10502])).
% 2.24/2.45 tff(10871,plain,
% 2.24/2.45 (b(z, s(z))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[2263, 10870])).
% 2.24/2.45 tff(10872,plain,
% 2.24/2.45 (~b(s(s(s(z))), s(z))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[5016, 10851, 5])).
% 2.24/2.45 tff(10873,plain,
% 2.24/2.45 (r(s(s(s(z))), s(z))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[113, 10872])).
% 2.24/2.45 tff(10874,plain,
% 2.24/2.45 (s(s(s(z))) = elem!1),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[4555, 10851])).
% 2.24/2.45 tff(10875,plain,
% 2.24/2.45 (r(s(s(s(z))), z)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[2204, 10874, 10502])).
% 2.24/2.45 tff(10876,plain,
% 2.24/2.45 (~r(s(s(s(s(z)))), s(z))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[10128, 2013, 206])).
% 2.24/2.45 tff(10877,plain,
% 2.24/2.45 (b(s(s(s(s(z)))), s(z))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[4490, 10876])).
% 2.24/2.45 tff(10878,plain,
% 2.24/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(10879,plain,
% 2.24/2.45 (((~b(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(10880,plain,
% 2.24/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z))))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[10879])).
% 2.24/2.45 tff(10881,plain,
% 2.24/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)))),
% 2.24/2.45 inference(transitivity,[status(thm)],[10880, 10878])).
% 2.24/2.45 tff(10882,plain,
% 2.24/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 2.24/2.45 inference(quant_inst,[status(thm)],[])).
% 2.24/2.45 tff(10883,plain,
% 2.24/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[10882, 10881])).
% 2.24/2.45 tff(10884,plain,
% 2.24/2.45 (~b(s(s(s(s(z)))), z)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[10883, 306, 838, 4419, 485, 10877])).
% 2.24/2.45 tff(10885,plain,
% 2.24/2.45 (r(s(s(s(s(z)))), z)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[695, 10884])).
% 2.24/2.45 tff(10886,plain,
% 2.24/2.45 ($false),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[4478, 124, 205, 10885, 2013])).
% 2.24/2.45 tff(10887,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.45 tff(10888,plain,
% 2.24/2.45 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[10887, 10875, 10868, 10873, 10871])).
% 2.24/2.45 tff(10889,plain,
% 2.24/2.45 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[4481, 10888])).
% 2.24/2.45 tff(10890,plain,
% 2.24/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(10891,plain,
% 2.24/2.45 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(10892,plain,
% 2.24/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z))))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[10891])).
% 2.24/2.45 tff(10893,plain,
% 2.24/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.24/2.45 inference(transitivity,[status(thm)],[10892, 10890])).
% 2.24/2.45 tff(10894,plain,
% 2.24/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.24/2.45 inference(quant_inst,[status(thm)],[])).
% 2.24/2.45 tff(10895,plain,
% 2.24/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[10894, 10893])).
% 2.24/2.45 tff(10896,plain,
% 2.24/2.45 (~b(s(s(s(s(s(z))))), s(z))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[10895, 306, 10889, 10869, 10836, 10863])).
% 2.24/2.45 tff(10897,plain,
% 2.24/2.45 ($false),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[10896, 10859])).
% 2.24/2.45 tff(10898,plain,(b(s(z), elem!1) | b(elem!1, s(z)) | b(elem!1, s(s(s(z)))) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 2.24/2.45 tff(10899,plain,
% 2.24/2.45 (b(s(z), elem!1)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[10898, 2, 3, 5])).
% 2.24/2.45 tff(10900,plain,
% 2.24/2.45 ((elem!1 = s(z)) <=> (z = s(z))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[1620])).
% 2.24/2.45 tff(10901,plain,
% 2.24/2.45 ((elem!1 = s(z)) <=> (s(z) = z)),
% 2.24/2.45 inference(transitivity,[status(thm)],[10900, 375])).
% 2.24/2.45 tff(10902,plain,
% 2.24/2.45 ((s(z) = z) <=> (elem!1 = s(z))),
% 2.24/2.45 inference(symmetry,[status(thm)],[10901])).
% 2.24/2.45 tff(10903,plain,
% 2.24/2.45 ((~(s(z) = z)) <=> (~(elem!1 = s(z)))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[10902])).
% 2.24/2.46 tff(10904,plain,
% 2.24/2.46 (~(elem!1 = s(z))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[216, 10903])).
% 2.24/2.46 tff(10905,plain,
% 2.24/2.46 (r(elem!1, s(z))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[97, 10904])).
% 2.24/2.46 tff(10906,plain,
% 2.24/2.46 (r(s(s(z)), elem!1) <=> r(s(s(z)), z)),
% 2.24/2.46 inference(monotonicity,[status(thm)],[1620])).
% 2.24/2.46 tff(10907,plain,
% 2.24/2.46 (r(s(s(z)), z) <=> r(s(s(z)), elem!1)),
% 2.24/2.46 inference(symmetry,[status(thm)],[10906])).
% 2.24/2.46 tff(10908,plain,
% 2.24/2.46 (r(s(s(elem!1)), z) <=> r(s(s(z)), z)),
% 2.24/2.46 inference(monotonicity,[status(thm)],[1622])).
% 2.24/2.46 tff(10909,plain,
% 2.24/2.46 (r(s(s(elem!1)), z) <=> r(s(s(z)), elem!1)),
% 2.24/2.46 inference(transitivity,[status(thm)],[10908, 10907])).
% 2.24/2.46 tff(10910,plain,
% 2.24/2.46 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), z)),
% 2.24/2.46 inference(monotonicity,[status(thm)],[1620])).
% 2.24/2.46 tff(10911,plain,
% 2.24/2.46 (r(s(s(elem!1)), z)),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[1730, 10910])).
% 2.24/2.46 tff(10912,plain,
% 2.24/2.46 (r(s(s(z)), elem!1)),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[10911, 10909])).
% 2.24/2.46 tff(10913,plain,
% 2.24/2.46 (~r(s(s(z)), s(z))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[2484, 10912, 10905])).
% 2.24/2.46 tff(10914,plain,
% 2.24/2.46 (b(s(s(z)), s(z))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[2476, 10913])).
% 2.24/2.46 tff(10915,plain,
% 2.24/2.46 (r(z, s(s(s(z))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[2415, 43, 9970, 2405])).
% 2.24/2.46 tff(10916,plain,
% 2.24/2.46 (r(s(s(z)), z)),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[10911, 10908])).
% 2.24/2.46 tff(10917,plain,
% 2.24/2.46 (~r(s(s(z)), s(s(s(z))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[2523, 10916, 10915])).
% 2.24/2.46 tff(10918,plain,
% 2.24/2.46 (b(s(s(z)), s(s(s(z))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[2514, 10917])).
% 2.24/2.46 tff(10919,plain,
% 2.24/2.46 (~r(s(z), s(s(s(z))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[3293, 9946, 10905])).
% 2.24/2.46 tff(10920,plain,
% 2.24/2.46 (b(s(z), s(s(s(z))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[3302, 10919])).
% 2.24/2.46 tff(10921,plain,
% 2.24/2.46 (b(z, s(elem!1)) <=> b(z, s(z))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[1621])).
% 2.24/2.46 tff(10922,plain,
% 2.24/2.46 (b(z, s(z)) <=> b(z, s(elem!1))),
% 2.24/2.46 inference(symmetry,[status(thm)],[10921])).
% 2.24/2.46 tff(10923,plain,
% 2.24/2.46 ((~b(z, s(z))) <=> (~b(z, s(elem!1)))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[10922])).
% 2.24/2.46 tff(10924,plain,
% 2.24/2.46 ((~b(elem!1, s(z))) <=> (~b(z, s(z)))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[4345])).
% 2.24/2.46 tff(10925,plain,
% 2.24/2.46 (~b(z, s(z))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[5, 10924])).
% 2.24/2.46 tff(10926,plain,
% 2.24/2.46 (~b(z, s(elem!1))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[10925, 10923])).
% 2.24/2.46 tff(10927,plain,
% 2.24/2.46 (r(z, s(elem!1))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[275, 10926])).
% 2.24/2.46 tff(10928,plain,
% 2.24/2.46 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[5741, 10927, 9972])).
% 2.24/2.46 tff(10929,plain,
% 2.24/2.46 (b(s(s(s(elem!1))), s(elem!1))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[664, 10928, 4353])).
% 2.24/2.46 tff(10930,plain,
% 2.24/2.46 (b(s(s(s(z))), s(z))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[10929, 10332])).
% 2.24/2.46 tff(10931,plain,
% 2.24/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(10932,plain,
% 2.24/2.46 (((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), 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(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(10933,plain,
% 2.24/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z)))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[10932])).
% 2.24/2.46 tff(10934,plain,
% 2.24/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 2.24/2.46 inference(transitivity,[status(thm)],[10933, 10931])).
% 2.24/2.46 tff(10935,plain,
% 2.24/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 2.24/2.46 inference(quant_inst,[status(thm)],[])).
% 2.24/2.46 tff(10936,plain,
% 2.24/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z)))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[10935, 10934])).
% 2.24/2.46 tff(10937,plain,
% 2.24/2.46 ($false),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[10936, 306, 10930, 10920, 10918, 10914])).
% 2.24/2.46 tff(10938,plain,((~(elem!1 = z)) | b(elem!1, s(z)) | b(elem!1, s(s(s(z)))) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.46 tff(10939,plain,
% 2.24/2.46 (~(elem!1 = z)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[10938, 10461, 3, 5])).
% 2.24/2.46 tff(10940,plain,
% 2.24/2.46 (r(elem!1, z)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[174, 10939, 2])).
% 2.24/2.46 tff(10941,plain,
% 2.24/2.46 (~r(z, s(z))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[2273, 359, 246])).
% 2.24/2.46 tff(10942,plain,
% 2.24/2.46 (b(z, s(z))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[2263, 10941])).
% 2.24/2.46 tff(10943,plain,
% 2.24/2.46 (r(s(z), s(s(s(z))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[3302, 3300])).
% 2.24/2.46 tff(10944,plain,
% 2.24/2.46 (~r(elem!1, s(s(s(z))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[3293, 10943, 359])).
% 2.24/2.46 tff(10945,plain,
% 2.24/2.46 (elem!1 = s(s(s(z)))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[2304, 10944, 3])).
% 2.24/2.46 tff(10946,plain,
% 2.24/2.46 (b(s(z), elem!1) <=> b(s(z), s(s(s(z))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[10945])).
% 2.24/2.46 tff(10947,plain,
% 2.24/2.46 (b(s(z), s(s(s(z)))) <=> b(s(z), elem!1)),
% 2.24/2.46 inference(symmetry,[status(thm)],[10946])).
% 2.24/2.46 tff(10948,plain,
% 2.24/2.46 ((~b(s(z), s(s(s(z))))) <=> (~b(s(z), elem!1))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[10947])).
% 2.24/2.46 tff(10949,plain,
% 2.24/2.46 (~b(s(z), elem!1)),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[3300, 10948])).
% 2.24/2.46 tff(10950,plain,
% 2.24/2.46 ($false),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[2831, 10949])).
% 2.24/2.46 tff(10951,plain,(b(s(z), s(s(s(z)))) | (~b(s(z), elem!1)) | b(elem!1, s(s(s(z)))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.46 tff(10952,plain,
% 2.24/2.46 (b(s(z), s(s(s(z))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[10951, 359, 3, 2831])).
% 2.24/2.46 tff(10953,plain,
% 2.24/2.46 (~r(z, s(s(s(z))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[3392, 3313, 246])).
% 2.24/2.46 tff(10954,plain,
% 2.24/2.46 (b(z, s(s(s(z))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[2415, 43, 10953, 2405])).
% 2.24/2.46 tff(10955,plain,
% 2.24/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(10956,plain,
% 2.24/2.46 (((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(10957,plain,
% 2.24/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(z, s(s(s(z)))))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[10956])).
% 2.24/2.46 tff(10958,plain,
% 2.24/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))),
% 2.24/2.46 inference(transitivity,[status(thm)],[10957, 10955])).
% 2.24/2.46 tff(10959,plain,
% 2.24/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))))),
% 2.24/2.46 inference(quant_inst,[status(thm)],[])).
% 2.24/2.46 tff(10960,plain,
% 2.24/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(z, s(s(s(z)))))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[10959, 10958])).
% 2.24/2.46 tff(10961,plain,
% 2.24/2.46 ($false),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[10960, 306, 8, 10115, 10954, 485])).
% 2.24/2.46 tff(10962,plain,((~r(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.46 tff(10963,plain,
% 2.24/2.46 (~r(elem!1, s(s(s(z))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[10962, 10952, 10942, 246])).
% 2.24/2.46 tff(10964,plain,
% 2.24/2.46 (elem!1 = s(s(s(z)))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[2304, 10963, 3])).
% 2.24/2.46 tff(10965,plain,
% 2.24/2.46 (s(elem!1) = s(s(s(s(z))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[10964])).
% 2.24/2.46 tff(10966,plain,
% 2.24/2.46 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[10965])).
% 2.24/2.46 tff(10967,plain,
% 2.24/2.46 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 2.24/2.46 inference(symmetry,[status(thm)],[10966])).
% 2.24/2.46 tff(10968,plain,
% 2.24/2.46 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[10967])).
% 2.24/2.46 tff(10969,plain,
% 2.24/2.46 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(s(s(z))))), s(z))),
% 2.24/2.46 inference(symmetry,[status(thm)],[10968])).
% 2.24/2.46 tff(10970,plain,
% 2.24/2.46 (~r(s(s(elem!1)), s(z))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[9725, 359, 1730])).
% 2.24/2.46 tff(10971,plain,
% 2.24/2.46 (b(s(s(elem!1)), s(z))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[3989, 10970])).
% 2.24/2.46 tff(10972,plain,
% 2.24/2.46 (b(s(s(s(s(s(z))))), s(z))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[10971, 10969])).
% 2.24/2.46 tff(10973,plain,
% 2.24/2.46 (b(s(s(elem!1)), z) <=> b(s(s(s(s(s(z))))), z)),
% 2.24/2.46 inference(monotonicity,[status(thm)],[10966])).
% 2.24/2.46 tff(10974,plain,
% 2.24/2.46 (b(s(s(s(s(s(z))))), z)),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[7788, 10973])).
% 2.24/2.46 tff(10975,plain,
% 2.24/2.46 (s(s(s(z))) = elem!1),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[4555, 10964])).
% 2.24/2.46 tff(10976,plain,
% 2.24/2.46 (r(s(s(s(z))), z)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[2204, 10975, 246])).
% 2.24/2.46 tff(10977,plain,
% 2.24/2.46 (~b(s(s(s(z))), s(z))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[5016, 10964, 5])).
% 2.24/2.46 tff(10978,plain,
% 2.24/2.46 (r(s(s(s(z))), s(z))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[113, 10977])).
% 2.24/2.46 tff(10979,plain,
% 2.24/2.46 (~r(s(z), z)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[211, 10978, 10976])).
% 2.24/2.46 tff(10980,plain,
% 2.24/2.46 (b(s(z), z)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[221, 10979])).
% 2.24/2.46 tff(10981,plain,
% 2.24/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(10982,plain,
% 2.24/2.46 (((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(10983,plain,
% 2.24/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[10982])).
% 2.24/2.46 tff(10984,plain,
% 2.24/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.24/2.46 inference(transitivity,[status(thm)],[10983, 10981])).
% 2.24/2.46 tff(10985,plain,
% 2.24/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.24/2.46 inference(quant_inst,[status(thm)],[])).
% 2.24/2.46 tff(10986,plain,
% 2.24/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[10985, 10984])).
% 2.24/2.46 tff(10987,plain,
% 2.24/2.46 (~b(s(s(s(s(s(z))))), s(z))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[10986, 306, 10952, 10980, 10974, 10942])).
% 2.24/2.46 tff(10988,plain,
% 2.24/2.46 ($false),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[10987, 10972])).
% 2.24/2.46 tff(10989,plain,((~r(elem!1, s(z))) | (~r(elem!1, z)) | b(elem!1, s(z)) | b(elem!1, s(s(s(z)))) | (~b(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.46 tff(10990,plain,
% 2.24/2.46 (~r(elem!1, s(z))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[10989, 10940, 5, 3, 10899, 10461])).
% 2.24/2.46 tff(10991,plain,
% 2.24/2.46 (elem!1 = s(z)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[97, 10990])).
% 2.24/2.46 tff(10992,plain,
% 2.24/2.46 (s(z) = elem!1),
% 2.24/2.46 inference(symmetry,[status(thm)],[10991])).
% 2.24/2.46 tff(10993,plain,
% 2.24/2.46 (b(s(z), elem!1) <=> b(elem!1, elem!1)),
% 2.24/2.46 inference(monotonicity,[status(thm)],[10992])).
% 2.24/2.46 tff(10994,plain,
% 2.24/2.46 (b(elem!1, elem!1) <=> b(s(z), elem!1)),
% 2.24/2.46 inference(symmetry,[status(thm)],[10993])).
% 2.24/2.46 tff(10995,plain,
% 2.24/2.46 ((~b(elem!1, elem!1)) <=> (~b(s(z), elem!1))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[10994])).
% 2.24/2.46 tff(10996,plain,
% 2.24/2.46 (~b(s(z), elem!1)),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[1468, 10995])).
% 2.24/2.46 tff(10997,plain,
% 2.24/2.46 ($false),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[10899, 10996])).
% 2.24/2.46 tff(10998,plain,(b(elem!1, z) | b(elem!1, s(z)) | b(elem!1, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.46 tff(10999,plain,
% 2.24/2.46 (b(elem!1, z)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[10998, 3, 5])).
% 2.24/2.46 tff(11000,plain,
% 2.24/2.46 (b(elem!1, z) <=> b(elem!1, elem!1)),
% 2.24/2.46 inference(monotonicity,[status(thm)],[1502])).
% 2.24/2.46 tff(11001,plain,
% 2.24/2.46 (b(elem!1, elem!1) <=> b(elem!1, z)),
% 2.24/2.46 inference(symmetry,[status(thm)],[11000])).
% 2.24/2.46 tff(11002,plain,
% 2.24/2.46 ((~b(elem!1, elem!1)) <=> (~b(elem!1, z))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[11001])).
% 2.24/2.46 tff(11003,plain,
% 2.24/2.46 (~b(elem!1, z)),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[1468, 11002])).
% 2.24/2.46 tff(11004,plain,
% 2.24/2.46 ($false),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[4012, 11003])).
% 2.24/2.46 tff(11005,plain,((~(z = elem!1)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.46 tff(11006,plain,
% 2.24/2.46 (~(z = elem!1)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[11005, 10999])).
% 2.24/2.46 tff(11007,plain,
% 2.24/2.46 (~(s(elem!1) = s(z))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[2689, 11006])).
% 2.24/2.46 tff(11008,plain,
% 2.24/2.46 (r(elem!1, s(s(s(z))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[2304, 2301, 3])).
% 2.24/2.46 tff(11009,plain,
% 2.24/2.46 (b(s(z), s(s(s(s(s(z)))))) <=> b(s(z), s(s(elem!1)))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[236])).
% 2.24/2.46 tff(11010,assumption,(s(z) = s(s(s(s(s(z)))))), introduced(assumption)).
% 2.24/2.46 tff(11011,plain,
% 2.24/2.46 (s(s(s(s(s(z))))) = s(z)),
% 2.24/2.46 inference(symmetry,[status(thm)],[11010])).
% 2.24/2.46 tff(11012,plain,
% 2.24/2.46 ($false),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[500, 11011])).
% 2.24/2.46 tff(11013,plain,(~(s(z) = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.46 tff(11014,plain,
% 2.24/2.46 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(s(s(elem!1)), elem!1)),
% 2.24/2.46 inference(monotonicity,[status(thm)],[236, 248])).
% 2.24/2.46 tff(11015,plain,
% 2.24/2.46 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.24/2.46 inference(symmetry,[status(thm)],[11014])).
% 2.24/2.46 tff(11016,plain,
% 2.24/2.46 (s(s(s(z))) = elem!1),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[4555, 231])).
% 2.24/2.46 tff(11017,plain,
% 2.24/2.46 (r(elem!1, s(z))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[5326, 11016, 206])).
% 2.24/2.46 tff(11018,plain,
% 2.24/2.46 (~b(s(z), elem!1)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[10951, 11017, 3, 3300])).
% 2.24/2.46 tff(11019,plain,
% 2.24/2.46 (r(z, elem!1)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[835, 5318, 11006])).
% 2.24/2.46 tff(11020,plain,
% 2.24/2.46 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(s(s(s(z))))))),
% 2.24/2.46 inference(symmetry,[status(thm)],[11009])).
% 2.24/2.46 tff(11021,plain,
% 2.24/2.46 ((~b(s(z), s(s(elem!1)))) <=> (~b(s(z), s(s(s(s(s(z)))))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[11020])).
% 2.24/2.46 tff(11022,plain,
% 2.24/2.46 ((~(s(s(elem!1)) = elem!1)) | b(elem!1, s(s(s(z)))) | (~r(s(s(s(z))), s(z))) | b(elem!1, s(z))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[1446, 80])).
% 2.24/2.46 tff(11023,plain,
% 2.24/2.46 (~(s(s(elem!1)) = elem!1)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[11022, 206, 5, 3])).
% 2.24/2.46 tff(11024,plain,
% 2.24/2.46 (~(s(elem!1) = elem!1)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[180, 11023])).
% 2.24/2.46 tff(11025,plain,
% 2.24/2.46 (~(s(s(elem!1)) = s(elem!1))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[195, 11024])).
% 2.24/2.46 tff(11026,plain,
% 2.24/2.46 (~r(s(s(s(z))), elem!1)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[1481, 11017, 206])).
% 2.24/2.46 tff(11027,plain,
% 2.24/2.46 (b(s(s(s(z))), z)),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[10999, 1529])).
% 2.24/2.46 tff(11028,plain,
% 2.24/2.46 (r(z, elem!1) <=> r(z, s(s(s(z))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[231])).
% 2.24/2.46 tff(11029,plain,
% 2.24/2.46 (r(z, s(s(s(z))))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[374, 11028])).
% 2.24/2.46 tff(11030,plain,
% 2.24/2.46 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~r(z, s(s(s(z))))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(11031,plain,
% 2.24/2.46 (((~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~r(z, s(s(s(z))))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(11032,plain,
% 2.24/2.46 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~r(z, s(s(s(z)))))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[11031])).
% 2.24/2.46 tff(11033,plain,
% 2.24/2.46 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~r(z, s(s(s(z))))))),
% 2.24/2.46 inference(transitivity,[status(thm)],[11032, 11030])).
% 2.24/2.46 tff(11034,plain,
% 2.24/2.46 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))),
% 2.24/2.46 inference(quant_inst,[status(thm)],[])).
% 2.24/2.46 tff(11035,plain,
% 2.24/2.46 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~r(z, s(s(s(z)))))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[11034, 11033])).
% 2.24/2.46 tff(11036,plain,
% 2.24/2.46 (~r(s(z), z)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[11035, 124, 10943, 11029])).
% 2.24/2.46 tff(11037,plain,
% 2.24/2.46 (b(s(z), z)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[221, 11036])).
% 2.24/2.46 tff(11038,plain,
% 2.24/2.46 (~r(s(elem!1), elem!1)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[8733, 11037, 10943, 11027, 11007, 374, 11026])).
% 2.24/2.46 tff(11039,plain,
% 2.24/2.46 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[7090, 11038, 11006, 11023])).
% 2.24/2.46 tff(11040,plain,
% 2.24/2.46 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[240, 234])).
% 2.24/2.46 tff(11041,plain,
% 2.24/2.46 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(elem!1))),
% 2.24/2.46 inference(symmetry,[status(thm)],[11040])).
% 2.24/2.46 tff(11042,plain,
% 2.24/2.46 (~r(z, s(z))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[385, 11017, 374])).
% 2.24/2.46 tff(11043,plain,
% 2.24/2.46 (b(z, s(z))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[2263, 11042])).
% 2.24/2.46 tff(11044,plain,
% 2.24/2.46 (b(s(s(s(s(s(s(z)))))), elem!1) <=> b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[231])).
% 2.24/2.46 tff(11045,plain,
% 2.24/2.46 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[7480, 11037, 11017, 374])).
% 2.24/2.46 tff(11046,plain,
% 2.24/2.46 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[1144, 11045, 1127])).
% 2.24/2.46 tff(11047,plain,
% 2.24/2.46 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[11046, 11044])).
% 2.24/2.46 tff(11048,plain,
% 2.24/2.46 (r(s(elem!1), s(s(s(z)))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[234])).
% 2.24/2.46 tff(11049,plain,
% 2.24/2.46 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(s(s(z))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[231])).
% 2.24/2.46 tff(11050,plain,
% 2.24/2.46 (r(s(elem!1), elem!1) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 2.24/2.46 inference(transitivity,[status(thm)],[11049, 11048])).
% 2.24/2.46 tff(11051,plain,
% 2.24/2.46 ((~r(s(elem!1), elem!1)) <=> (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[11050])).
% 2.24/2.46 tff(11052,plain,
% 2.24/2.46 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[11038, 11051])).
% 2.24/2.46 tff(11053,plain,
% 2.24/2.46 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[4471, 11052])).
% 2.24/2.46 tff(11054,plain,
% 2.24/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(11055,plain,
% 2.24/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.24/2.47 inference(quant_inst,[status(thm)],[])).
% 2.24/2.47 tff(11056,plain,
% 2.24/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[11055, 11054])).
% 2.24/2.47 tff(11057,plain,
% 2.24/2.47 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[11056, 306, 11027, 11053, 11047, 11043])).
% 2.24/2.47 tff(11058,plain,
% 2.24/2.47 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[10662, 11057])).
% 2.24/2.47 tff(11059,plain,
% 2.24/2.47 (r(s(s(s(elem!1))), s(elem!1))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[11058, 11041])).
% 2.24/2.47 tff(11060,plain,
% 2.24/2.47 (~r(s(s(elem!1)), s(elem!1))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[659, 11059, 11039])).
% 2.24/2.47 tff(11061,plain,
% 2.24/2.47 (b(s(s(elem!1)), s(elem!1))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[994, 11060, 11025])).
% 2.24/2.47 tff(11062,plain,
% 2.24/2.47 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[143, 11023])).
% 2.24/2.47 tff(11063,plain,
% 2.24/2.47 ((elem!1 = s(z)) <=> (s(s(s(z))) = s(z))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[231])).
% 2.24/2.47 tff(11064,plain,
% 2.24/2.47 ((s(s(s(z))) = s(z)) <=> (elem!1 = s(z))),
% 2.24/2.47 inference(symmetry,[status(thm)],[11063])).
% 2.24/2.47 tff(11065,plain,
% 2.24/2.47 ((s(s(s(z))) = s(z)) <=> (s(z) = elem!1)),
% 2.24/2.47 inference(transitivity,[status(thm)],[11064, 3092])).
% 2.24/2.47 tff(11066,plain,
% 2.24/2.47 ((~(s(s(s(z))) = s(z))) <=> (~(s(z) = elem!1))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[11065])).
% 2.24/2.47 tff(11067,plain,
% 2.24/2.47 (~(s(z) = elem!1)),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[108, 11066])).
% 2.24/2.47 tff(11068,plain,
% 2.24/2.47 (b(s(elem!1), elem!1)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[813, 11038, 11024])).
% 2.24/2.47 tff(11069,plain,
% 2.24/2.47 (b(s(s(s(z))), elem!1) <=> b(elem!1, elem!1)),
% 2.24/2.47 inference(monotonicity,[status(thm)],[248])).
% 2.24/2.47 tff(11070,plain,
% 2.24/2.47 (b(elem!1, elem!1) <=> b(s(s(s(z))), elem!1)),
% 2.24/2.47 inference(symmetry,[status(thm)],[11069])).
% 2.24/2.47 tff(11071,plain,
% 2.24/2.47 ((~b(elem!1, elem!1)) <=> (~b(s(s(s(z))), elem!1))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[11070])).
% 2.24/2.47 tff(11072,plain,
% 2.24/2.47 (~b(s(s(s(z))), elem!1)),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[1468, 11071])).
% 2.24/2.47 tff(11073,plain,
% 2.24/2.47 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[240, 234])).
% 2.24/2.47 tff(11074,plain,
% 2.24/2.47 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 2.24/2.47 inference(symmetry,[status(thm)],[11073])).
% 2.24/2.47 tff(11075,plain,
% 2.24/2.47 ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) <=> (~b(s(s(s(elem!1))), s(elem!1)))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[11074])).
% 2.24/2.47 tff(11076,plain,
% 2.24/2.47 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[11057, 11075])).
% 2.24/2.47 tff(11077,plain,
% 2.24/2.47 (~b(s(s(s(z))), s(z))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[5016, 231, 5])).
% 2.24/2.47 tff(11078,plain,
% 2.24/2.47 (r(s(s(s(z))), s(z))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[113, 11077])).
% 2.24/2.47 tff(11079,plain,
% 2.24/2.47 (~(s(s(elem!1)) = elem!1)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[11022, 11078, 5, 3])).
% 2.24/2.47 tff(11080,plain,
% 2.24/2.47 (~(elem!1 = s(z))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[82, 11077, 6])).
% 2.24/2.47 tff(11081,plain,
% 2.24/2.47 (~(s(z) = elem!1)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[89, 11080])).
% 2.24/2.47 tff(11082,plain,
% 2.24/2.47 (r(s(z), elem!1)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[4192, 11081])).
% 2.24/2.47 tff(11083,plain,
% 2.24/2.47 (b(s(s(elem!1)), elem!1)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[47, 11079, 6])).
% 2.24/2.47 tff(11084,plain,
% 2.24/2.47 ((z = elem!1) <=> (z = s(s(s(z))))),
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% 2.24/2.47 inference(symmetry,[status(thm)],[11085])).
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% 2.24/2.47 inference(monotonicity,[status(thm)],[11086])).
% 2.24/2.47 tff(11088,plain,
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% 2.24/2.47 inference(modus_ponens,[status(thm)],[169, 11087])).
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% 2.24/2.47 inference(unit_resolution,[status(thm)],[5326, 206, 11016])).
% 2.24/2.47 tff(11090,plain,
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% 2.24/2.47 inference(modus_ponens,[status(thm)],[4012, 1529])).
% 2.24/2.47 tff(11091,plain,
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% 2.24/2.47 inference(unit_resolution,[status(thm)],[2263, 386])).
% 2.24/2.47 tff(11092,plain,
% 2.24/2.47 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[7480, 374, 359, 247])).
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% 2.24/2.47 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[1144, 11092, 1127])).
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% 2.24/2.47 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[11093, 11044])).
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% 2.24/2.47 inference(monotonicity,[status(thm)],[234])).
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% 2.24/2.47 ((s(s(s(s(z)))) = s(z)) <=> (s(elem!1) = s(z))),
% 2.24/2.47 inference(symmetry,[status(thm)],[11095])).
% 2.24/2.47 tff(11097,plain,
% 2.24/2.47 ((~(s(s(s(s(z)))) = s(z))) <=> (~(s(elem!1) = s(z)))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[11096])).
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% 2.24/2.47 inference(modus_ponens,[status(thm)],[324, 11097])).
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% 2.24/2.47 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[11099, 11051])).
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% 2.24/2.47 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[4471, 11100])).
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% 2.24/2.47 inference(modus_ponens,[status(thm)],[11102, 11075])).
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% 2.24/2.47 tff(11106,plain,
% 2.24/2.47 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(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)))))))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
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% 2.24/2.47 inference(monotonicity,[status(thm)],[11106])).
% 2.24/2.47 tff(11108,plain,
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% 2.24/2.47 inference(transitivity,[status(thm)],[11107, 11105])).
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% 2.24/2.47 inference(quant_inst,[status(thm)],[])).
% 2.24/2.47 tff(11110,plain,
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% 2.24/2.47 inference(modus_ponens,[status(thm)],[11109, 11108])).
% 2.24/2.47 tff(11111,plain,
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% 2.24/2.47 inference(unit_resolution,[status(thm)],[11110, 306, 393, 762, 1027, 245])).
% 2.24/2.47 tff(11112,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.47 tff(11113,plain,
% 2.24/2.47 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[11112, 762, 393, 245])).
% 2.24/2.47 tff(11114,plain,
% 2.24/2.47 (~b(s(s(elem!1)), s(elem!1))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[11113, 1119])).
% 2.24/2.47 tff(11115,plain,
% 2.24/2.47 (r(s(s(elem!1)), s(elem!1))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[994, 11114, 403])).
% 2.24/2.47 tff(11116,plain,
% 2.24/2.47 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(11117,plain,
% 2.24/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[11116])).
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% 2.24/2.47 inference(modus_ponens,[status(thm)],[11119, 11118])).
% 2.24/2.47 tff(11121,plain,
% 2.24/2.47 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[11120, 306, 393, 762, 1330])).
% 2.24/2.47 tff(11122,plain,
% 2.24/2.47 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[11121, 1353])).
% 2.24/2.47 tff(11123,plain,
% 2.24/2.47 (r(s(s(s(elem!1))), s(elem!1))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[664, 11122, 150])).
% 2.24/2.47 tff(11124,plain,
% 2.24/2.47 ($false),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[659, 11123, 11115, 653])).
% 2.24/2.47 tff(11125,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(s(elem!1))) = s(elem!1)) | (s(s(elem!1)) = s(elem!1)) | (~(elem!1 = s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.47 tff(11126,plain,
% 2.24/2.47 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[11125, 11101, 245, 231, 144, 196, 11094, 11104])).
% 2.24/2.47 tff(11127,plain,
% 2.24/2.47 (r(elem!1, s(elem!1)) | b(s(s(s(z))), s(s(s(s(z))))) | (~(elem!1 = s(s(s(z)))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[353, 4470])).
% 2.24/2.47 tff(11128,plain,
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% 2.24/2.47 tff(11129,plain,
% 2.24/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(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)))))))),
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% 2.24/2.47 tff(11130,plain,
% 2.24/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.24/2.47 inference(quant_inst,[status(thm)],[])).
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% 2.24/2.47 inference(modus_ponens,[status(thm)],[11130, 11129])).
% 2.24/2.47 tff(11132,plain,
% 2.24/2.47 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[11131, 306, 1531, 11101, 245, 11091])).
% 2.24/2.47 tff(11133,plain,
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% 2.24/2.47 inference(unit_resolution,[status(thm)],[1010, 11132, 231])).
% 2.24/2.47 tff(11134,plain,
% 2.24/2.47 (r(s(s(elem!1)), s(elem!1))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[994, 11133, 196])).
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% 2.24/2.47 (b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[1587, 600])).
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% 2.24/2.47 inference(modus_ponens,[status(thm)],[1589, 877])).
% 2.24/2.47 tff(11137,plain,
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% 2.24/2.47 inference(modus_ponens,[status(thm)],[5852, 481])).
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% 2.24/2.47 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[11137, 480])).
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% 2.24/2.47 inference(modus_ponens,[status(thm)],[4084, 535])).
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% 2.24/2.47 inference(unit_resolution,[status(thm)],[559, 43, 556])).
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% 2.24/2.47 inference(monotonicity,[status(thm)],[11143])).
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% 2.24/2.47 inference(modus_ponens,[status(thm)],[11146, 11145])).
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% 2.24/2.47 inference(unit_resolution,[status(thm)],[11147, 306, 11141])).
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% 2.24/2.47 inference(unit_resolution,[status(thm)],[11148, 11138, 11136, 11135])).
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% 2.24/2.47 tff(11151,plain,
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% 2.24/2.47 inference(unit_resolution,[status(thm)],[11150, 11134, 231, 187, 11128, 153])).
% 2.24/2.47 tff(11152,plain,
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% 2.24/2.47 inference(unit_resolution,[status(thm)],[664, 11151, 144])).
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% 2.24/2.47 inference(unit_resolution,[status(thm)],[11152, 11103])).
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% 2.24/2.48 inference(monotonicity,[status(thm)],[231, 240])).
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% 2.24/2.48 ((s(s(s(z))) = s(s(s(s(s(s(z))))))) <=> (elem!1 = s(s(s(elem!1))))),
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% 2.24/2.48 ((s(s(s(z))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(elem!1))) = elem!1)),
% 2.24/2.48 inference(transitivity,[status(thm)],[11159, 1555])).
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% 2.24/2.48 inference(monotonicity,[status(thm)],[11160])).
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% 2.24/2.48 inference(modus_ponens,[status(thm)],[556, 11161])).
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% 2.24/2.48 inference(unit_resolution,[status(thm)],[11176, 953])).
% 2.24/2.48 tff(11178,plain,((~b(z, s(s(s(elem!1))))) | (~(elem!1 = s(s(s(z))))) | (~b(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~b(elem!1, z)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.48 tff(11179,plain,
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% 2.24/2.48 tff(11180,plain,
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% 2.24/2.48 inference(symmetry,[status(thm)],[11181])).
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% 2.24/2.48 inference(monotonicity,[status(thm)],[11182])).
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% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(11186,plain,
% 2.24/2.48 (((~b(z, s(s(s(z))))) | (~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(s(s(s(z))), z)) | (~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))))))))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(11187,plain,
% 2.24/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z)))))))))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[11186])).
% 2.24/2.48 tff(11188,plain,
% 2.24/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))))),
% 2.24/2.48 inference(transitivity,[status(thm)],[11187, 11185])).
% 2.24/2.48 tff(11189,plain,
% 2.24/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~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))))))))),
% 2.24/2.48 inference(quant_inst,[status(thm)],[])).
% 2.24/2.48 tff(11190,plain,
% 2.24/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~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)))))))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[11189, 11188])).
% 2.24/2.48 tff(11191,plain,
% 2.24/2.48 (~b(z, s(s(s(s(s(z))))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[11190, 306, 11090, 11184, 1016])).
% 2.24/2.48 tff(11192,plain,
% 2.24/2.48 (~b(z, s(s(elem!1)))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[11191, 11183])).
% 2.24/2.48 tff(11193,plain,
% 2.24/2.48 (r(z, s(s(elem!1)))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[460, 11192])).
% 2.24/2.48 tff(11194,plain,
% 2.24/2.48 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[950, 11193, 11180])).
% 2.24/2.48 tff(11195,plain,
% 2.24/2.48 (r(s(elem!1), elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[7090, 11194, 11088, 91])).
% 2.24/2.48 tff(11196,plain,
% 2.24/2.48 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[805, 11195, 231])).
% 2.24/2.48 tff(11197,plain,
% 2.24/2.48 (~r(s(s(s(s(z)))), s(z))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[1040, 124, 1034, 11196])).
% 2.24/2.48 tff(11198,plain,
% 2.24/2.48 (b(s(s(s(s(z)))), s(z))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[4490, 11197])).
% 2.24/2.48 tff(11199,plain,
% 2.24/2.48 (~b(s(s(elem!1)), z)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[3976, 11155, 3062, 11088, 30])).
% 2.24/2.48 tff(11200,plain,
% 2.24/2.48 (r(s(s(elem!1)), z)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[476, 11199])).
% 2.24/2.48 tff(11201,plain,
% 2.24/2.48 (~r(s(z), s(s(s(s(z)))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[3585, 124, 1034, 11196])).
% 2.24/2.48 tff(11202,plain,
% 2.24/2.48 (b(s(z), s(s(s(s(z)))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[5135, 11201])).
% 2.24/2.48 tff(11203,plain,
% 2.24/2.48 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[610, 11194, 160])).
% 2.24/2.48 tff(11204,plain,
% 2.24/2.48 (b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[605, 11203, 231])).
% 2.24/2.48 tff(11205,plain,
% 2.24/2.48 (b(s(elem!1), z) <=> b(s(s(s(s(z)))), z)),
% 2.24/2.48 inference(monotonicity,[status(thm)],[234])).
% 2.24/2.48 tff(11206,plain,
% 2.24/2.48 ((~b(s(elem!1), z)) <=> (~b(s(s(s(s(z)))), z))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[11205])).
% 2.24/2.48 tff(11207,plain,
% 2.24/2.48 (~b(s(s(s(s(z)))), z)),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[2378, 11206])).
% 2.24/2.48 tff(11208,plain,
% 2.24/2.48 (r(s(s(s(s(z)))), z)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[695, 11207])).
% 2.24/2.48 tff(11209,plain,
% 2.24/2.48 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[448, 11208, 231, 437])).
% 2.24/2.48 tff(11210,plain,
% 2.24/2.48 ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) | b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[432, 43, 11209])).
% 2.24/2.48 tff(11211,plain,
% 2.24/2.48 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[11210, 404])).
% 2.24/2.48 tff(11212,plain,
% 2.24/2.48 (r(s(elem!1), z)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[2380, 2378])).
% 2.24/2.48 tff(11213,plain,
% 2.24/2.48 (~r(s(s(elem!1)), s(elem!1))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[471, 11212, 465])).
% 2.24/2.48 tff(11214,plain,
% 2.24/2.48 (b(s(s(elem!1)), s(elem!1))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[994, 11213, 403])).
% 2.24/2.48 tff(11215,plain,
% 2.24/2.48 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[1010, 11214, 231])).
% 2.24/2.48 tff(11216,plain,
% 2.24/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(11217,plain,
% 2.24/2.48 (((~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(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(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(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(11218,plain,
% 2.24/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[11217])).
% 2.24/2.48 tff(11219,plain,
% 2.24/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.24/2.48 inference(transitivity,[status(thm)],[11218, 11216])).
% 2.24/2.48 tff(11220,plain,
% 2.24/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.24/2.48 inference(quant_inst,[status(thm)],[])).
% 2.24/2.48 tff(11221,plain,
% 2.24/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[11220, 11219])).
% 2.24/2.48 tff(11222,plain,
% 2.24/2.48 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[11221, 306, 11215, 521, 3620, 11211])).
% 2.24/2.48 tff(11223,plain,
% 2.24/2.48 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[11222, 11075])).
% 2.24/2.48 tff(11224,plain,
% 2.24/2.48 (r(elem!1, s(s(elem!1))) <=> r(s(s(s(z))), s(s(elem!1)))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[231])).
% 2.24/2.48 tff(11225,plain,
% 2.24/2.48 (r(s(s(s(z))), s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 2.24/2.48 inference(symmetry,[status(thm)],[11224])).
% 2.24/2.48 tff(11226,plain,
% 2.24/2.48 (r(s(s(s(z))), s(s(s(s(s(z)))))) <=> r(s(s(s(z))), s(s(elem!1)))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[236])).
% 2.24/2.48 tff(11227,plain,
% 2.24/2.48 (r(s(s(s(z))), s(s(s(s(s(z)))))) <=> r(elem!1, s(s(elem!1)))),
% 2.24/2.48 inference(transitivity,[status(thm)],[11226, 11225])).
% 2.24/2.48 tff(11228,plain,
% 2.24/2.48 ((~r(s(s(s(z))), s(s(s(s(s(z))))))) <=> (~r(elem!1, s(s(elem!1))))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[11227])).
% 2.24/2.48 tff(11229,plain,
% 2.24/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(11230,plain,
% 2.24/2.48 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(11231,plain,
% 2.24/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[11230])).
% 2.24/2.48 tff(11232,plain,
% 2.24/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.24/2.48 inference(transitivity,[status(thm)],[11231, 11229])).
% 2.24/2.48 tff(11233,plain,
% 2.24/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.24/2.48 inference(quant_inst,[status(thm)],[])).
% 2.24/2.48 tff(11234,plain,
% 2.24/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[11233, 11232])).
% 2.24/2.48 tff(11235,plain,
% 2.24/2.48 (~b(s(s(s(s(s(z))))), s(z))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[11234, 306, 3603, 11215, 3620])).
% 2.24/2.48 tff(11236,plain,
% 2.24/2.48 (r(s(s(s(s(s(z))))), s(z))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[503, 43, 500, 11235])).
% 2.24/2.48 tff(11237,plain,
% 2.24/2.48 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[510, 124, 206, 11236])).
% 2.24/2.48 tff(11238,plain,
% 2.24/2.48 (~r(elem!1, s(s(elem!1)))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[11237, 11228])).
% 2.24/2.48 tff(11239,plain,
% 2.24/2.48 (b(elem!1, s(s(elem!1)))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[516, 11238, 360])).
% 2.24/2.48 tff(11240,plain,
% 2.24/2.48 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[11239, 482])).
% 2.24/2.48 tff(11241,plain,
% 2.24/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(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(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(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(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(11242,plain,
% 2.24/2.48 (((~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(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(11243,plain,
% 2.24/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[11242])).
% 2.24/2.48 tff(11244,plain,
% 2.24/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.24/2.48 inference(transitivity,[status(thm)],[11243, 11241])).
% 2.24/2.48 tff(11245,plain,
% 2.24/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.24/2.48 inference(quant_inst,[status(thm)],[])).
% 2.24/2.48 tff(11246,plain,
% 2.24/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(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(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[11245, 11244])).
% 2.24/2.48 tff(11247,plain,
% 2.24/2.48 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[11246, 306, 11215, 11240, 3620, 11211])).
% 2.24/2.48 tff(11248,plain,
% 2.24/2.48 (r(elem!1, s(elem!1))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[11127, 11247, 231])).
% 2.24/2.48 tff(11249,plain,
% 2.24/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(11250,plain,
% 2.24/2.48 (((~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(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(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(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(11251,plain,
% 2.24/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[11250])).
% 2.24/2.49 tff(11252,plain,
% 2.24/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 2.24/2.49 inference(transitivity,[status(thm)],[11251, 11249])).
% 2.24/2.49 tff(11253,plain,
% 2.24/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 2.24/2.49 inference(quant_inst,[status(thm)],[])).
% 2.24/2.49 tff(11254,plain,
% 2.24/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[11253, 11252])).
% 2.24/2.49 tff(11255,plain,
% 2.24/2.49 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[11254, 306, 11215, 11240, 521, 11211])).
% 2.24/2.49 tff(11256,plain,
% 2.24/2.49 (r(elem!1, s(s(s(elem!1))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[562, 11255, 231])).
% 2.24/2.49 tff(11257,plain,
% 2.24/2.49 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[4083, 11256, 11248])).
% 2.24/2.49 tff(11258,plain,
% 2.24/2.49 (b(s(s(s(elem!1))), s(elem!1))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[664, 11257, 150])).
% 2.24/2.49 tff(11259,plain,
% 2.24/2.49 ($false),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[11258, 11223])).
% 2.24/2.49 tff(11260,plain,(b(s(elem!1), z) | (~(elem!1 = s(s(s(z))))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (elem!1 = s(s(elem!1))) | (s(s(elem!1)) = s(elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(elem!1)))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.49 tff(11261,plain,
% 2.24/2.49 (b(s(elem!1), z)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[11260, 11198, 144, 231, 11193, 187, 196, 206, 11204, 11202, 11200])).
% 2.24/2.49 tff(11262,plain,
% 2.24/2.49 (~b(elem!1, s(elem!1))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[4020, 11261, 4012, 11156])).
% 2.24/2.49 tff(11263,plain,
% 2.24/2.49 (r(elem!1, s(elem!1))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[372, 11262, 5621])).
% 2.24/2.49 tff(11264,plain,
% 2.24/2.49 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[5852, 482])).
% 2.24/2.49 tff(11265,plain,
% 2.24/2.49 (~r(s(elem!1), z)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[471, 244, 465])).
% 2.24/2.49 tff(11266,plain,
% 2.24/2.49 (~r(s(s(s(s(z)))), z)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[411, 11265, 231])).
% 2.24/2.49 tff(11267,plain,
% 2.24/2.49 (b(s(s(s(s(z)))), z)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[695, 11266])).
% 2.24/2.49 tff(11268,plain,
% 2.24/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(11269,plain,
% 2.24/2.49 (((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(11270,plain,
% 2.24/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[11269])).
% 2.24/2.49 tff(11271,plain,
% 2.24/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.24/2.49 inference(transitivity,[status(thm)],[11270, 11268])).
% 2.24/2.49 tff(11272,plain,
% 2.24/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 2.24/2.49 inference(quant_inst,[status(thm)],[])).
% 2.24/2.49 tff(11273,plain,
% 2.24/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[11272, 11271])).
% 2.24/2.49 tff(11274,plain,
% 2.24/2.49 ($false),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[11273, 306, 11267, 859, 247, 3603, 11264])).
% 2.24/2.49 tff(11275,plain,((~r(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~(elem!1 = s(s(s(z))))) | (elem!1 = s(s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.49 tff(11276,plain,
% 2.24/2.49 (~r(s(s(elem!1)), s(elem!1))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[11275, 11184, 247, 11202, 231, 187, 11263, 11200])).
% 2.24/2.49 tff(11277,plain,
% 2.24/2.49 (b(s(s(elem!1)), s(elem!1))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[994, 11276, 196])).
% 2.24/2.49 tff(11278,plain,
% 2.24/2.49 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[1010, 11277, 231])).
% 2.24/2.49 tff(11279,plain,
% 2.24/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(11280,plain,
% 2.24/2.49 (((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(11281,plain,
% 2.24/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z)))))))))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[11280])).
% 2.24/2.49 tff(11282,plain,
% 2.24/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.24/2.49 inference(transitivity,[status(thm)],[11281, 11279])).
% 2.24/2.49 tff(11283,plain,
% 2.24/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.24/2.49 inference(quant_inst,[status(thm)],[])).
% 2.24/2.49 tff(11284,plain,
% 2.24/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z)))))))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[11283, 11282])).
% 2.24/2.49 tff(11285,plain,
% 2.24/2.49 (~b(s(z), s(s(s(s(s(z))))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[11284, 306, 247, 11202, 11278, 11198])).
% 2.24/2.49 tff(11286,plain,
% 2.24/2.49 (r(z, s(s(elem!1))) <=> r(z, s(s(s(s(s(z))))))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[235])).
% 2.24/2.49 tff(11287,plain,
% 2.24/2.49 (r(z, s(s(s(s(s(z))))))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[11193, 11286])).
% 2.24/2.49 tff(11288,plain,
% 2.24/2.49 ((~(s(elem!1) = elem!1)) <=> (~(s(elem!1) = s(s(s(z)))))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[10212])).
% 2.24/2.49 tff(11289,plain,
% 2.24/2.49 (~(s(elem!1) = s(s(s(z))))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[181, 11288])).
% 2.24/2.49 tff(11290,plain,
% 2.24/2.49 (~b(z, s(z))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[8078, 11261, 11098, 11090, 247, 1034, 11289])).
% 2.24/2.49 tff(11291,plain,
% 2.24/2.49 (r(z, s(z))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[2263, 11290])).
% 2.24/2.49 tff(11292,assumption,(r(s(z), s(s(s(s(s(z))))))), introduced(assumption)).
% 2.24/2.49 tff(11293,assumption,(r(z, s(s(s(s(s(z))))))), introduced(assumption)).
% 2.24/2.49 tff(11294,plain,
% 2.24/2.49 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(11295,plain,
% 2.24/2.49 (((~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(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(11296,plain,
% 2.24/2.49 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z)))))))))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[11295])).
% 2.24/2.49 tff(11297,plain,
% 2.24/2.49 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.24/2.49 inference(transitivity,[status(thm)],[11296, 11294])).
% 2.24/2.49 tff(11298,plain,
% 2.24/2.49 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(z))))),
% 2.24/2.49 inference(quant_inst,[status(thm)],[])).
% 2.24/2.49 tff(11299,plain,
% 2.24/2.49 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z)))))))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[11298, 11297])).
% 2.24/2.49 tff(11300,plain,
% 2.24/2.49 ($false),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[11299, 124, 2265, 11293, 11292])).
% 2.24/2.49 tff(11301,plain,((~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.49 tff(11302,plain,
% 2.24/2.49 (~r(s(z), s(s(s(s(s(z))))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[11301, 11291, 11287])).
% 2.24/2.49 tff(11303,plain,
% 2.24/2.49 ($false),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[626, 43, 11302, 11013, 11285])).
% 2.24/2.49 tff(11304,plain,((~b(s(z), z)) | (~(elem!1 = s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~b(elem!1, z)) | (~r(s(s(s(z))), s(z))) | (s(s(elem!1)) = elem!1) | r(elem!1, z) | (~b(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.49 tff(11305,plain,
% 2.24/2.49 (~b(s(z), z)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[11304, 231, 1034, 10999, 11078, 11079, 3062, 11083, 11082])).
% 2.24/2.49 tff(11306,plain,
% 2.24/2.49 (r(s(z), z)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[221, 11305])).
% 2.24/2.49 tff(11307,plain,
% 2.24/2.49 (r(z, elem!1)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[4167, 11306, 5, 6, 3062, 2715, 11079])).
% 2.24/2.49 tff(11308,plain,
% 2.24/2.49 (r(z, s(s(s(z))))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[11307, 11028])).
% 2.24/2.49 tff(11309,plain,
% 2.24/2.49 ($false),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[11035, 124, 11306, 1034, 11308])).
% 2.24/2.49 tff(11310,plain,((~(elem!1 = s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | b(elem!1, s(z)) | r(s(s(elem!1)), elem!1) | r(elem!1, z) | b(s(z), elem!1) | b(elem!1, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.49 tff(11311,plain,
% 2.24/2.49 (r(elem!1, z)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[11310, 6, 5, 1034, 2715, 231, 3])).
% 2.24/2.49 tff(11312,plain,
% 2.24/2.49 (~r(elem!1, s(s(elem!1)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[1364, 11311, 653, 231, 9171, 181, 144])).
% 2.24/2.49 tff(11313,plain,
% 2.24/2.49 (~b(elem!1, s(s(elem!1)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[1024, 9171, 816, 1005])).
% 2.24/2.49 tff(11314,plain,
% 2.24/2.49 ($false),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[516, 11313, 11312, 187])).
% 2.24/2.49 tff(11315,plain,(r(s(s(elem!1)), elem!1) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~(elem!1 = s(s(s(z))))) | (s(s(elem!1)) = elem!1) | b(elem!1, s(z)) | (~r(s(z), s(s(s(z))))) | b(s(z), elem!1) | b(elem!1, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.49 tff(11316,plain,
% 2.24/2.49 (r(s(s(elem!1)), elem!1)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[11315, 11068, 11061, 11039, 231, 11023, 5, 10943, 11018, 3])).
% 2.24/2.49 tff(11317,plain,
% 2.24/2.49 (~r(s(s(s(elem!1))), elem!1)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[7780, 1730, 653])).
% 2.24/2.49 tff(11318,plain,
% 2.24/2.49 (~(elem!1 = s(elem!1))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[364, 1176])).
% 2.24/2.49 tff(11319,plain,
% 2.24/2.49 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[2974, 5331])).
% 2.24/2.49 tff(11320,plain,
% 2.24/2.49 (r(s(s(s(elem!1))), s(elem!1))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[664, 6236, 150])).
% 2.24/2.49 tff(11321,plain,
% 2.24/2.49 (~r(s(s(elem!1)), s(elem!1))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[659, 11320, 653])).
% 2.24/2.49 tff(11322,plain,
% 2.24/2.49 (b(s(s(elem!1)), s(elem!1))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[994, 11321, 1182])).
% 2.24/2.49 tff(11323,plain,
% 2.24/2.49 (r(s(elem!1), s(z))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[2964, 2609, 3099])).
% 2.24/2.49 tff(11324,plain,
% 2.24/2.49 (~(s(elem!1) = s(s(elem!1)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[4689, 1182])).
% 2.24/2.49 tff(11325,plain,
% 2.24/2.49 (~b(elem!1, s(z))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[8234, 838, 247, 4012])).
% 2.24/2.49 tff(11326,plain,
% 2.24/2.49 (r(elem!1, s(z))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[96, 43, 11325, 87])).
% 2.24/2.49 tff(11327,plain,
% 2.24/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(11328,plain,
% 2.24/2.49 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1)))) <=> ((~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(11329,plain,
% 2.24/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1))))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[11328])).
% 2.24/2.49 tff(11330,plain,
% 2.24/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)))),
% 2.24/2.49 inference(transitivity,[status(thm)],[11329, 11327])).
% 2.24/2.49 tff(11331,plain,
% 2.24/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))),
% 2.24/2.49 inference(quant_inst,[status(thm)],[])).
% 2.24/2.49 tff(11332,plain,
% 2.24/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[11331, 11330])).
% 2.24/2.49 tff(11333,plain,
% 2.24/2.49 (~b(z, s(elem!1))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[11332, 306, 838, 4012, 816])).
% 2.24/2.49 tff(11334,plain,
% 2.24/2.49 (r(z, s(elem!1))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[275, 11333])).
% 2.24/2.49 tff(11335,plain,
% 2.24/2.49 (~r(z, s(s(s(elem!1))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[5741, 11334, 654])).
% 2.24/2.49 tff(11336,plain,
% 2.24/2.49 (b(z, s(s(s(elem!1))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[585, 11335])).
% 2.24/2.49 tff(11337,plain,
% 2.24/2.49 (~b(s(s(s(elem!1))), elem!1)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[6150, 11336, 838, 4012])).
% 2.24/2.49 tff(11338,plain,
% 2.24/2.49 (s(s(s(elem!1))) = elem!1),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[1636, 11337, 7789])).
% 2.24/2.49 tff(11339,plain,
% 2.24/2.49 (~b(elem!1, s(elem!1))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[6239, 11338, 6236])).
% 2.24/2.49 tff(11340,plain,
% 2.24/2.49 (r(elem!1, s(elem!1))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[372, 11339, 366])).
% 2.24/2.49 tff(11341,plain,
% 2.24/2.49 ($false),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[7653, 124, 11340, 11326, 2626])).
% 2.24/2.49 tff(11342,plain,((~b(z, elem!1)) | (~r(s(elem!1), s(z))) | (elem!1 = s(elem!1)) | b(s(s(s(elem!1))), s(elem!1)) | r(s(s(s(elem!1))), elem!1) | (~b(elem!1, z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (elem!1 = s(z)) | (~b(s(elem!1), elem!1)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.50 tff(11343,plain,
% 2.24/2.50 (~b(z, elem!1)),
% 2.24/2.50 inference(unit_resolution,[status(thm)],[11342, 4012, 366, 6236, 7789, 2626, 654, 5331, 816, 247])).
% 2.24/2.50 tff(11344,plain,
% 2.24/2.50 (r(z, elem!1)),
% 2.24/2.50 inference(unit_resolution,[status(thm)],[835, 11343, 2170])).
% 2.24/2.50 tff(11345,plain,
% 2.24/2.50 (~r(s(s(elem!1)), z)),
% 2.24/2.50 inference(unit_resolution,[status(thm)],[6539, 124, 11344, 1730])).
% 2.24/2.50 tff(11346,plain,
% 2.24/2.50 (b(s(s(elem!1)), z)),
% 2.24/2.50 inference(unit_resolution,[status(thm)],[476, 11345])).
% 2.24/2.50 tff(11347,plain,
% 2.24/2.50 (~r(z, s(s(elem!1)))),
% 2.24/2.50 inference(unit_resolution,[status(thm)],[5837, 11344, 1730])).
% 2.24/2.50 tff(11348,plain,
% 2.24/2.50 (b(z, s(s(elem!1)))),
% 2.24/2.50 inference(unit_resolution,[status(thm)],[460, 11347])).
% 2.24/2.50 tff(11349,plain,
% 2.24/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)))),
% 2.24/2.50 inference(rewrite,[status(thm)],[])).
% 2.24/2.50 tff(11350,plain,
% 2.24/2.50 (((~b(s(s(elem!1)), s(elem!1))) | (~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)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)))),
% 2.24/2.50 inference(rewrite,[status(thm)],[])).
% 2.24/2.50 tff(11351,plain,
% 2.24/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z))))),
% 2.24/2.50 inference(monotonicity,[status(thm)],[11350])).
% 2.24/2.50 tff(11352,plain,
% 2.24/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)))),
% 2.24/2.50 inference(transitivity,[status(thm)],[11351, 11349])).
% 2.24/2.50 tff(11353,plain,
% 2.24/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))),
% 2.24/2.50 inference(quant_inst,[status(thm)],[])).
% 2.24/2.50 tff(11354,plain,
% 2.24/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z))),
% 2.24/2.50 inference(modus_ponens,[status(thm)],[11353, 11352])).
% 2.24/2.50 tff(11355,plain,
% 2.24/2.50 (~b(s(s(elem!1)), s(z))),
% 2.24/2.50 inference(unit_resolution,[status(thm)],[11354, 306, 1005, 11348, 11346, 247])).
% 2.24/2.50 tff(11356,plain,
% 2.24/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), z)))),
% 2.34/2.50 inference(rewrite,[status(thm)],[])).
% 2.34/2.50 tff(11357,plain,
% 2.34/2.50 (((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1))) <=> ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), z)))),
% 2.34/2.50 inference(rewrite,[status(thm)],[])).
% 2.34/2.50 tff(11358,plain,
% 2.34/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), z))))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[11357])).
% 2.34/2.50 tff(11359,plain,
% 2.34/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), z)))),
% 2.34/2.50 inference(transitivity,[status(thm)],[11358, 11356])).
% 2.34/2.50 tff(11360,plain,
% 2.34/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 2.34/2.50 inference(quant_inst,[status(thm)],[])).
% 2.34/2.50 tff(11361,plain,
% 2.34/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), z))),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[11360, 11359])).
% 2.34/2.50 tff(11362,plain,
% 2.34/2.50 (~b(s(z), elem!1)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[11361, 306, 4012, 1005, 11348, 247])).
% 2.34/2.50 tff(11363,plain,
% 2.34/2.50 (r(s(z), elem!1)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[1500, 43, 11362, 3094])).
% 2.34/2.50 tff(11364,plain,
% 2.34/2.50 (~r(s(s(elem!1)), s(z))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[8826, 11363, 1730])).
% 2.34/2.50 tff(11365,plain,
% 2.34/2.50 ($false),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[3989, 11364, 11355])).
% 2.34/2.50 tff(11366,plain,((~b(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), z)) | (s(z) = elem!1) | (z = elem!1) | (elem!1 = s(elem!1)) | b(s(s(s(elem!1))), s(elem!1)) | r(s(s(s(elem!1))), elem!1) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.50 tff(11367,plain,
% 2.34/2.50 (~b(elem!1, z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[11366, 247, 1005, 1730, 3094, 2170, 366, 6236, 11317, 2626, 654, 816])).
% 2.34/2.50 tff(11368,plain,
% 2.34/2.50 (r(elem!1, z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[174, 11367, 3103])).
% 2.34/2.50 tff(11369,plain,
% 2.34/2.50 (~b(elem!1, s(elem!1))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[6239, 2184, 6236])).
% 2.34/2.50 tff(11370,plain,
% 2.34/2.50 (r(elem!1, s(elem!1))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[372, 11369, 366])).
% 2.34/2.50 tff(11371,plain,
% 2.34/2.50 (~r(s(elem!1), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[287, 11370, 246])).
% 2.34/2.50 tff(11372,plain,
% 2.34/2.50 (b(s(elem!1), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[2380, 11371])).
% 2.34/2.50 tff(11373,plain,
% 2.34/2.50 (~r(s(s(s(z))), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[2561, 4107, 246])).
% 2.34/2.50 tff(11374,plain,
% 2.34/2.50 (b(s(s(s(z))), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[2197, 11373])).
% 2.34/2.50 tff(11375,plain,
% 2.34/2.50 (~r(z, s(elem!1))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[265, 11370, 246])).
% 2.34/2.50 tff(11376,plain,
% 2.34/2.50 (b(z, s(elem!1))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[275, 11375])).
% 2.34/2.50 tff(11377,plain,
% 2.34/2.50 ($false),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[6790, 11376, 11374, 247, 11372, 4129, 2626])).
% 2.34/2.50 tff(11378,plain,((~(s(s(s(elem!1))) = elem!1)) | (~b(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(elem!1, z)) | (elem!1 = s(elem!1)) | b(s(s(s(z))), elem!1) | b(s(s(s(elem!1))), s(elem!1)) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.50 tff(11379,plain,
% 2.34/2.50 (~(s(s(s(elem!1))) = elem!1)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[11378, 247, 2626, 11368, 366, 1, 6236, 3099])).
% 2.34/2.50 tff(11380,plain,
% 2.34/2.50 (b(s(s(s(elem!1))), elem!1)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[1636, 11379, 11317])).
% 2.34/2.50 tff(11381,plain,
% 2.34/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)))),
% 2.34/2.50 inference(rewrite,[status(thm)],[])).
% 2.34/2.50 tff(11382,plain,
% 2.34/2.50 (((~b(s(z), z)) | (~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(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)))),
% 2.34/2.50 inference(rewrite,[status(thm)],[])).
% 2.34/2.50 tff(11383,plain,
% 2.34/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z))))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[11382])).
% 2.34/2.50 tff(11384,plain,
% 2.34/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)))),
% 2.34/2.50 inference(transitivity,[status(thm)],[11383, 11381])).
% 2.34/2.50 tff(11385,plain,
% 2.34/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))),
% 2.34/2.50 inference(quant_inst,[status(thm)],[])).
% 2.34/2.50 tff(11386,plain,
% 2.34/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z))),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[11385, 11384])).
% 2.34/2.50 tff(11387,plain,
% 2.34/2.50 (~b(z, s(s(s(elem!1))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[11386, 306, 838, 1664, 4346, 247])).
% 2.34/2.50 tff(11388,plain,
% 2.34/2.50 (r(z, s(s(s(elem!1))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[585, 11387])).
% 2.34/2.50 tff(11389,plain,
% 2.34/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)))),
% 2.34/2.50 inference(rewrite,[status(thm)],[])).
% 2.34/2.50 tff(11390,plain,
% 2.34/2.50 (((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1)))) <=> ((~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)))),
% 2.34/2.50 inference(rewrite,[status(thm)],[])).
% 2.34/2.50 tff(11391,plain,
% 2.34/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z))))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[11390])).
% 2.34/2.50 tff(11392,plain,
% 2.34/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)))),
% 2.34/2.50 inference(transitivity,[status(thm)],[11391, 11389])).
% 2.34/2.50 tff(11393,plain,
% 2.34/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))),
% 2.34/2.50 inference(quant_inst,[status(thm)],[])).
% 2.34/2.50 tff(11394,plain,
% 2.34/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z))),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[11393, 11392])).
% 2.34/2.50 tff(11395,plain,
% 2.34/2.50 (~b(z, s(elem!1))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[11394, 306, 838, 816, 4346, 247])).
% 2.34/2.50 tff(11396,plain,
% 2.34/2.50 (r(z, s(elem!1))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[275, 11395])).
% 2.34/2.50 tff(11397,plain,
% 2.34/2.50 ($false),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[5741, 11396, 11388, 654])).
% 2.34/2.50 tff(11398,plain,((~b(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.50 tff(11399,plain,
% 2.34/2.50 (~b(elem!1, s(z))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[11398, 1664, 838, 816, 247, 654])).
% 2.34/2.50 tff(11400,plain,
% 2.34/2.50 (r(elem!1, s(z))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[96, 43, 11399, 87])).
% 2.34/2.50 tff(11401,plain,
% 2.34/2.50 (~r(elem!1, s(elem!1))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[7653, 124, 11400, 2626])).
% 2.34/2.50 tff(11402,plain,
% 2.34/2.50 (b(elem!1, s(elem!1))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[372, 11401, 366])).
% 2.34/2.50 tff(11403,plain,
% 2.34/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))))),
% 2.34/2.50 inference(rewrite,[status(thm)],[])).
% 2.34/2.50 tff(11404,plain,
% 2.34/2.50 (((~b(s(elem!1), elem!1)) | (~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(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))))),
% 2.34/2.50 inference(rewrite,[status(thm)],[])).
% 2.34/2.50 tff(11405,plain,
% 2.34/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1)))))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[11404])).
% 2.34/2.50 tff(11406,plain,
% 2.34/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))))),
% 2.34/2.50 inference(transitivity,[status(thm)],[11405, 11403])).
% 2.34/2.50 tff(11407,plain,
% 2.34/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~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))))))),
% 2.34/2.50 inference(quant_inst,[status(thm)],[])).
% 2.34/2.50 tff(11408,plain,
% 2.34/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1)))),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[11407, 11406])).
% 2.34/2.50 tff(11409,plain,
% 2.34/2.50 (~b(z, s(s(s(elem!1))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[11408, 306, 838, 1664, 816, 11402])).
% 2.34/2.50 tff(11410,plain,
% 2.34/2.50 (r(z, s(s(s(elem!1))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[585, 11409])).
% 2.34/2.50 tff(11411,plain,
% 2.34/2.50 (~b(z, s(elem!1))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[6681, 306, 838, 816, 11402])).
% 2.34/2.50 tff(11412,plain,
% 2.34/2.50 (r(z, s(elem!1))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[275, 11411])).
% 2.34/2.50 tff(11413,plain,
% 2.34/2.50 ($false),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[5741, 11412, 11410, 654])).
% 2.34/2.50 tff(11414,plain,((~b(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (elem!1 = s(elem!1)) | (~r(s(elem!1), s(z))) | (elem!1 = s(z)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.50 tff(11415,plain,
% 2.34/2.50 (~b(z, elem!1)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[11414, 11380, 654, 816, 366, 2626, 5331, 247])).
% 2.34/2.50 tff(11416,plain,
% 2.34/2.50 (r(z, elem!1)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[835, 11415, 2170])).
% 2.34/2.50 tff(11417,plain,
% 2.34/2.50 (~r(s(s(elem!1)), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[6539, 124, 11416, 1730])).
% 2.34/2.50 tff(11418,plain,
% 2.34/2.50 (b(s(s(elem!1)), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[476, 11417])).
% 2.34/2.50 tff(11419,plain,
% 2.34/2.50 (~r(z, s(s(elem!1)))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[5837, 11416, 1730])).
% 2.34/2.50 tff(11420,plain,
% 2.34/2.50 (b(z, s(s(elem!1)))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[460, 11419])).
% 2.34/2.50 tff(11421,plain,
% 2.34/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), z)))),
% 2.34/2.50 inference(rewrite,[status(thm)],[])).
% 2.34/2.50 tff(11422,plain,
% 2.34/2.50 (((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), z)))),
% 2.34/2.50 inference(rewrite,[status(thm)],[])).
% 2.34/2.50 tff(11423,plain,
% 2.34/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), z))))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[11422])).
% 2.34/2.51 tff(11424,plain,
% 2.34/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), z)))),
% 2.34/2.51 inference(transitivity,[status(thm)],[11423, 11421])).
% 2.34/2.51 tff(11425,plain,
% 2.34/2.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))))),
% 2.34/2.51 inference(quant_inst,[status(thm)],[])).
% 2.34/2.51 tff(11426,plain,
% 2.34/2.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), z))),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[11425, 11424])).
% 2.34/2.51 tff(11427,plain,
% 2.34/2.51 (~b(s(z), s(s(elem!1)))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[11426, 306, 1005, 11420, 11418, 247])).
% 2.34/2.51 tff(11428,plain,
% 2.34/2.51 (r(s(z), s(s(elem!1)))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[3997, 43, 11427, 79])).
% 2.34/2.51 tff(11429,plain,
% 2.34/2.51 (~r(s(s(s(elem!1))), s(z))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[9146, 124, 653, 11428])).
% 2.34/2.51 tff(11430,plain,
% 2.34/2.51 ((s(s(s(elem!1))) = s(z)) | b(s(s(s(elem!1))), s(z))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[5924, 43, 11429])).
% 2.34/2.51 tff(11431,plain,
% 2.34/2.51 (b(s(s(s(elem!1))), s(z))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[11430, 5909])).
% 2.34/2.51 tff(11432,plain,
% 2.34/2.51 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(11433,plain,
% 2.34/2.51 (((~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(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(11434,plain,
% 2.34/2.51 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1))))))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[11433])).
% 2.34/2.51 tff(11435,plain,
% 2.34/2.51 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))))),
% 2.34/2.51 inference(transitivity,[status(thm)],[11434, 11432])).
% 2.34/2.51 tff(11436,plain,
% 2.34/2.51 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))))),
% 2.34/2.51 inference(quant_inst,[status(thm)],[])).
% 2.34/2.51 tff(11437,plain,
% 2.34/2.51 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1))))),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[11436, 11435])).
% 2.34/2.51 tff(11438,plain,
% 2.34/2.51 (~r(s(z), s(s(s(elem!1))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[11437, 124, 653, 11428])).
% 2.34/2.51 tff(11439,plain,
% 2.34/2.51 (b(s(z), s(s(s(elem!1))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[3017, 43, 645, 11438])).
% 2.34/2.51 tff(11440,plain,
% 2.34/2.51 (~b(s(s(elem!1)), s(z))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[11354, 306, 1005, 11420, 11418, 247])).
% 2.34/2.51 tff(11441,plain,
% 2.34/2.51 (r(s(s(elem!1)), s(z))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[3989, 11440])).
% 2.34/2.51 tff(11442,plain,
% 2.34/2.51 (~r(s(z), elem!1)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[8826, 11441, 1730])).
% 2.34/2.51 tff(11443,plain,
% 2.34/2.51 (b(s(z), elem!1)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[1500, 43, 11442, 3094])).
% 2.34/2.51 tff(11444,plain,
% 2.34/2.51 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(z))))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(11445,plain,
% 2.34/2.51 (((~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(z))))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(11446,plain,
% 2.34/2.51 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(z)))))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[11445])).
% 2.34/2.51 tff(11447,plain,
% 2.34/2.51 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(z))))),
% 2.34/2.51 inference(transitivity,[status(thm)],[11446, 11444])).
% 2.34/2.51 tff(11448,plain,
% 2.34/2.51 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(elem!1)))))),
% 2.34/2.51 inference(quant_inst,[status(thm)],[])).
% 2.34/2.51 tff(11449,plain,
% 2.34/2.51 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(z)))),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[11448, 11447])).
% 2.34/2.51 tff(11450,plain,
% 2.34/2.51 (~r(s(elem!1), s(s(elem!1)))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[11449, 124, 2626, 11441])).
% 2.34/2.51 tff(11451,plain,
% 2.34/2.51 (b(s(elem!1), s(s(elem!1)))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[1684, 43, 11450, 8870])).
% 2.34/2.51 tff(11452,plain,
% 2.34/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(11453,plain,
% 2.34/2.51 (((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1)))) <=> ((~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(11454,plain,
% 2.34/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1)))))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[11453])).
% 2.34/2.51 tff(11455,plain,
% 2.34/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.34/2.51 inference(transitivity,[status(thm)],[11454, 11452])).
% 2.34/2.51 tff(11456,plain,
% 2.34/2.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))))),
% 2.34/2.51 inference(quant_inst,[status(thm)],[])).
% 2.34/2.51 tff(11457,plain,
% 2.34/2.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1)))),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[11456, 11455])).
% 2.34/2.51 tff(11458,plain,
% 2.34/2.51 (~b(z, s(elem!1))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[11457, 306, 1005, 11420, 816, 11451])).
% 2.34/2.51 tff(11459,plain,
% 2.34/2.51 (r(z, s(elem!1))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[275, 11458])).
% 2.34/2.51 tff(11460,plain,
% 2.34/2.51 (~r(z, s(s(s(elem!1))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[5741, 11459, 654])).
% 2.34/2.51 tff(11461,plain,
% 2.34/2.51 (b(z, s(s(s(elem!1))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[585, 11460])).
% 2.34/2.51 tff(11462,plain,
% 2.34/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(11463,plain,
% 2.34/2.51 (((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(11464,plain,
% 2.34/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[11463])).
% 2.34/2.51 tff(11465,plain,
% 2.34/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 2.34/2.51 inference(transitivity,[status(thm)],[11464, 11462])).
% 2.34/2.51 tff(11466,plain,
% 2.34/2.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)))),
% 2.34/2.51 inference(quant_inst,[status(thm)],[])).
% 2.34/2.51 tff(11467,plain,
% 2.34/2.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[11466, 11465])).
% 2.34/2.51 tff(11468,plain,
% 2.34/2.51 ($false),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[11467, 306, 11461, 11443, 247, 11439, 11431])).
% 2.34/2.51 tff(11469,plain,((~b(s(z), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (s(elem!1) = s(s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (s(z) = elem!1) | (~r(s(s(elem!1)), elem!1)) | (z = elem!1) | (elem!1 = s(elem!1)) | b(s(s(s(z))), elem!1) | b(s(s(s(elem!1))), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.51 tff(11470,plain,
% 2.34/2.51 (~b(s(z), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[11469, 11320, 11322, 816, 11324, 653, 11323, 3094, 1730, 2170, 11318, 1, 6236])).
% 2.34/2.51 tff(11471,plain,
% 2.34/2.51 (r(s(z), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[221, 11470])).
% 2.34/2.51 tff(11472,plain,
% 2.34/2.51 (~r(s(elem!1), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[2634, 11471, 11323])).
% 2.34/2.51 tff(11473,plain,
% 2.34/2.51 (b(s(elem!1), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[2380, 11472])).
% 2.34/2.51 tff(11474,plain,
% 2.34/2.51 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[2184])).
% 2.34/2.51 tff(11475,plain,
% 2.34/2.51 (r(elem!1, s(s(elem!1)))),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[653, 11474])).
% 2.34/2.51 tff(11476,plain,
% 2.34/2.51 (r(elem!1, s(s(s(s(elem!1))))) <=> r(elem!1, s(elem!1))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[5713])).
% 2.34/2.51 tff(11477,plain,
% 2.34/2.51 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(s(elem!1)))))),
% 2.34/2.51 inference(symmetry,[status(thm)],[11476])).
% 2.34/2.51 tff(11478,plain,
% 2.34/2.51 (r(elem!1, s(s(s(s(elem!1)))))),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[11370, 11477])).
% 2.34/2.51 tff(11479,plain,
% 2.34/2.51 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[1918, 11478, 11475])).
% 2.34/2.51 tff(11480,plain,
% 2.34/2.51 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[1302, 11479, 1717])).
% 2.34/2.51 tff(11481,plain,
% 2.34/2.51 (b(s(elem!1), s(s(elem!1)))),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[11480, 6753])).
% 2.34/2.51 tff(11482,plain,
% 2.34/2.51 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(11483,plain,
% 2.34/2.51 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.34/2.51 inference(quant_inst,[status(thm)],[])).
% 2.34/2.51 tff(11484,plain,
% 2.34/2.51 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(elem!1))))),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[11483, 11482])).
% 2.34/2.51 tff(11485,plain,
% 2.34/2.51 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[11484, 124, 1730, 4107])).
% 2.34/2.51 tff(11486,plain,
% 2.34/2.51 (b(s(s(s(z))), s(s(elem!1)))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[2986, 43, 11485, 2976])).
% 2.34/2.51 tff(11487,plain,
% 2.34/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(11488,plain,
% 2.34/2.51 (((~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1)))) <=> ((~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(11489,plain,
% 2.34/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1)))))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[11488])).
% 2.34/2.51 tff(11490,plain,
% 2.34/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))))),
% 2.34/2.51 inference(transitivity,[status(thm)],[11489, 11487])).
% 2.34/2.51 tff(11491,plain,
% 2.34/2.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))))),
% 2.34/2.51 inference(quant_inst,[status(thm)],[])).
% 2.34/2.51 tff(11492,plain,
% 2.34/2.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1)))),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[11491, 11490])).
% 2.34/2.51 tff(11493,plain,
% 2.34/2.51 (~b(s(s(s(z))), s(elem!1))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[11492, 306, 1199, 1005, 11486, 11481])).
% 2.34/2.51 tff(11494,plain,
% 2.34/2.51 (r(s(s(s(z))), s(elem!1))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[4132, 43, 4129, 11493])).
% 2.34/2.51 tff(11495,plain,
% 2.34/2.51 ($false),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[8272, 124, 11370, 4107, 11494])).
% 2.34/2.51 tff(11496,plain,((~(s(s(s(elem!1))) = 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(s(elem!1)))) = s(s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (elem!1 = s(elem!1)) | b(s(s(s(z))), elem!1) | b(s(s(s(elem!1))), s(elem!1)) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.51 tff(11497,plain,
% 2.34/2.51 (~(s(s(s(elem!1))) = elem!1)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[11496, 11473, 11322, 11319, 1285, 1730, 653, 11318, 1, 6236, 3099])).
% 2.34/2.51 tff(11498,plain,
% 2.34/2.51 (b(s(s(s(elem!1))), elem!1)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[1636, 11497, 11317])).
% 2.34/2.51 tff(11499,plain,
% 2.34/2.51 (~(elem!1 = s(s(s(elem!1))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[1641, 11497])).
% 2.34/2.51 tff(11500,plain,
% 2.34/2.51 (~r(s(elem!1), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[2634, 204, 11323])).
% 2.34/2.51 tff(11501,plain,
% 2.34/2.51 (b(s(elem!1), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[2380, 11500])).
% 2.34/2.51 tff(11502,plain,
% 2.34/2.51 (~r(s(s(s(elem!1))), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[10578, 124, 654, 791])).
% 2.34/2.51 tff(11503,plain,
% 2.34/2.51 (b(s(s(s(elem!1))), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[3033, 43, 579, 11502])).
% 2.34/2.51 tff(11504,plain,
% 2.34/2.51 (~b(s(s(elem!1)), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[9394, 6243, 11503, 11501, 1005])).
% 2.34/2.51 tff(11505,plain,
% 2.34/2.51 (r(s(s(elem!1)), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[476, 11504])).
% 2.34/2.51 tff(11506,plain,
% 2.34/2.51 (~r(s(z), s(s(elem!1)))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[3993, 124, 11505, 204])).
% 2.34/2.51 tff(11507,plain,
% 2.34/2.51 (b(s(z), s(s(elem!1)))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[3997, 43, 79, 11506])).
% 2.34/2.51 tff(11508,plain,
% 2.34/2.51 (b(elem!1, s(s(s(elem!1))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[3284, 1257, 1653])).
% 2.34/2.51 tff(11509,plain,
% 2.34/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(11510,plain,
% 2.34/2.51 (((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(11511,plain,
% 2.34/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[11510])).
% 2.34/2.51 tff(11512,plain,
% 2.34/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 2.34/2.51 inference(transitivity,[status(thm)],[11511, 11509])).
% 2.34/2.51 tff(11513,plain,
% 2.34/2.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))),
% 2.34/2.51 inference(quant_inst,[status(thm)],[])).
% 2.34/2.51 tff(11514,plain,
% 2.34/2.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[11513, 11512])).
% 2.34/2.51 tff(11515,plain,
% 2.34/2.51 (~b(elem!1, z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[11514, 306, 11508, 818, 6445])).
% 2.34/2.51 tff(11516,plain,
% 2.34/2.51 (r(elem!1, z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[174, 11515, 1616])).
% 2.34/2.51 tff(11517,plain,
% 2.34/2.51 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z)))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(11518,plain,
% 2.34/2.51 (((~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z)))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(11519,plain,
% 2.34/2.52 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z))))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[11518])).
% 2.34/2.52 tff(11520,plain,
% 2.34/2.52 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z)))),
% 2.34/2.52 inference(transitivity,[status(thm)],[11519, 11517])).
% 2.34/2.52 tff(11521,plain,
% 2.34/2.52 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))))),
% 2.34/2.52 inference(quant_inst,[status(thm)],[])).
% 2.34/2.52 tff(11522,plain,
% 2.34/2.52 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z))),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[11521, 11520])).
% 2.34/2.52 tff(11523,plain,
% 2.34/2.52 ($false),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[11522, 124, 11516, 970, 465])).
% 2.34/2.52 tff(11524,plain,((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (elem!1 = z) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (elem!1 = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.52 tff(11525,plain,
% 2.34/2.52 (~r(elem!1, s(s(elem!1)))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[11524, 11505, 3103, 6243, 11503, 1653, 653])).
% 2.34/2.52 tff(11526,plain,
% 2.34/2.52 (b(elem!1, s(s(elem!1)))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[516, 11525, 360])).
% 2.34/2.52 tff(11527,plain,
% 2.34/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(11528,plain,
% 2.34/2.52 (((~b(s(elem!1), z)) | (~b(s(s(elem!1)), 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), s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(11529,plain,
% 2.34/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1)))))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[11528])).
% 2.34/2.52 tff(11530,plain,
% 2.34/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.34/2.52 inference(transitivity,[status(thm)],[11529, 11527])).
% 2.34/2.52 tff(11531,plain,
% 2.34/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)))),
% 2.34/2.52 inference(quant_inst,[status(thm)],[])).
% 2.34/2.52 tff(11532,plain,
% 2.34/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1)))),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[11531, 11530])).
% 2.34/2.52 tff(11533,plain,
% 2.34/2.52 (~b(s(z), elem!1)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[11532, 306, 11501, 1005, 11526, 11507])).
% 2.34/2.52 tff(11534,plain,
% 2.34/2.52 (r(s(z), elem!1)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[1500, 43, 11533, 3094])).
% 2.34/2.52 tff(11535,plain,
% 2.34/2.52 (~r(elem!1, z)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[1049, 11534, 204])).
% 2.34/2.52 tff(11536,plain,
% 2.34/2.52 (b(elem!1, z)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[174, 11535, 3103])).
% 2.34/2.52 tff(11537,plain,
% 2.34/2.52 (r(z, elem!1)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[3113, 11535, 2609, 2170, 816, 204])).
% 2.34/2.52 tff(11538,plain,
% 2.34/2.52 (~r(z, s(s(elem!1)))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[5837, 11537, 1730])).
% 2.34/2.52 tff(11539,plain,
% 2.34/2.52 (b(z, s(s(elem!1)))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[460, 11538])).
% 2.34/2.52 tff(11540,plain,
% 2.34/2.52 (~(s(s(elem!1)) = elem!1)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[1174, 360])).
% 2.34/2.52 tff(11541,plain,
% 2.34/2.52 (~(s(elem!1) = elem!1)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[180, 11540])).
% 2.34/2.52 tff(11542,plain,
% 2.34/2.52 (~(elem!1 = s(elem!1))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[364, 11541])).
% 2.34/2.52 tff(11543,plain,
% 2.34/2.52 (~r(elem!1, s(elem!1))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[5668, 11537, 791])).
% 2.34/2.52 tff(11544,plain,
% 2.34/2.52 (b(elem!1, s(elem!1))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[372, 11543, 11542])).
% 2.34/2.52 tff(11545,plain,
% 2.34/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(11546,plain,
% 2.34/2.52 (((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(11547,plain,
% 2.34/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1)))))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[11546])).
% 2.34/2.52 tff(11548,plain,
% 2.34/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 2.34/2.52 inference(transitivity,[status(thm)],[11547, 11545])).
% 2.34/2.52 tff(11549,plain,
% 2.34/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))))),
% 2.34/2.52 inference(quant_inst,[status(thm)],[])).
% 2.34/2.52 tff(11550,plain,
% 2.34/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1)))),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[11549, 11548])).
% 2.34/2.52 tff(11551,plain,
% 2.34/2.52 ($false),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[11550, 306, 4012, 1199, 1005, 1198, 815])).
% 2.34/2.52 tff(11552,plain,((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.52 tff(11553,plain,
% 2.34/2.52 ($false),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[11552, 11544, 11539, 1005, 11501, 11536])).
% 2.34/2.52 tff(11554,plain,((~r(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | b(s(elem!1), s(z)) | (z = elem!1) | (~b(s(elem!1), elem!1)) | (~r(s(z), z)) | (s(z) = elem!1) | (elem!1 = s(s(elem!1))) | (elem!1 = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.52 tff(11555,plain,
% 2.34/2.52 (~r(z, s(elem!1))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[11554, 11322, 1730, 2609, 2170, 816, 11471, 3094, 1169, 11499, 653, 11320])).
% 2.34/2.52 tff(11556,plain,
% 2.34/2.52 (b(z, s(elem!1))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[275, 11555])).
% 2.34/2.52 tff(11557,plain,
% 2.34/2.52 (~b(z, s(s(elem!1)))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[1218, 11556, 11322, 11473])).
% 2.34/2.52 tff(11558,plain,
% 2.34/2.52 (r(z, s(s(elem!1)))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[460, 11557])).
% 2.34/2.52 tff(11559,plain,
% 2.34/2.52 (~r(z, elem!1)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[5837, 11558, 1730])).
% 2.34/2.52 tff(11560,plain,
% 2.34/2.52 (r(elem!1, z)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[3113, 11559, 2609, 2170, 816, 11471])).
% 2.34/2.52 tff(11561,plain,
% 2.34/2.52 (~r(elem!1, s(s(elem!1)))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[978, 11560, 11558])).
% 2.34/2.52 tff(11562,plain,
% 2.34/2.52 (b(elem!1, s(s(elem!1)))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[516, 11561, 1169])).
% 2.34/2.52 tff(11563,plain,
% 2.34/2.52 (~r(z, s(s(s(elem!1))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[950, 11558, 653])).
% 2.34/2.52 tff(11564,plain,
% 2.34/2.52 (b(z, s(s(s(elem!1))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[585, 11563])).
% 2.34/2.52 tff(11565,plain,
% 2.34/2.52 (b(z, elem!1)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[835, 11559, 2170])).
% 2.34/2.52 tff(11566,plain,
% 2.34/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(11567,plain,
% 2.34/2.52 (((~b(s(s(elem!1)), s(elem!1))) | (~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, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(11568,plain,
% 2.34/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[11567])).
% 2.34/2.52 tff(11569,plain,
% 2.34/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.34/2.52 inference(transitivity,[status(thm)],[11568, 11566])).
% 2.34/2.52 tff(11570,plain,
% 2.34/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~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))))))),
% 2.34/2.52 inference(quant_inst,[status(thm)],[])).
% 2.34/2.52 tff(11571,plain,
% 2.34/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[11570, 11569])).
% 2.34/2.52 tff(11572,plain,
% 2.34/2.52 ($false),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[11571, 306, 11565, 11564, 11322, 11562, 11498])).
% 2.34/2.52 tff(11573,plain,(b(s(s(s(elem!1))), s(elem!1)) | b(s(elem!1), s(z)) | (z = elem!1) | (~b(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (s(z) = elem!1) | b(s(s(s(z))), elem!1) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.52 tff(11574,plain,
% 2.34/2.52 (b(s(elem!1), s(z))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[11573, 11316, 11076, 11006, 11072, 11068, 11067, 11039, 11062])).
% 2.34/2.52 tff(11575,plain,
% 2.34/2.52 (~r(s(s(elem!1)), s(z))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[9725, 11316, 11017])).
% 2.34/2.52 tff(11576,plain,
% 2.34/2.52 (b(s(s(elem!1)), s(z))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[3989, 11575])).
% 2.34/2.52 tff(11577,plain,
% 2.34/2.52 (~b(s(z), s(s(elem!1)))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[4007, 11576, 11574, 11061])).
% 2.34/2.52 tff(11578,plain,
% 2.34/2.52 (~b(s(z), s(s(s(s(s(z))))))),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[11577, 11021])).
% 2.34/2.52 tff(11579,plain,
% 2.34/2.52 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[11316, 11015])).
% 2.34/2.52 tff(11580,plain,
% 2.34/2.52 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(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))))))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(11581,plain,
% 2.34/2.52 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.34/2.52 inference(quant_inst,[status(thm)],[])).
% 2.34/2.52 tff(11582,plain,
% 2.34/2.52 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[11581, 11580])).
% 2.34/2.52 tff(11583,plain,
% 2.34/2.52 ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[11582, 124, 10943])).
% 2.34/2.52 tff(11584,plain,
% 2.34/2.52 (~r(s(z), s(s(s(s(s(z))))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[11583, 11579])).
% 2.34/2.52 tff(11585,plain,
% 2.34/2.52 (b(s(z), s(s(s(s(s(z)))))) | r(s(z), s(s(s(s(s(z))))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[626, 43, 11013])).
% 2.34/2.52 tff(11586,plain,
% 2.34/2.52 ($false),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[11585, 11584, 11578])).
% 2.34/2.52 tff(11587,plain,((~(elem!1 = s(s(s(z))))) | b(elem!1, s(z)) | b(elem!1, s(s(s(z)))) | (~r(z, elem!1)) | (~r(s(s(s(z))), s(z))) | b(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.52 tff(11588,plain,
% 2.34/2.52 (~(elem!1 = s(s(s(z))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[11587, 114, 3, 374, 5, 3300])).
% 2.34/2.52 tff(11589,plain,
% 2.34/2.52 (r(elem!1, s(s(s(z))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[2304, 11588, 3])).
% 2.34/2.52 tff(11590,plain,
% 2.34/2.52 ($false),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[127, 124, 206, 359, 3313])).
% 2.34/2.52 tff(11591,plain,((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.52 tff(11592,plain,
% 2.34/2.52 (~r(elem!1, s(z))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[11591, 11589, 114])).
% 2.34/2.52 tff(11593,plain,
% 2.34/2.52 (elem!1 = s(z)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[97, 11592])).
% 2.34/2.52 tff(11594,plain,
% 2.34/2.52 (s(elem!1) = s(s(z))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[11593])).
% 2.34/2.52 tff(11595,plain,
% 2.34/2.52 (s(s(elem!1)) = s(s(s(z)))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[11594])).
% 2.34/2.52 tff(11596,plain,
% 2.34/2.52 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(z))), s(s(z)))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[11595, 11594])).
% 2.34/2.52 tff(11597,plain,
% 2.34/2.52 (~(s(s(elem!1)) = elem!1)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[11022, 114, 5, 3])).
% 2.34/2.52 tff(11598,plain,
% 2.34/2.52 (~(s(elem!1) = elem!1)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[180, 11597])).
% 2.34/2.52 tff(11599,plain,
% 2.34/2.52 (~(s(s(elem!1)) = s(elem!1))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[195, 11598])).
% 2.34/2.52 tff(11600,plain,
% 2.34/2.52 (r(s(s(elem!1)), elem!1)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[82, 11593, 9])).
% 2.34/2.52 tff(11601,plain,
% 2.34/2.52 (~r(z, s(s(elem!1)))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[5837, 11600, 374])).
% 2.34/2.52 tff(11602,plain,
% 2.34/2.52 (b(z, s(s(elem!1)))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[460, 11601])).
% 2.34/2.52 tff(11603,plain,
% 2.34/2.52 (b(s(s(elem!1)), z) <=> b(s(s(s(z))), z)),
% 2.34/2.52 inference(monotonicity,[status(thm)],[11595])).
% 2.34/2.52 tff(11604,plain,
% 2.34/2.52 (b(s(s(s(z))), z) <=> b(s(s(elem!1)), z)),
% 2.34/2.52 inference(symmetry,[status(thm)],[11603])).
% 2.34/2.52 tff(11605,plain,
% 2.34/2.52 (~(s(s(s(z))) = elem!1)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[5326, 11592, 114])).
% 2.34/2.52 tff(11606,plain,
% 2.34/2.52 (s(z) = elem!1),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[3096, 11593])).
% 2.34/2.52 tff(11607,plain,
% 2.34/2.52 (~b(s(s(s(z))), elem!1)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[2235, 11606, 9])).
% 2.34/2.52 tff(11608,plain,
% 2.34/2.52 (r(s(s(s(z))), elem!1)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[1489, 11607, 11605])).
% 2.34/2.52 tff(11609,plain,
% 2.34/2.52 (~r(s(s(s(z))), z)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[6831, 11608, 374])).
% 2.34/2.52 tff(11610,plain,
% 2.34/2.52 (b(s(s(s(z))), z)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[2197, 11609])).
% 2.34/2.52 tff(11611,plain,
% 2.34/2.52 (b(s(s(elem!1)), z)),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[11610, 11604])).
% 2.34/2.52 tff(11612,plain,
% 2.34/2.52 (~r(s(elem!1), elem!1)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[10562, 11611, 374, 11599, 11600, 11602])).
% 2.34/2.52 tff(11613,plain,
% 2.34/2.52 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[7090, 11612, 11006, 11597])).
% 2.34/2.52 tff(11614,plain,
% 2.34/2.52 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[143, 11597])).
% 2.34/2.52 tff(11615,plain,
% 2.34/2.52 ((elem!1 = s(s(s(elem!1)))) <=> (s(z) = s(s(s(elem!1))))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[11593])).
% 2.34/2.52 tff(11616,plain,
% 2.34/2.52 ((s(z) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 2.34/2.52 inference(symmetry,[status(thm)],[11615])).
% 2.34/2.52 tff(11617,plain,
% 2.34/2.52 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 2.34/2.52 inference(transitivity,[status(thm)],[11616, 1555])).
% 2.34/2.52 tff(11618,plain,
% 2.34/2.52 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[11617])).
% 2.34/2.52 tff(11619,plain,
% 2.34/2.52 (~(s(s(s(elem!1))) = elem!1)),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[645, 11618])).
% 2.34/2.52 tff(11620,plain,
% 2.34/2.52 (~r(s(s(s(elem!1))), elem!1)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[7780, 11613, 11600])).
% 2.34/2.52 tff(11621,plain,
% 2.34/2.52 (b(s(elem!1), elem!1)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[813, 11612, 11598])).
% 2.34/2.52 tff(11622,plain,
% 2.34/2.52 (r(elem!1, s(s(s(elem!1)))) <=> r(s(z), s(s(s(elem!1))))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[11593])).
% 2.34/2.52 tff(11623,plain,
% 2.34/2.52 (r(s(z), s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 2.34/2.52 inference(symmetry,[status(thm)],[11622])).
% 2.34/2.52 tff(11624,plain,
% 2.34/2.52 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[11595])).
% 2.34/2.52 tff(11625,plain,
% 2.34/2.52 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(s(s(s(z)))))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[11624])).
% 2.34/2.52 tff(11626,plain,
% 2.34/2.52 (r(s(z), s(s(s(s(z))))) <=> r(s(z), s(s(s(elem!1))))),
% 2.34/2.52 inference(symmetry,[status(thm)],[11625])).
% 2.34/2.52 tff(11627,plain,
% 2.34/2.52 (r(s(z), s(s(s(s(z))))) <=> r(elem!1, s(s(s(elem!1))))),
% 2.34/2.52 inference(transitivity,[status(thm)],[11626, 11623])).
% 2.34/2.52 tff(11628,plain,
% 2.34/2.52 ((~r(s(z), s(s(s(s(z)))))) <=> (~r(elem!1, s(s(s(elem!1)))))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[11627])).
% 2.34/2.52 tff(11629,plain,
% 2.34/2.52 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[11624, 11595])).
% 2.34/2.52 tff(11630,plain,
% 2.34/2.52 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[11613, 11629])).
% 2.34/2.52 tff(11631,plain,
% 2.34/2.52 (~r(s(z), s(s(s(s(z)))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[3585, 124, 10943, 11630])).
% 2.34/2.52 tff(11632,plain,
% 2.34/2.52 (~r(elem!1, s(s(s(elem!1))))),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[11631, 11628])).
% 2.34/2.52 tff(11633,plain,
% 2.34/2.52 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[7793, 11632, 11621, 11620, 11619])).
% 2.34/2.52 tff(11634,plain,
% 2.34/2.52 (r(s(s(s(elem!1))), s(elem!1))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[664, 11633, 11614])).
% 2.34/2.52 tff(11635,plain,
% 2.34/2.52 (~r(s(s(elem!1)), s(elem!1))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[659, 11634, 11613])).
% 2.34/2.52 tff(11636,plain,
% 2.34/2.52 (b(s(s(elem!1)), s(elem!1))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[994, 11635, 11599])).
% 2.34/2.52 tff(11637,plain,
% 2.34/2.52 (b(s(s(s(z))), s(s(z)))),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[11636, 11596])).
% 2.34/2.52 tff(11638,plain,
% 2.34/2.52 (r(s(elem!1), s(z)) <=> r(s(s(z)), s(z))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[11594])).
% 2.34/2.52 tff(11639,plain,
% 2.34/2.52 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(z))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[11593])).
% 2.34/2.52 tff(11640,plain,
% 2.34/2.52 (r(s(elem!1), elem!1) <=> r(s(s(z)), s(z))),
% 2.34/2.52 inference(transitivity,[status(thm)],[11639, 11638])).
% 2.34/2.52 tff(11641,plain,
% 2.34/2.52 ((~r(s(elem!1), elem!1)) <=> (~r(s(s(z)), s(z)))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[11640])).
% 2.34/2.52 tff(11642,plain,
% 2.34/2.52 (~r(s(s(z)), s(z))),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[11612, 11641])).
% 2.34/2.52 tff(11643,plain,
% 2.34/2.52 (b(s(s(z)), s(z))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[2474, 43, 2470, 11642])).
% 2.34/2.52 tff(11644,plain,
% 2.34/2.52 (b(elem!1, z) <=> b(s(z), z)),
% 2.34/2.52 inference(monotonicity,[status(thm)],[11593])).
% 2.34/2.52 tff(11645,plain,
% 2.34/2.52 (b(s(z), z)),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[10999, 11644])).
% 2.34/2.52 tff(11646,plain,
% 2.34/2.52 (b(z, s(s(elem!1))) <=> b(z, s(s(s(z))))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[11595])).
% 2.34/2.52 tff(11647,plain,
% 2.34/2.52 (b(z, s(s(s(z))))),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[11602, 11646])).
% 2.34/2.52 tff(11648,plain,
% 2.34/2.52 (b(z, s(elem!1)) <=> b(z, s(s(z)))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[11594])).
% 2.34/2.52 tff(11649,plain,
% 2.34/2.52 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(z)))), s(z))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[11624, 11593])).
% 2.34/2.52 tff(11650,plain,
% 2.34/2.52 (b(s(s(s(elem!1))), elem!1)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[1636, 11620, 11619])).
% 2.34/2.52 tff(11651,plain,
% 2.34/2.52 (b(s(s(s(s(z)))), s(z))),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[11650, 11649])).
% 2.34/2.52 tff(11652,plain,
% 2.34/2.52 (b(s(z), s(s(s(s(z)))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[5135, 11631])).
% 2.34/2.52 tff(11653,plain,
% 2.34/2.52 (b(z, s(s(s(s(z))))) <=> b(z, s(s(s(elem!1))))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[5225])).
% 2.34/2.52 tff(11654,plain,
% 2.34/2.52 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(s(s(z)))))),
% 2.34/2.52 inference(symmetry,[status(thm)],[11653])).
% 2.34/2.52 tff(11655,plain,
% 2.34/2.52 (b(z, s(s(s(s(z)))))),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[818, 11654])).
% 2.34/2.52 tff(11656,plain,
% 2.34/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(11657,plain,
% 2.34/2.53 (((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(11658,plain,
% 2.34/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z))))))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[11657])).
% 2.34/2.53 tff(11659,plain,
% 2.34/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.34/2.53 inference(transitivity,[status(thm)],[11658, 11656])).
% 2.34/2.53 tff(11660,plain,
% 2.34/2.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))),
% 2.34/2.53 inference(quant_inst,[status(thm)],[])).
% 2.34/2.53 tff(11661,plain,
% 2.34/2.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z))))))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[11660, 11659])).
% 2.34/2.53 tff(11662,plain,
% 2.34/2.53 (~b(z, s(s(s(s(z)))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[11661, 306, 247, 3603, 3620])).
% 2.34/2.53 tff(11663,plain,
% 2.34/2.53 ($false),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[11662, 11655])).
% 2.34/2.53 tff(11664,plain,((~b(z, s(s(s(elem!1))))) | (~(elem!1 = s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.53 tff(11665,plain,
% 2.34/2.53 (~b(z, s(s(s(elem!1))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[11664, 11593, 11645, 11652, 11651])).
% 2.34/2.53 tff(11666,plain,
% 2.34/2.53 (r(z, s(s(s(elem!1))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[585, 11665])).
% 2.34/2.53 tff(11667,plain,
% 2.34/2.53 (~r(z, s(elem!1))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[5741, 11666, 11634])).
% 2.34/2.53 tff(11668,plain,
% 2.34/2.53 (b(z, s(elem!1))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[275, 11667])).
% 2.34/2.53 tff(11669,plain,
% 2.34/2.53 (b(z, s(s(z)))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[11668, 11648])).
% 2.34/2.53 tff(11670,plain,
% 2.34/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(11671,plain,
% 2.34/2.53 (((~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(11672,plain,
% 2.34/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z))))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[11671])).
% 2.34/2.53 tff(11673,plain,
% 2.34/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.34/2.53 inference(transitivity,[status(thm)],[11672, 11670])).
% 2.34/2.53 tff(11674,plain,
% 2.34/2.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))),
% 2.34/2.53 inference(quant_inst,[status(thm)],[])).
% 2.34/2.53 tff(11675,plain,
% 2.34/2.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z))))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[11674, 11673])).
% 2.34/2.53 tff(11676,plain,
% 2.34/2.53 ($false),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[11675, 306, 11669, 11647, 11645, 11643, 11637])).
% 2.34/2.53 tff(11677,plain,(b(s(s(s(z))), s(z)) | (~r(z, elem!1)) | b(elem!1, s(z)) | b(elem!1, s(s(s(z)))) | b(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.53 tff(11678,plain,
% 2.34/2.53 (b(s(s(s(z))), s(z))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[11677, 3300, 5, 3, 374])).
% 2.34/2.53 tff(11679,plain,
% 2.34/2.53 (~(elem!1 = s(s(s(z))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[5016, 11678, 5])).
% 2.34/2.53 tff(11680,plain,
% 2.34/2.53 (r(elem!1, s(s(s(z))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[2304, 11679, 3])).
% 2.34/2.53 tff(11681,plain,
% 2.34/2.53 (~r(elem!1, s(z))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[3293, 11680, 10943])).
% 2.34/2.53 tff(11682,plain,
% 2.34/2.53 (elem!1 = s(z)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[97, 11681])).
% 2.34/2.53 tff(11683,plain,
% 2.34/2.53 (s(elem!1) = s(s(z))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[11682])).
% 2.34/2.53 tff(11684,plain,
% 2.34/2.53 (s(s(elem!1)) = s(s(s(z)))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[11683])).
% 2.34/2.53 tff(11685,plain,
% 2.34/2.53 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[11684])).
% 2.34/2.53 tff(11686,plain,
% 2.34/2.53 (r(s(s(s(elem!1))), z) <=> r(s(s(s(s(z)))), z)),
% 2.34/2.53 inference(monotonicity,[status(thm)],[11685])).
% 2.34/2.53 tff(11687,plain,
% 2.34/2.53 (r(s(s(s(s(z)))), z) <=> r(s(s(s(elem!1))), z)),
% 2.34/2.53 inference(symmetry,[status(thm)],[11686])).
% 2.34/2.53 tff(11688,plain,
% 2.34/2.53 (b(elem!1, z) <=> b(s(z), z)),
% 2.34/2.53 inference(monotonicity,[status(thm)],[11682])).
% 2.34/2.53 tff(11689,plain,
% 2.34/2.53 (b(s(z), z)),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[10999, 11688])).
% 2.34/2.53 tff(11690,plain,
% 2.34/2.53 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(z))), s(s(z)))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[15, 14])).
% 2.34/2.53 tff(11691,plain,
% 2.34/2.53 ((s(s(s(z))) = s(s(z))) <=> (s(s(z)) = s(s(s(z))))),
% 2.34/2.53 inference(commutativity,[status(thm)],[])).
% 2.34/2.53 tff(11692,plain,
% 2.34/2.53 ((s(s(elem!1)) = s(elem!1)) <=> (s(s(s(z))) = s(s(z)))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[15, 14])).
% 2.34/2.53 tff(11693,plain,
% 2.34/2.53 ((s(s(elem!1)) = s(elem!1)) <=> (s(s(z)) = s(s(s(z))))),
% 2.34/2.53 inference(transitivity,[status(thm)],[11692, 11691])).
% 2.34/2.53 tff(11694,plain,
% 2.34/2.53 ((s(s(z)) = s(s(s(z)))) <=> (s(s(elem!1)) = s(elem!1))),
% 2.34/2.53 inference(symmetry,[status(thm)],[11693])).
% 2.34/2.53 tff(11695,plain,
% 2.34/2.53 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[11694])).
% 2.34/2.53 tff(11696,plain,
% 2.34/2.53 (~(s(s(elem!1)) = s(elem!1))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[2508, 11695])).
% 2.34/2.53 tff(11697,plain,
% 2.34/2.53 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[3589, 15])).
% 2.34/2.53 tff(11698,plain,
% 2.34/2.53 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.34/2.53 inference(symmetry,[status(thm)],[11697])).
% 2.34/2.53 tff(11699,plain,
% 2.34/2.53 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[1033, 11698])).
% 2.34/2.53 tff(11700,plain,
% 2.34/2.53 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(z)))) = s(s(z)))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[3589, 14])).
% 2.34/2.53 tff(11701,plain,
% 2.34/2.53 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(z)) = s(s(s(s(z)))))),
% 2.34/2.53 inference(transitivity,[status(thm)],[11700, 1707])).
% 2.34/2.53 tff(11702,plain,
% 2.34/2.53 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 2.34/2.53 inference(symmetry,[status(thm)],[11701])).
% 2.34/2.53 tff(11703,plain,
% 2.34/2.53 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[11702])).
% 2.34/2.53 tff(11704,plain,
% 2.34/2.53 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[1612, 11703])).
% 2.34/2.53 tff(11705,plain,
% 2.34/2.53 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(z)))), s(z))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[3589, 10])).
% 2.34/2.53 tff(11706,plain,
% 2.34/2.53 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(elem!1))), elem!1)),
% 2.34/2.53 inference(symmetry,[status(thm)],[11705])).
% 2.34/2.53 tff(11707,plain,
% 2.34/2.53 ((~r(s(s(s(s(z)))), s(z))) <=> (~r(s(s(s(elem!1))), elem!1))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[11706])).
% 2.34/2.53 tff(11708,plain,
% 2.34/2.53 (~r(s(s(s(elem!1))), elem!1)),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[1041, 11707])).
% 2.34/2.53 tff(11709,plain,
% 2.34/2.53 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(z))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[10])).
% 2.34/2.53 tff(11710,plain,
% 2.34/2.53 ((s(elem!1) = s(z)) <=> (s(elem!1) = elem!1)),
% 2.34/2.53 inference(symmetry,[status(thm)],[11709])).
% 2.34/2.53 tff(11711,plain,
% 2.34/2.53 ((s(elem!1) = s(z)) <=> (s(s(z)) = s(z))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[14])).
% 2.34/2.53 tff(11712,plain,
% 2.34/2.53 ((s(s(z)) = s(z)) <=> (s(elem!1) = s(z))),
% 2.34/2.53 inference(symmetry,[status(thm)],[11711])).
% 2.34/2.53 tff(11713,plain,
% 2.34/2.53 ((s(s(z)) = s(z)) <=> (s(elem!1) = elem!1)),
% 2.34/2.53 inference(transitivity,[status(thm)],[11712, 11710])).
% 2.34/2.53 tff(11714,plain,
% 2.34/2.53 ((~(s(s(z)) = s(z))) <=> (~(s(elem!1) = elem!1))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[11713])).
% 2.34/2.53 tff(11715,plain,
% 2.34/2.53 (~(s(elem!1) = elem!1)),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[2470, 11714])).
% 2.34/2.53 tff(11716,plain,
% 2.34/2.53 (r(elem!1, s(s(elem!1))) <=> r(s(z), s(s(elem!1)))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[10])).
% 2.34/2.53 tff(11717,plain,
% 2.34/2.53 (r(s(z), s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 2.34/2.53 inference(symmetry,[status(thm)],[11716])).
% 2.34/2.53 tff(11718,plain,
% 2.34/2.53 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(s(z))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[15])).
% 2.34/2.53 tff(11719,plain,
% 2.34/2.53 (r(s(z), s(s(s(z)))) <=> r(s(z), s(s(elem!1)))),
% 2.34/2.53 inference(symmetry,[status(thm)],[11718])).
% 2.34/2.53 tff(11720,plain,
% 2.34/2.53 (r(s(z), s(s(s(z)))) <=> r(elem!1, s(s(elem!1)))),
% 2.34/2.53 inference(transitivity,[status(thm)],[11719, 11717])).
% 2.34/2.53 tff(11721,plain,
% 2.34/2.53 (r(elem!1, s(s(elem!1)))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[1034, 11720])).
% 2.34/2.53 tff(11722,plain,
% 2.34/2.53 (~r(s(elem!1), elem!1)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[1325, 11699, 5073, 11721, 374, 11704])).
% 2.34/2.53 tff(11723,plain,
% 2.34/2.53 (b(s(elem!1), elem!1)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[813, 11722, 11715])).
% 2.34/2.53 tff(11724,plain,
% 2.34/2.53 (r(elem!1, s(s(s(elem!1)))) <=> r(s(z), s(s(s(elem!1))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[10])).
% 2.34/2.53 tff(11725,plain,
% 2.34/2.53 (r(s(z), s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 2.34/2.53 inference(symmetry,[status(thm)],[11724])).
% 2.34/2.53 tff(11726,plain,
% 2.34/2.53 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(s(s(s(z)))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[3589])).
% 2.34/2.53 tff(11727,plain,
% 2.34/2.53 (r(s(z), s(s(s(s(z))))) <=> r(s(z), s(s(s(elem!1))))),
% 2.34/2.53 inference(symmetry,[status(thm)],[11726])).
% 2.34/2.53 tff(11728,plain,
% 2.34/2.53 (r(s(z), s(s(s(s(z))))) <=> r(elem!1, s(s(s(elem!1))))),
% 2.34/2.53 inference(transitivity,[status(thm)],[11727, 11725])).
% 2.34/2.53 tff(11729,plain,
% 2.34/2.53 ((~r(s(z), s(s(s(s(z)))))) <=> (~r(elem!1, s(s(s(elem!1)))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[11728])).
% 2.34/2.53 tff(11730,plain,
% 2.34/2.53 (~r(s(z), s(s(s(s(z)))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[3585, 124, 1034, 1033])).
% 2.34/2.53 tff(11731,plain,
% 2.34/2.53 (~r(elem!1, s(s(s(elem!1))))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[11730, 11729])).
% 2.34/2.53 tff(11732,plain,
% 2.34/2.53 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[7793, 11731, 11723, 11708, 5076])).
% 2.34/2.53 tff(11733,plain,
% 2.34/2.53 (r(s(s(s(elem!1))), s(elem!1))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[664, 11732, 11704])).
% 2.34/2.53 tff(11734,plain,
% 2.34/2.53 (~r(s(s(elem!1)), s(elem!1))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[659, 11733, 11699])).
% 2.34/2.53 tff(11735,plain,
% 2.34/2.53 (b(s(s(elem!1)), s(elem!1))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[994, 11734, 11696])).
% 2.34/2.53 tff(11736,plain,
% 2.34/2.53 (b(s(s(s(z))), s(s(z)))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[11735, 11690])).
% 2.34/2.53 tff(11737,plain,
% 2.34/2.53 (r(s(elem!1), s(z)) <=> r(s(s(z)), s(z))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[14])).
% 2.34/2.53 tff(11738,plain,
% 2.34/2.53 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(z))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[10])).
% 2.34/2.53 tff(11739,plain,
% 2.34/2.53 (r(s(elem!1), elem!1) <=> r(s(s(z)), s(z))),
% 2.34/2.53 inference(transitivity,[status(thm)],[11738, 11737])).
% 2.34/2.53 tff(11740,plain,
% 2.34/2.53 ((~r(s(elem!1), elem!1)) <=> (~r(s(s(z)), s(z)))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[11739])).
% 2.34/2.53 tff(11741,plain,
% 2.34/2.53 (~r(s(s(z)), s(z))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[11722, 11740])).
% 2.34/2.53 tff(11742,plain,
% 2.34/2.53 (b(s(s(z)), s(z))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[2474, 43, 2470, 11741])).
% 2.34/2.53 tff(11743,plain,
% 2.34/2.53 (b(z, s(s(elem!1))) <=> b(z, s(s(s(z))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[15])).
% 2.34/2.53 tff(11744,plain,
% 2.34/2.53 (~r(z, s(s(elem!1)))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[1194, 374, 11721])).
% 2.34/2.53 tff(11745,plain,
% 2.34/2.53 (b(z, s(s(elem!1)))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[460, 11744])).
% 2.34/2.53 tff(11746,plain,
% 2.34/2.53 (b(z, s(s(s(z))))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[11745, 11743])).
% 2.34/2.53 tff(11747,plain,
% 2.34/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(11748,plain,
% 2.34/2.53 (((~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(11749,plain,
% 2.34/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z))))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[11748])).
% 2.34/2.53 tff(11750,plain,
% 2.34/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.34/2.53 inference(transitivity,[status(thm)],[11749, 11747])).
% 2.34/2.53 tff(11751,plain,
% 2.34/2.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.34/2.53 inference(quant_inst,[status(thm)],[])).
% 2.34/2.53 tff(11752,plain,
% 2.34/2.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z))))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[11751, 11750])).
% 2.34/2.53 tff(11753,plain,
% 2.34/2.53 ($false),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[11752, 306, 2284, 11746, 247, 11742, 11736])).
% 2.34/2.53 tff(11754,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~(elem!1 = s(z))) | (~r(z, elem!1)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.53 tff(11755,plain,
% 2.34/2.53 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[11754, 11689, 374, 11678, 11682, 10943])).
% 2.34/2.53 tff(11756,plain,
% 2.34/2.53 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[4471, 11755])).
% 2.34/2.53 tff(11757,plain,
% 2.34/2.53 (b(z, s(s(elem!1))) <=> b(z, s(s(s(z))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[11684])).
% 2.34/2.53 tff(11758,plain,
% 2.34/2.53 (r(elem!1, s(s(elem!1))) <=> r(s(z), s(s(elem!1)))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[11682])).
% 2.34/2.53 tff(11759,plain,
% 2.34/2.53 (r(s(z), s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 2.34/2.53 inference(symmetry,[status(thm)],[11758])).
% 2.34/2.53 tff(11760,plain,
% 2.34/2.53 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(s(z))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[11684])).
% 2.34/2.53 tff(11761,plain,
% 2.34/2.53 (r(s(z), s(s(s(z)))) <=> r(s(z), s(s(elem!1)))),
% 2.34/2.53 inference(symmetry,[status(thm)],[11760])).
% 2.34/2.53 tff(11762,plain,
% 2.34/2.53 (r(s(z), s(s(s(z)))) <=> r(elem!1, s(s(elem!1)))),
% 2.34/2.53 inference(transitivity,[status(thm)],[11761, 11759])).
% 2.34/2.53 tff(11763,plain,
% 2.34/2.53 (r(elem!1, s(s(elem!1)))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[10943, 11762])).
% 2.34/2.53 tff(11764,plain,
% 2.34/2.53 (~r(z, s(s(elem!1)))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[1194, 11763, 374])).
% 2.34/2.53 tff(11765,plain,
% 2.34/2.53 (b(z, s(s(elem!1)))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[460, 11764])).
% 2.34/2.53 tff(11766,plain,
% 2.34/2.53 (b(z, s(s(s(z))))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[11765, 11757])).
% 2.34/2.53 tff(11767,plain,
% 2.34/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z)))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(11768,plain,
% 2.34/2.53 (((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z)))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(11769,plain,
% 2.34/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[11768])).
% 2.34/2.53 tff(11770,plain,
% 2.34/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z)))),
% 2.34/2.53 inference(transitivity,[status(thm)],[11769, 11767])).
% 2.34/2.53 tff(11771,plain,
% 2.34/2.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 2.34/2.53 inference(quant_inst,[status(thm)],[])).
% 2.34/2.53 tff(11772,plain,
% 2.34/2.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[11771, 11770])).
% 2.34/2.53 tff(11773,plain,
% 2.34/2.53 (~b(s(s(s(s(z)))), z)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[11772, 306, 11678, 11766, 11689, 11756])).
% 2.34/2.53 tff(11774,plain,
% 2.34/2.53 (r(s(s(s(s(z)))), z)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[695, 11773])).
% 2.34/2.53 tff(11775,plain,
% 2.34/2.53 (r(s(s(s(elem!1))), z)),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[11774, 11687])).
% 2.34/2.53 tff(11776,plain,
% 2.34/2.53 (b(s(z), elem!1) <=> b(elem!1, elem!1)),
% 2.34/2.53 inference(monotonicity,[status(thm)],[3595])).
% 2.34/2.53 tff(11777,plain,
% 2.34/2.53 (b(elem!1, elem!1) <=> b(s(z), elem!1)),
% 2.34/2.53 inference(symmetry,[status(thm)],[11776])).
% 2.34/2.53 tff(11778,plain,
% 2.34/2.53 ((~b(elem!1, elem!1)) <=> (~b(s(z), elem!1))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[11777])).
% 2.34/2.53 tff(11779,plain,
% 2.34/2.53 (~b(s(z), elem!1)),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[1468, 11778])).
% 2.34/2.53 tff(11780,plain,
% 2.34/2.53 ($false),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[2831, 11779])).
% 2.34/2.53 tff(11781,plain,((~(elem!1 = s(z))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.53 tff(11782,plain,
% 2.34/2.53 (~b(s(z), elem!1)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[11781, 11682])).
% 2.34/2.53 tff(11783,plain,
% 2.34/2.53 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(z))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[11682])).
% 2.34/2.53 tff(11784,plain,
% 2.34/2.53 ((s(elem!1) = s(z)) <=> (s(elem!1) = elem!1)),
% 2.34/2.53 inference(symmetry,[status(thm)],[11783])).
% 2.34/2.53 tff(11785,plain,
% 2.34/2.53 ((~(s(elem!1) = s(z))) <=> (~(s(elem!1) = elem!1))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[11784])).
% 2.34/2.53 tff(11786,plain,
% 2.34/2.53 (~(s(elem!1) = elem!1)),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[11007, 11785])).
% 2.34/2.53 tff(11787,plain,
% 2.34/2.53 ((s(s(elem!1)) = elem!1) <=> (s(s(elem!1)) = s(z))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[11682])).
% 2.34/2.53 tff(11788,plain,
% 2.34/2.53 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 2.34/2.53 inference(symmetry,[status(thm)],[11787])).
% 2.34/2.53 tff(11789,plain,
% 2.34/2.53 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = elem!1))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[11788])).
% 2.34/2.53 tff(11790,plain,
% 2.34/2.53 (~(s(s(elem!1)) = elem!1)),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[80, 11789])).
% 2.34/2.53 tff(11791,plain,
% 2.34/2.53 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[11685, 11684])).
% 2.34/2.53 tff(11792,plain,
% 2.34/2.53 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.34/2.53 inference(symmetry,[status(thm)],[11791])).
% 2.34/2.53 tff(11793,plain,
% 2.34/2.53 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[11756, 11792])).
% 2.34/2.53 tff(11794,plain,
% 2.34/2.53 (~b(s(elem!1), elem!1)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[7044, 11793, 10999, 11006, 11790])).
% 2.34/2.53 tff(11795,plain,
% 2.34/2.53 (r(s(elem!1), elem!1)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[813, 11794, 11786])).
% 2.34/2.53 tff(11796,plain,
% 2.34/2.53 ((s(s(elem!1)) = s(elem!1)) <=> (s(s(s(z))) = s(s(z)))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[11684, 11683])).
% 2.34/2.53 tff(11797,plain,
% 2.34/2.53 ((s(s(elem!1)) = s(elem!1)) <=> (s(s(z)) = s(s(s(z))))),
% 2.34/2.53 inference(transitivity,[status(thm)],[11796, 11691])).
% 2.34/2.53 tff(11798,plain,
% 2.34/2.53 ((s(s(z)) = s(s(s(z)))) <=> (s(s(elem!1)) = s(elem!1))),
% 2.34/2.53 inference(symmetry,[status(thm)],[11797])).
% 2.34/2.53 tff(11799,plain,
% 2.34/2.53 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[11798])).
% 2.34/2.53 tff(11800,plain,
% 2.34/2.53 (~(s(s(elem!1)) = s(elem!1))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[2508, 11799])).
% 2.34/2.53 tff(11801,plain,
% 2.34/2.53 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(z))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[11682])).
% 2.34/2.53 tff(11802,plain,
% 2.34/2.53 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), elem!1)),
% 2.34/2.54 inference(symmetry,[status(thm)],[11801])).
% 2.34/2.54 tff(11803,plain,
% 2.34/2.54 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(z))), s(z))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[11684])).
% 2.34/2.54 tff(11804,plain,
% 2.34/2.54 (b(s(s(s(z))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 2.34/2.54 inference(symmetry,[status(thm)],[11803])).
% 2.34/2.54 tff(11805,plain,
% 2.34/2.54 (b(s(s(s(z))), s(z)) <=> b(s(s(elem!1)), elem!1)),
% 2.34/2.54 inference(transitivity,[status(thm)],[11804, 11802])).
% 2.34/2.54 tff(11806,plain,
% 2.34/2.54 (b(s(s(elem!1)), elem!1)),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[11678, 11805])).
% 2.34/2.54 tff(11807,plain,
% 2.34/2.54 (~r(s(elem!1), z)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[416, 11795, 374])).
% 2.34/2.54 tff(11808,plain,
% 2.34/2.54 (b(s(elem!1), z)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[2380, 11807])).
% 2.34/2.54 tff(11809,plain,
% 2.34/2.54 (~b(s(s(elem!1)), s(elem!1))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[1228, 11808, 11806, 374, 11786, 11765])).
% 2.34/2.54 tff(11810,plain,
% 2.34/2.54 (r(s(s(elem!1)), s(elem!1))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[994, 11809, 11800])).
% 2.34/2.54 tff(11811,plain,
% 2.34/2.54 (~r(s(s(elem!1)), elem!1)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[7985, 11810, 11795])).
% 2.34/2.54 tff(11812,plain,
% 2.34/2.54 (~(elem!1 = s(s(s(z))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[11310, 1034, 5, 6, 3062, 2715, 3])).
% 2.34/2.54 tff(11813,plain,
% 2.34/2.54 (r(elem!1, s(s(s(z))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[2304, 11812, 3])).
% 2.34/2.54 tff(11814,plain,
% 2.34/2.54 (~r(elem!1, s(z))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[3293, 11813, 1034])).
% 2.34/2.54 tff(11815,plain,
% 2.34/2.54 (elem!1 = s(z)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[97, 11814])).
% 2.34/2.54 tff(11816,plain,
% 2.34/2.54 (s(elem!1) = s(s(z))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[11815])).
% 2.34/2.54 tff(11817,plain,
% 2.34/2.54 (s(s(elem!1)) = s(s(s(z)))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[11816])).
% 2.34/2.54 tff(11818,plain,
% 2.34/2.54 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[11817])).
% 2.34/2.54 tff(11819,plain,
% 2.34/2.54 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(z)))), s(z))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[11818, 11815])).
% 2.34/2.54 tff(11820,plain,
% 2.34/2.54 ((elem!1 = s(s(s(elem!1)))) <=> (s(z) = s(s(s(elem!1))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[11815])).
% 2.34/2.54 tff(11821,plain,
% 2.34/2.54 ((s(z) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 2.34/2.54 inference(symmetry,[status(thm)],[11820])).
% 2.34/2.54 tff(11822,plain,
% 2.34/2.54 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 2.34/2.54 inference(transitivity,[status(thm)],[11821, 1555])).
% 2.34/2.54 tff(11823,plain,
% 2.34/2.54 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[11822])).
% 2.34/2.54 tff(11824,plain,
% 2.34/2.54 (~(s(s(s(elem!1))) = elem!1)),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[645, 11823])).
% 2.34/2.54 tff(11825,plain,
% 2.34/2.54 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[11818, 11817])).
% 2.34/2.54 tff(11826,plain,
% 2.34/2.54 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.34/2.54 inference(symmetry,[status(thm)],[11825])).
% 2.34/2.54 tff(11827,plain,
% 2.34/2.54 ((z = elem!1) <=> (z = s(z))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[11815])).
% 2.34/2.54 tff(11828,plain,
% 2.34/2.54 ((z = elem!1) <=> (s(z) = z)),
% 2.34/2.54 inference(transitivity,[status(thm)],[11827, 375])).
% 2.34/2.54 tff(11829,plain,
% 2.34/2.54 ((s(z) = z) <=> (z = elem!1)),
% 2.34/2.54 inference(symmetry,[status(thm)],[11828])).
% 2.34/2.54 tff(11830,plain,
% 2.34/2.54 ((~(s(z) = z)) <=> (~(z = elem!1))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[11829])).
% 2.34/2.54 tff(11831,plain,
% 2.34/2.54 (~(z = elem!1)),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[216, 11830])).
% 2.34/2.54 tff(11832,plain,
% 2.34/2.54 (~r(s(z), elem!1)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[3347, 11813, 1034])).
% 2.34/2.54 tff(11833,plain,
% 2.34/2.54 (s(z) = elem!1),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[4192, 11832])).
% 2.34/2.54 tff(11834,plain,
% 2.34/2.54 (~r(s(z), z)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[3089, 11833, 3062])).
% 2.34/2.54 tff(11835,plain,
% 2.34/2.54 (b(s(z), z)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[221, 11834])).
% 2.34/2.54 tff(11836,plain,
% 2.34/2.54 (b(s(s(s(z))), s(z))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[82, 11815, 6])).
% 2.34/2.54 tff(11837,plain,
% 2.34/2.54 ((s(s(elem!1)) = elem!1) <=> (s(s(elem!1)) = s(z))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[10])).
% 2.34/2.54 tff(11838,plain,
% 2.34/2.54 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 2.34/2.54 inference(symmetry,[status(thm)],[11837])).
% 2.34/2.54 tff(11839,plain,
% 2.34/2.54 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = elem!1))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[11838])).
% 2.34/2.54 tff(11840,plain,
% 2.34/2.54 (~(s(s(elem!1)) = elem!1)),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[80, 11839])).
% 2.34/2.54 tff(11841,plain,
% 2.34/2.54 ((z = elem!1) <=> (z = s(z))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[10])).
% 2.34/2.54 tff(11842,plain,
% 2.34/2.54 ((z = elem!1) <=> (s(z) = z)),
% 2.34/2.54 inference(transitivity,[status(thm)],[11841, 375])).
% 2.34/2.54 tff(11843,plain,
% 2.34/2.54 ((s(z) = z) <=> (z = elem!1)),
% 2.34/2.54 inference(symmetry,[status(thm)],[11842])).
% 2.34/2.54 tff(11844,plain,
% 2.34/2.54 ((~(s(z) = z)) <=> (~(z = elem!1))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[11843])).
% 2.34/2.54 tff(11845,plain,
% 2.34/2.54 (~(z = elem!1)),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[216, 11844])).
% 2.34/2.54 tff(11846,plain,
% 2.34/2.54 (b(z, s(s(s(z)))) <=> b(z, s(s(elem!1)))),
% 2.34/2.54 inference(symmetry,[status(thm)],[11743])).
% 2.34/2.54 tff(11847,plain,
% 2.34/2.54 ((~b(z, s(s(s(z))))) <=> (~b(z, s(s(elem!1))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[11846])).
% 2.34/2.54 tff(11848,plain,
% 2.34/2.54 (b(z, elem!1) <=> b(z, s(z))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[10])).
% 2.34/2.54 tff(11849,plain,
% 2.34/2.54 (b(z, s(z))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[838, 11848])).
% 2.34/2.54 tff(11850,plain,
% 2.34/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(11851,plain,
% 2.34/2.54 (((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(11852,plain,
% 2.34/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), z))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[11851])).
% 2.34/2.54 tff(11853,plain,
% 2.34/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)))),
% 2.34/2.54 inference(transitivity,[status(thm)],[11852, 11850])).
% 2.34/2.54 tff(11854,plain,
% 2.34/2.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))),
% 2.34/2.54 inference(quant_inst,[status(thm)],[])).
% 2.34/2.54 tff(11855,plain,
% 2.34/2.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), z))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[11854, 11853])).
% 2.34/2.54 tff(11856,plain,
% 2.34/2.54 (~b(z, s(s(s(z))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[11855, 306, 2284, 247, 11849])).
% 2.34/2.54 tff(11857,plain,
% 2.34/2.54 (~b(z, s(s(elem!1)))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[11856, 11847])).
% 2.34/2.54 tff(11858,plain,
% 2.34/2.54 (r(z, s(s(elem!1)))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[460, 11857])).
% 2.34/2.54 tff(11859,plain,
% 2.34/2.54 (~b(s(s(s(elem!1))), elem!1)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[6150, 952, 4012, 838])).
% 2.34/2.54 tff(11860,plain,
% 2.34/2.54 (r(s(s(s(elem!1))), elem!1)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[1636, 11859, 5076])).
% 2.34/2.54 tff(11861,plain,
% 2.34/2.54 (r(s(s(s(s(z)))), s(z))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[11860, 11705])).
% 2.34/2.54 tff(11862,plain,
% 2.34/2.54 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[653, 11697])).
% 2.34/2.54 tff(11863,plain,
% 2.34/2.54 ($false),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[1040, 124, 1034, 11862, 11861])).
% 2.34/2.54 tff(11864,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~(elem!1 = s(z))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.54 tff(11865,plain,
% 2.34/2.54 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[11864, 838, 10, 4012, 1034, 11858])).
% 2.34/2.54 tff(11866,plain,
% 2.34/2.54 (r(s(elem!1), elem!1)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[7090, 11865, 11845, 11840])).
% 2.34/2.54 tff(11867,plain,
% 2.34/2.54 (r(s(s(z)), s(z))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[11866, 11739])).
% 2.34/2.54 tff(11868,plain,
% 2.34/2.54 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(s(z))) = s(s(s(s(z)))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[15, 3589])).
% 2.34/2.54 tff(11869,plain,
% 2.34/2.54 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 2.34/2.54 inference(transitivity,[status(thm)],[11868, 339])).
% 2.34/2.54 tff(11870,plain,
% 2.34/2.54 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 2.34/2.54 inference(symmetry,[status(thm)],[11869])).
% 2.34/2.54 tff(11871,plain,
% 2.34/2.54 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 2.34/2.54 inference(transitivity,[status(thm)],[11870, 2425])).
% 2.34/2.54 tff(11872,plain,
% 2.34/2.54 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(elem!1))) = s(s(elem!1))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[11871])).
% 2.34/2.54 tff(11873,plain,
% 2.34/2.54 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[4470, 11872])).
% 2.34/2.54 tff(11874,plain,
% 2.34/2.54 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[610, 11865, 11873])).
% 2.34/2.54 tff(11875,plain,
% 2.34/2.54 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[11874, 5095])).
% 2.34/2.54 tff(11876,plain,
% 2.34/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(11877,plain,
% 2.34/2.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.34/2.54 inference(quant_inst,[status(thm)],[])).
% 2.34/2.54 tff(11878,plain,
% 2.34/2.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[11877, 11876])).
% 2.34/2.54 tff(11879,plain,
% 2.34/2.54 ($false),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[11878, 306, 2284, 247, 762, 485, 3620])).
% 2.34/2.54 tff(11880,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.54 tff(11881,plain,
% 2.34/2.54 (~b(s(s(s(s(z)))), s(z))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[11880, 11875, 247, 2284, 11849])).
% 2.34/2.54 tff(11882,plain,
% 2.34/2.54 (r(s(s(s(s(z)))), s(z))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[4490, 11881])).
% 2.34/2.54 tff(11883,plain,
% 2.34/2.54 (~r(s(s(z)), s(s(s(z))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[3833, 2479, 1034])).
% 2.34/2.54 tff(11884,plain,
% 2.34/2.54 (b(s(s(z)), s(s(s(z))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[2514, 11883])).
% 2.34/2.54 tff(11885,plain,
% 2.34/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(11886,plain,
% 2.34/2.54 (((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(11887,plain,
% 2.34/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(z)))))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[11886])).
% 2.34/2.54 tff(11888,plain,
% 2.34/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 2.34/2.54 inference(transitivity,[status(thm)],[11887, 11885])).
% 2.34/2.54 tff(11889,plain,
% 2.34/2.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 2.34/2.54 inference(quant_inst,[status(thm)],[])).
% 2.34/2.54 tff(11890,plain,
% 2.34/2.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(z)))))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[11889, 11888])).
% 2.34/2.54 tff(11891,plain,
% 2.34/2.54 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[11890, 306, 2284, 247, 11884, 762])).
% 2.34/2.54 tff(11892,plain,
% 2.34/2.54 (r(s(s(z)), s(s(s(s(z)))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[4510, 11891])).
% 2.34/2.54 tff(11893,plain,
% 2.34/2.54 ($false),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[4514, 124, 11892, 10126, 2479])).
% 2.34/2.54 tff(11894,plain,((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.54 tff(11895,plain,
% 2.34/2.54 (~r(s(s(z)), s(z))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[11894, 11882, 2284, 247, 11875, 1034])).
% 2.34/2.54 tff(11896,plain,
% 2.34/2.54 ($false),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[11895, 11867])).
% 2.34/2.54 tff(11897,plain,((~b(z, elem!1)) | (~(elem!1 = s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.54 tff(11898,plain,
% 2.34/2.54 (~b(z, elem!1)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[11897, 11815, 11836, 11835, 1034, 10999])).
% 2.34/2.54 tff(11899,plain,
% 2.34/2.54 (r(z, elem!1)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[835, 11898, 11831])).
% 2.34/2.54 tff(11900,plain,
% 2.34/2.54 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[11754, 11836, 11835, 11815, 11899, 1034])).
% 2.34/2.54 tff(11901,plain,
% 2.34/2.54 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[4471, 11900])).
% 2.34/2.54 tff(11902,plain,
% 2.34/2.54 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[11901, 11826])).
% 2.34/2.54 tff(11903,plain,
% 2.34/2.54 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(z))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[11815])).
% 2.34/2.54 tff(11904,plain,
% 2.34/2.54 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), elem!1)),
% 2.34/2.54 inference(symmetry,[status(thm)],[11903])).
% 2.34/2.54 tff(11905,plain,
% 2.34/2.54 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(z))), s(z))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[11817])).
% 2.34/2.54 tff(11906,plain,
% 2.34/2.54 (b(s(s(s(z))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 2.34/2.54 inference(symmetry,[status(thm)],[11905])).
% 2.34/2.54 tff(11907,plain,
% 2.34/2.54 (b(s(s(s(z))), s(z)) <=> b(s(s(elem!1)), elem!1)),
% 2.34/2.54 inference(transitivity,[status(thm)],[11906, 11904])).
% 2.34/2.54 tff(11908,plain,
% 2.34/2.54 (b(s(s(elem!1)), elem!1)),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[11836, 11907])).
% 2.34/2.54 tff(11909,plain,
% 2.34/2.54 ((~(s(z) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[11821])).
% 2.34/2.54 tff(11910,plain,
% 2.34/2.54 (~(elem!1 = s(s(s(elem!1))))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[645, 11909])).
% 2.34/2.54 tff(11911,plain,
% 2.34/2.54 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 2.34/2.54 inference(symmetry,[status(thm)],[11818])).
% 2.34/2.54 tff(11912,plain,
% 2.34/2.54 (b(z, s(s(s(s(z))))) <=> b(z, s(s(s(elem!1))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[11911])).
% 2.34/2.54 tff(11913,plain,
% 2.34/2.54 ((~b(z, s(s(s(s(z)))))) <=> (~b(z, s(s(s(elem!1)))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[11912])).
% 2.34/2.54 tff(11914,plain,
% 2.34/2.54 (b(z, s(s(elem!1))) <=> b(z, s(s(s(z))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[11817])).
% 2.34/2.54 tff(11915,plain,
% 2.34/2.54 (r(elem!1, s(s(elem!1))) <=> r(s(z), s(s(elem!1)))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[11815])).
% 2.34/2.54 tff(11916,plain,
% 2.34/2.54 (r(s(z), s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 2.34/2.54 inference(symmetry,[status(thm)],[11915])).
% 2.34/2.54 tff(11917,plain,
% 2.34/2.54 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(s(z))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[11817])).
% 2.34/2.54 tff(11918,plain,
% 2.34/2.54 (r(s(z), s(s(s(z)))) <=> r(s(z), s(s(elem!1)))),
% 2.34/2.54 inference(symmetry,[status(thm)],[11917])).
% 2.34/2.54 tff(11919,plain,
% 2.34/2.54 (r(s(z), s(s(s(z)))) <=> r(elem!1, s(s(elem!1)))),
% 2.34/2.54 inference(transitivity,[status(thm)],[11918, 11916])).
% 2.34/2.54 tff(11920,plain,
% 2.34/2.54 (r(elem!1, s(s(elem!1)))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[1034, 11919])).
% 2.34/2.54 tff(11921,plain,
% 2.34/2.54 (~r(z, s(s(elem!1)))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[1194, 11899, 11920])).
% 2.34/2.54 tff(11922,plain,
% 2.34/2.54 (b(z, s(s(elem!1)))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[460, 11921])).
% 2.34/2.54 tff(11923,plain,
% 2.34/2.54 (b(z, s(s(s(z))))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[11922, 11914])).
% 2.34/2.54 tff(11924,plain,
% 2.34/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(11925,plain,
% 2.34/2.54 (((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(11926,plain,
% 2.34/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z))))))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[11925])).
% 2.34/2.54 tff(11927,plain,
% 2.34/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.34/2.54 inference(transitivity,[status(thm)],[11926, 11924])).
% 2.34/2.54 tff(11928,plain,
% 2.34/2.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))),
% 2.34/2.54 inference(quant_inst,[status(thm)],[])).
% 2.34/2.54 tff(11929,plain,
% 2.34/2.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z))))))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[11928, 11927])).
% 2.34/2.54 tff(11930,plain,
% 2.34/2.54 (~b(z, s(s(s(s(z)))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[11929, 306, 11836, 11923, 11835, 11901])).
% 2.34/2.54 tff(11931,plain,
% 2.34/2.54 (~b(z, s(s(s(elem!1))))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[11930, 11913])).
% 2.34/2.54 tff(11932,plain,
% 2.34/2.54 (r(z, s(s(s(elem!1))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[585, 11931])).
% 2.34/2.54 tff(11933,plain,
% 2.34/2.54 (~r(elem!1, s(s(s(elem!1))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[573, 11932, 11899])).
% 2.34/2.54 tff(11934,plain,
% 2.34/2.54 (b(elem!1, s(s(s(elem!1))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[3284, 11933, 11910])).
% 2.34/2.54 tff(11935,plain,
% 2.34/2.54 (~b(s(s(s(elem!1))), elem!1)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[1672, 11934, 11908, 11902])).
% 2.34/2.54 tff(11936,plain,
% 2.34/2.54 (r(s(s(s(elem!1))), elem!1)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[1636, 11935, 11824])).
% 2.34/2.54 tff(11937,plain,
% 2.34/2.54 (r(s(s(s(s(z)))), s(z))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[11936, 11819])).
% 2.34/2.54 tff(11938,plain,
% 2.34/2.54 (~b(s(s(s(s(z)))), z)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[11772, 306, 11836, 11923, 11835, 11901])).
% 2.34/2.54 tff(11939,plain,
% 2.34/2.54 (r(s(s(s(s(z)))), z)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[695, 11938])).
% 2.34/2.54 tff(11940,plain,
% 2.34/2.54 (r(z, elem!1) <=> r(z, s(z))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[11815])).
% 2.34/2.54 tff(11941,plain,
% 2.34/2.54 (r(z, s(z))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[11899, 11940])).
% 2.34/2.54 tff(11942,plain,
% 2.34/2.54 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(11943,plain,
% 2.34/2.54 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 2.34/2.54 inference(quant_inst,[status(thm)],[])).
% 2.34/2.54 tff(11944,plain,
% 2.34/2.54 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[11943, 11942])).
% 2.34/2.54 tff(11945,plain,
% 2.34/2.54 ($false),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[11944, 124, 11941, 11939, 11937])).
% 2.34/2.54 tff(11946,plain,((~r(s(z), s(s(s(z))))) | r(elem!1, z) | r(s(s(elem!1)), elem!1) | b(s(z), elem!1) | b(elem!1, s(z)) | b(elem!1, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.54 tff(11947,plain,
% 2.34/2.54 (r(elem!1, z)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[11946, 11811, 10943, 11782, 5, 3])).
% 2.34/2.54 tff(11948,plain,
% 2.34/2.54 ((elem!1 = s(s(s(elem!1)))) <=> (s(z) = s(s(s(elem!1))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[11682])).
% 2.34/2.54 tff(11949,plain,
% 2.34/2.54 ((s(z) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 2.34/2.54 inference(symmetry,[status(thm)],[11948])).
% 2.34/2.54 tff(11950,plain,
% 2.34/2.54 ((~(s(z) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[11949])).
% 2.34/2.54 tff(11951,plain,
% 2.34/2.54 (~(elem!1 = s(s(s(elem!1))))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[645, 11950])).
% 2.34/2.54 tff(11952,plain,
% 2.34/2.54 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 2.34/2.54 inference(transitivity,[status(thm)],[11949, 1555])).
% 2.34/2.54 tff(11953,plain,
% 2.34/2.54 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[11952])).
% 2.34/2.54 tff(11954,plain,
% 2.34/2.54 (~(s(s(s(elem!1))) = elem!1)),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[645, 11953])).
% 2.34/2.54 tff(11955,plain,
% 2.34/2.54 ((s(elem!1) = s(z)) <=> (elem!1 = s(elem!1))),
% 2.34/2.54 inference(transitivity,[status(thm)],[11784, 1163])).
% 2.34/2.54 tff(11956,plain,
% 2.34/2.54 ((~(s(elem!1) = s(z))) <=> (~(elem!1 = s(elem!1)))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[11955])).
% 2.34/2.54 tff(11957,plain,
% 2.34/2.54 (~(elem!1 = s(elem!1))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[11007, 11956])).
% 2.34/2.54 tff(11958,plain,
% 2.34/2.54 (~r(elem!1, s(elem!1))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[1238, 11810, 11763])).
% 2.34/2.54 tff(11959,plain,
% 2.34/2.54 (b(elem!1, s(elem!1))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[372, 11958, 11957])).
% 2.34/2.54 tff(11960,plain,
% 2.34/2.54 (~r(s(s(s(elem!1))), elem!1)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[5088, 11947, 11793, 11806, 11763, 11959])).
% 2.34/2.54 tff(11961,plain,
% 2.34/2.54 (b(s(s(s(elem!1))), elem!1)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[1636, 11960, 11954])).
% 2.34/2.54 tff(11962,plain,
% 2.34/2.54 (~b(elem!1, s(s(s(elem!1))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[1672, 11961, 11806, 11793])).
% 2.34/2.54 tff(11963,plain,
% 2.34/2.54 (r(elem!1, s(s(s(elem!1))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[3284, 11962, 11951])).
% 2.34/2.54 tff(11964,plain,
% 2.34/2.54 (~r(s(s(s(elem!1))), z)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[851, 11963, 11947])).
% 2.34/2.54 tff(11965,plain,
% 2.34/2.54 ($false),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[11964, 11775])).
% 2.34/2.54 tff(11966,plain,(b(s(z), s(s(s(z)))) | b(elem!1, s(z)) | b(elem!1, s(s(s(z)))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.55 tff(11967,plain,
% 2.34/2.55 (b(s(z), s(s(s(z))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[11966, 11019, 3, 5])).
% 2.34/2.55 tff(11968,plain,
% 2.34/2.55 (~(s(z) = elem!1)),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[10431, 11967, 3])).
% 2.34/2.55 tff(11969,plain,
% 2.34/2.55 (~(elem!1 = s(z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[3096, 11968])).
% 2.34/2.55 tff(11970,plain,
% 2.34/2.55 (r(elem!1, s(z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[97, 11969])).
% 2.34/2.55 tff(11971,plain,
% 2.34/2.55 (~r(z, s(z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[385, 11970, 11019])).
% 2.34/2.55 tff(11972,plain,
% 2.34/2.55 (b(z, s(z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[2263, 11971])).
% 2.34/2.55 tff(11973,plain,
% 2.34/2.55 (b(s(z), s(s(s(z))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[11966, 374, 3, 5])).
% 2.34/2.55 tff(11974,plain,
% 2.34/2.55 (~(s(z) = elem!1)),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[10431, 11973, 3])).
% 2.34/2.55 tff(11975,plain,
% 2.34/2.55 (~(elem!1 = s(z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[3096, 11974])).
% 2.34/2.55 tff(11976,plain,
% 2.34/2.55 (r(elem!1, s(z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[97, 11975])).
% 2.34/2.55 tff(11977,plain,
% 2.34/2.55 (~r(z, s(z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[385, 11976, 374])).
% 2.34/2.55 tff(11978,plain,
% 2.34/2.55 (b(z, s(z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[2263, 11977])).
% 2.34/2.55 tff(11979,plain,
% 2.34/2.55 (~b(z, s(s(s(z))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[2298, 306, 2284, 11973, 11978])).
% 2.34/2.55 tff(11980,assumption,(~r(z, s(s(s(z))))), introduced(assumption)).
% 2.34/2.55 tff(11981,plain,
% 2.34/2.55 ($false),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[2415, 43, 11980, 840, 2405])).
% 2.34/2.55 tff(11982,plain,(r(z, s(s(s(z)))) | b(z, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.55 tff(11983,plain,
% 2.34/2.55 (r(z, s(s(s(z))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[11982, 11979])).
% 2.34/2.55 tff(11984,plain,
% 2.34/2.55 (~(elem!1 = s(s(s(z))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[5016, 2284, 5])).
% 2.34/2.55 tff(11985,plain,
% 2.34/2.55 (r(elem!1, s(s(s(z))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[2304, 11984, 3])).
% 2.34/2.55 tff(11986,plain,
% 2.34/2.55 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(11987,plain,
% 2.34/2.55 (((~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(elem!1, s(s(s(z))))))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(11988,plain,
% 2.34/2.55 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[11987])).
% 2.34/2.55 tff(11989,plain,
% 2.34/2.55 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 2.34/2.55 inference(transitivity,[status(thm)],[11988, 11986])).
% 2.34/2.55 tff(11990,plain,
% 2.34/2.55 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, elem!1)))),
% 2.34/2.55 inference(quant_inst,[status(thm)],[])).
% 2.34/2.55 tff(11991,plain,
% 2.34/2.55 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[11990, 11989])).
% 2.34/2.55 tff(11992,plain,
% 2.34/2.55 ($false),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[11991, 124, 374, 11985, 11983])).
% 2.34/2.55 tff(11993,plain,((~b(s(s(s(z))), s(z))) | (~r(z, elem!1)) | b(elem!1, s(s(s(z)))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.55 tff(11994,plain,
% 2.34/2.55 (~b(s(s(s(z))), s(z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[11993, 11019, 3, 5])).
% 2.34/2.55 tff(11995,plain,
% 2.34/2.55 (r(s(s(s(z))), s(z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[113, 11994])).
% 2.34/2.55 tff(11996,plain,
% 2.34/2.55 (~r(elem!1, s(s(s(z))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[11591, 11995, 11970])).
% 2.34/2.55 tff(11997,plain,
% 2.34/2.55 (elem!1 = s(s(s(z)))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[2304, 11996, 3])).
% 2.34/2.55 tff(11998,plain,
% 2.34/2.55 (b(elem!1, z) <=> b(s(s(s(z))), z)),
% 2.34/2.55 inference(monotonicity,[status(thm)],[11997])).
% 2.34/2.55 tff(11999,plain,
% 2.34/2.55 (b(s(s(s(z))), z)),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[10999, 11998])).
% 2.34/2.55 tff(12000,plain,
% 2.34/2.55 (~b(s(z), z)),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[4218, 11999, 11967, 11972])).
% 2.34/2.55 tff(12001,plain,
% 2.34/2.55 (r(s(z), z)),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[221, 12000])).
% 2.34/2.55 tff(12002,plain,
% 2.34/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(12003,plain,
% 2.34/2.55 (((~b(s(z), s(s(s(z))))) | (~b(z, 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(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(12004,plain,
% 2.34/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z))))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[12003])).
% 2.34/2.55 tff(12005,plain,
% 2.34/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)))),
% 2.34/2.55 inference(transitivity,[status(thm)],[12004, 12002])).
% 2.34/2.55 tff(12006,plain,
% 2.34/2.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, 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)))))))),
% 2.34/2.55 inference(quant_inst,[status(thm)],[])).
% 2.34/2.55 tff(12007,plain,
% 2.34/2.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[12006, 12005])).
% 2.34/2.55 tff(12008,plain,
% 2.34/2.55 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[12007, 306, 8, 942, 1531, 485])).
% 2.34/2.55 tff(12009,plain,
% 2.34/2.55 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[10124, 12008])).
% 2.34/2.55 tff(12010,plain,
% 2.34/2.55 (~r(s(s(s(s(z)))), s(z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[10128, 12009, 206])).
% 2.34/2.55 tff(12011,plain,
% 2.34/2.55 (b(s(s(s(s(z)))), s(z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[4490, 12010])).
% 2.34/2.55 tff(12012,plain,
% 2.34/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(12013,plain,
% 2.34/2.55 (((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(12014,plain,
% 2.34/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z))))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[12013])).
% 2.34/2.55 tff(12015,plain,
% 2.34/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)))),
% 2.34/2.55 inference(transitivity,[status(thm)],[12014, 12012])).
% 2.34/2.55 tff(12016,plain,
% 2.34/2.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 2.34/2.55 inference(quant_inst,[status(thm)],[])).
% 2.34/2.55 tff(12017,plain,
% 2.34/2.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[12016, 12015])).
% 2.34/2.55 tff(12018,plain,
% 2.34/2.55 ($false),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[12017, 306, 8, 942, 1531, 485, 12011])).
% 2.34/2.55 tff(12019,plain,((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.55 tff(12020,plain,
% 2.34/2.55 (~b(s(s(s(s(z)))), z)),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[12019, 11999, 11967, 11972, 11995])).
% 2.34/2.55 tff(12021,plain,
% 2.34/2.55 (r(s(s(s(s(z)))), z)),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[695, 12020])).
% 2.34/2.55 tff(12022,plain,
% 2.34/2.55 (~r(s(s(s(s(z)))), s(z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[10160, 12021, 12001])).
% 2.34/2.55 tff(12023,plain,
% 2.34/2.55 (b(s(s(s(s(z)))), s(z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[4490, 12022])).
% 2.34/2.55 tff(12024,plain,
% 2.34/2.55 (s(elem!1) = s(s(s(s(z))))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[11997])).
% 2.34/2.55 tff(12025,plain,
% 2.34/2.55 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[12024])).
% 2.34/2.55 tff(12026,plain,
% 2.34/2.55 (b(z, s(s(elem!1))) <=> b(z, s(s(s(s(s(z))))))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[12025])).
% 2.34/2.55 tff(12027,plain,
% 2.34/2.55 (b(s(z), elem!1) <=> b(s(z), s(s(s(z))))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[231])).
% 2.34/2.55 tff(12028,plain,
% 2.34/2.55 (b(s(z), s(s(s(z)))) <=> b(s(z), elem!1)),
% 2.34/2.55 inference(symmetry,[status(thm)],[12027])).
% 2.34/2.55 tff(12029,plain,
% 2.34/2.55 (b(s(z), elem!1)),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[8, 12028])).
% 2.34/2.55 tff(12030,plain,
% 2.34/2.55 ($false),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[2715, 12029])).
% 2.34/2.55 tff(12031,plain,((~(elem!1 = s(s(s(z))))) | b(s(z), elem!1) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.55 tff(12032,plain,
% 2.34/2.55 (b(s(z), elem!1)),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[12031, 11997, 11967])).
% 2.34/2.55 tff(12033,plain,
% 2.34/2.55 (~r(elem!1, s(s(s(z))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[11591, 1474, 114])).
% 2.34/2.55 tff(12034,plain,
% 2.34/2.55 (elem!1 = s(s(s(z)))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[2304, 12033, 3])).
% 2.34/2.55 tff(12035,plain,
% 2.34/2.55 (r(elem!1, s(s(elem!1))) <=> r(s(s(s(z))), s(s(elem!1)))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[12034])).
% 2.34/2.55 tff(12036,plain,
% 2.34/2.55 (r(s(s(s(z))), s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 2.34/2.55 inference(symmetry,[status(thm)],[12035])).
% 2.34/2.55 tff(12037,plain,
% 2.34/2.55 (s(elem!1) = s(s(s(s(z))))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[12034])).
% 2.34/2.55 tff(12038,plain,
% 2.34/2.55 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[12037])).
% 2.34/2.55 tff(12039,plain,
% 2.34/2.55 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 2.34/2.55 inference(symmetry,[status(thm)],[12038])).
% 2.34/2.55 tff(12040,plain,
% 2.34/2.55 (r(s(s(s(z))), s(s(s(s(s(z)))))) <=> r(s(s(s(z))), s(s(elem!1)))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[12039])).
% 2.34/2.55 tff(12041,plain,
% 2.34/2.55 (r(s(s(s(z))), s(s(s(s(s(z)))))) <=> r(elem!1, s(s(elem!1)))),
% 2.34/2.55 inference(transitivity,[status(thm)],[12040, 12036])).
% 2.34/2.55 tff(12042,plain,
% 2.34/2.55 ((~r(s(s(s(z))), s(s(s(s(s(z))))))) <=> (~r(elem!1, s(s(elem!1))))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[12041])).
% 2.34/2.55 tff(12043,plain,
% 2.34/2.55 ((z = elem!1) <=> (z = s(s(s(z))))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[12034])).
% 2.34/2.55 tff(12044,plain,
% 2.34/2.55 ((z = elem!1) <=> (s(s(s(z))) = z)),
% 2.34/2.55 inference(transitivity,[status(thm)],[12043, 3382])).
% 2.34/2.55 tff(12045,plain,
% 2.34/2.55 ((s(s(s(z))) = z) <=> (z = elem!1)),
% 2.34/2.55 inference(symmetry,[status(thm)],[12044])).
% 2.34/2.55 tff(12046,plain,
% 2.34/2.55 ((~(s(s(s(z))) = z)) <=> (~(z = elem!1))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[12045])).
% 2.34/2.55 tff(12047,plain,
% 2.34/2.55 (~(z = elem!1)),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[169, 12046])).
% 2.34/2.55 tff(12048,plain,
% 2.34/2.55 (r(z, elem!1)),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[835, 12047, 5318])).
% 2.34/2.55 tff(12049,plain,
% 2.34/2.55 (~r(z, s(z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[385, 12048, 1474])).
% 2.34/2.55 tff(12050,plain,
% 2.34/2.55 (b(z, s(z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[2263, 12049])).
% 2.34/2.55 tff(12051,plain,
% 2.34/2.55 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[12039])).
% 2.34/2.55 tff(12052,plain,
% 2.34/2.55 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.34/2.55 inference(symmetry,[status(thm)],[12051])).
% 2.34/2.55 tff(12053,plain,
% 2.34/2.55 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(s(s(z))))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[12034])).
% 2.34/2.55 tff(12054,plain,
% 2.34/2.55 (b(s(s(elem!1)), elem!1)),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[47, 11597, 6])).
% 2.34/2.55 tff(12055,plain,
% 2.34/2.55 (b(s(s(elem!1)), s(s(s(z))))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[12054, 12053])).
% 2.34/2.55 tff(12056,plain,
% 2.34/2.55 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[12055, 12052])).
% 2.34/2.55 tff(12057,plain,
% 2.34/2.55 (b(elem!1, z) <=> b(s(s(s(z))), z)),
% 2.34/2.55 inference(monotonicity,[status(thm)],[12034])).
% 2.34/2.55 tff(12058,plain,
% 2.34/2.55 (b(s(s(s(z))), z)),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[10999, 12057])).
% 2.34/2.55 tff(12059,plain,
% 2.34/2.55 (b(s(z), s(s(s(z))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[10951, 1474, 3, 2831])).
% 2.34/2.55 tff(12060,plain,
% 2.34/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(12061,plain,
% 2.34/2.55 (((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(12062,plain,
% 2.34/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[12061])).
% 2.34/2.55 tff(12063,plain,
% 2.34/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.34/2.55 inference(transitivity,[status(thm)],[12062, 12060])).
% 2.34/2.55 tff(12064,plain,
% 2.34/2.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), 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))))),
% 2.34/2.55 inference(quant_inst,[status(thm)],[])).
% 2.34/2.55 tff(12065,plain,
% 2.34/2.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[12064, 12063])).
% 2.34/2.55 tff(12066,plain,
% 2.34/2.55 (~b(s(s(s(s(s(z))))), s(z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[12065, 306, 12059, 12058, 12056, 12050])).
% 2.34/2.55 tff(12067,plain,
% 2.34/2.55 (r(s(s(s(s(s(z))))), s(z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[503, 43, 500, 12066])).
% 2.34/2.55 tff(12068,plain,
% 2.34/2.55 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[510, 124, 114, 12067])).
% 2.34/2.55 tff(12069,plain,
% 2.34/2.55 (~r(elem!1, s(s(elem!1)))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[12068, 12042])).
% 2.34/2.55 tff(12070,plain,
% 2.34/2.55 (~b(s(s(s(s(z)))), z)),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[12019, 12059, 12058, 12050, 114])).
% 2.34/2.55 tff(12071,plain,
% 2.34/2.55 (r(s(s(s(s(z)))), z)),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[695, 12070])).
% 2.34/2.55 tff(12072,plain,
% 2.34/2.55 (r(s(elem!1), z)),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[411, 12071, 12034])).
% 2.34/2.55 tff(12073,plain,
% 2.34/2.55 (~r(s(elem!1), elem!1)),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[416, 12072, 12048])).
% 2.34/2.55 tff(12074,plain,
% 2.34/2.55 (b(s(elem!1), elem!1)),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[813, 12073, 11598])).
% 2.34/2.55 tff(12075,plain,
% 2.34/2.55 ((s(elem!1) = s(z)) <=> (s(s(s(s(z)))) = s(z))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[12037])).
% 2.34/2.55 tff(12076,plain,
% 2.34/2.55 ((s(s(s(s(z)))) = s(z)) <=> (s(elem!1) = s(z))),
% 2.34/2.55 inference(symmetry,[status(thm)],[12075])).
% 2.34/2.55 tff(12077,plain,
% 2.34/2.55 ((~(s(s(s(s(z)))) = s(z))) <=> (~(s(elem!1) = s(z)))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[12076])).
% 2.34/2.55 tff(12078,plain,
% 2.34/2.55 (~(s(elem!1) = s(z))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[324, 12077])).
% 2.34/2.55 tff(12079,plain,
% 2.34/2.55 (~b(s(z), z)),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[4218, 12050, 12059, 12058])).
% 2.34/2.55 tff(12080,plain,
% 2.34/2.55 (r(s(z), z)),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[221, 12079])).
% 2.34/2.55 tff(12081,plain,
% 2.34/2.55 (~r(s(elem!1), s(z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[2634, 12072, 12080])).
% 2.34/2.55 tff(12082,plain,
% 2.34/2.55 (b(s(elem!1), s(z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[2964, 12081, 12078])).
% 2.34/2.55 tff(12083,plain,
% 2.34/2.55 ($false),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[8912, 12082, 12074, 2831, 12069, 11597, 6])).
% 2.34/2.55 tff(12084,plain,(b(s(s(s(z))), s(z)) | (~b(s(z), elem!1)) | r(s(s(elem!1)), elem!1) | b(z, elem!1) | b(elem!1, s(s(s(z)))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.55 tff(12085,plain,
% 2.34/2.55 (r(s(s(elem!1)), elem!1)),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[12084, 12032, 5318, 11994, 3, 5])).
% 2.34/2.55 tff(12086,plain,
% 2.34/2.55 (~r(z, s(s(elem!1)))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[5837, 12085, 11019])).
% 2.34/2.55 tff(12087,plain,
% 2.34/2.55 (b(z, s(s(elem!1)))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[460, 12086])).
% 2.34/2.55 tff(12088,plain,
% 2.34/2.55 (b(z, s(s(s(s(s(z))))))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[12087, 12026])).
% 2.34/2.55 tff(12089,plain,
% 2.34/2.55 (r(s(elem!1), s(s(s(z)))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[12024])).
% 2.34/2.55 tff(12090,plain,
% 2.34/2.55 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(s(s(z))))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[11997])).
% 2.34/2.55 tff(12091,plain,
% 2.34/2.55 (r(s(elem!1), elem!1) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.55 inference(transitivity,[status(thm)],[12090, 12089])).
% 2.34/2.55 tff(12092,plain,
% 2.34/2.55 ((~r(s(elem!1), elem!1)) <=> (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[12091])).
% 2.34/2.55 tff(12093,plain,
% 2.34/2.55 (r(s(elem!1), z)),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[411, 12021, 11997])).
% 2.34/2.55 tff(12094,plain,
% 2.34/2.55 (~r(s(elem!1), elem!1)),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[416, 12093, 11019])).
% 2.34/2.55 tff(12095,plain,
% 2.34/2.55 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[12094, 12092])).
% 2.34/2.55 tff(12096,plain,
% 2.34/2.55 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[4471, 12095])).
% 2.34/2.55 tff(12097,plain,
% 2.34/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(12098,plain,
% 2.34/2.55 (((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(12099,plain,
% 2.34/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z)))))))))),
% 2.34/2.56 inference(monotonicity,[status(thm)],[12098])).
% 2.34/2.56 tff(12100,plain,
% 2.34/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))))),
% 2.34/2.56 inference(transitivity,[status(thm)],[12099, 12097])).
% 2.34/2.56 tff(12101,plain,
% 2.34/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.34/2.56 inference(quant_inst,[status(thm)],[])).
% 2.34/2.56 tff(12102,plain,
% 2.34/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z)))))))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[12101, 12100])).
% 2.34/2.56 tff(12103,plain,
% 2.34/2.56 ($false),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[12102, 306, 11967, 11999, 12096, 12088, 12023])).
% 2.34/2.56 tff(12104,plain,(b(z, elem!1) | b(elem!1, s(s(s(z)))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.56 tff(12105,plain,
% 2.34/2.56 (b(z, elem!1)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[12104, 3, 5])).
% 2.34/2.56 tff(12106,plain,
% 2.34/2.56 (~r(elem!1, z)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[1049, 204, 1045])).
% 2.34/2.56 tff(12107,plain,
% 2.34/2.56 (~r(s(z), s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[11946, 2715, 6, 3062, 5, 3])).
% 2.34/2.56 tff(12108,plain,
% 2.34/2.56 (b(s(z), s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[3302, 12107])).
% 2.34/2.56 tff(12109,plain,
% 2.34/2.56 (~(elem!1 = s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[12031, 2715, 12108])).
% 2.34/2.56 tff(12110,plain,
% 2.34/2.56 (r(elem!1, s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[2304, 12109, 3])).
% 2.34/2.56 tff(12111,plain,
% 2.34/2.56 (~(s(z) = elem!1)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[10431, 12108, 3])).
% 2.34/2.56 tff(12112,plain,
% 2.34/2.56 (r(s(z), elem!1)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[4192, 12111])).
% 2.34/2.56 tff(12113,plain,
% 2.34/2.56 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(12114,plain,
% 2.34/2.56 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))),
% 2.34/2.56 inference(quant_inst,[status(thm)],[])).
% 2.34/2.56 tff(12115,plain,
% 2.34/2.56 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[12114, 12113])).
% 2.34/2.56 tff(12116,plain,
% 2.34/2.56 ($false),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[12115, 124, 374, 4, 204])).
% 2.34/2.56 tff(12117,plain,((~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.56 tff(12118,plain,
% 2.34/2.56 (~r(z, elem!1)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[12117, 204, 12112])).
% 2.34/2.56 tff(12119,plain,
% 2.34/2.56 (s(s(elem!1)) = elem!1),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[4167, 12118, 5, 6, 3062, 2715, 204])).
% 2.34/2.56 tff(12120,plain,
% 2.34/2.56 (elem!1 = s(s(elem!1))),
% 2.34/2.56 inference(symmetry,[status(thm)],[12119])).
% 2.34/2.56 tff(12121,plain,
% 2.34/2.56 (~(elem!1 = s(z))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[3096, 12111])).
% 2.34/2.56 tff(12122,plain,
% 2.34/2.56 (r(elem!1, s(z))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[97, 12121])).
% 2.34/2.56 tff(12123,plain,
% 2.34/2.56 (elem!1 = s(s(elem!1))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[1174, 12119])).
% 2.34/2.56 tff(12124,plain,
% 2.34/2.56 (s(s(s(elem!1))) = s(elem!1)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[1168, 12123])).
% 2.34/2.56 tff(12125,plain,
% 2.34/2.56 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 2.34/2.56 inference(monotonicity,[status(thm)],[12124])).
% 2.34/2.56 tff(12126,plain,
% 2.34/2.56 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 2.34/2.56 inference(symmetry,[status(thm)],[12125])).
% 2.34/2.56 tff(12127,plain,
% 2.34/2.56 (elem!1 = s(s(s(s(elem!1))))),
% 2.34/2.56 inference(transitivity,[status(thm)],[12120, 12126])).
% 2.34/2.56 tff(12128,plain,
% 2.34/2.56 (~(s(s(s(z))) = elem!1)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[1443, 12127])).
% 2.34/2.56 tff(12129,plain,
% 2.34/2.56 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[2974, 12121])).
% 2.34/2.56 tff(12130,plain,
% 2.34/2.56 (~(elem!1 = s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[10068, 12119, 12129])).
% 2.34/2.56 tff(12131,plain,
% 2.34/2.56 (r(elem!1, s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[2304, 12130, 3])).
% 2.34/2.56 tff(12132,plain,
% 2.34/2.56 (~(s(elem!1) = s(z))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[2724, 12124])).
% 2.34/2.56 tff(12133,plain,
% 2.34/2.56 (~(z = elem!1)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[2251, 12132])).
% 2.34/2.56 tff(12134,plain,
% 2.34/2.56 (b(z, elem!1)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[835, 12133, 12118])).
% 2.34/2.56 tff(12135,plain,
% 2.34/2.56 (~(s(s(s(s(z)))) = elem!1)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[9813, 12119])).
% 2.34/2.56 tff(12136,plain,
% 2.34/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(12137,plain,
% 2.34/2.56 (((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(12138,plain,
% 2.34/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))))),
% 2.34/2.56 inference(monotonicity,[status(thm)],[12137])).
% 2.34/2.56 tff(12139,plain,
% 2.34/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.34/2.56 inference(transitivity,[status(thm)],[12138, 12136])).
% 2.34/2.56 tff(12140,plain,
% 2.34/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.34/2.56 inference(quant_inst,[status(thm)],[])).
% 2.34/2.56 tff(12141,plain,
% 2.34/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[12140, 12139])).
% 2.34/2.56 tff(12142,plain,
% 2.34/2.56 (~b(s(s(s(s(z)))), elem!1)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[12141, 306, 838, 4012, 10706])).
% 2.34/2.56 tff(12143,plain,
% 2.34/2.56 (~r(s(s(s(s(z)))), elem!1)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[9849, 124, 359, 10126])).
% 2.34/2.56 tff(12144,plain,
% 2.34/2.56 ($false),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[9832, 12143, 12142, 9815])).
% 2.34/2.56 tff(12145,plain,((~r(s(s(s(s(z)))), s(z))) | (s(s(s(s(z)))) = elem!1) | (~r(elem!1, s(z))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.56 tff(12146,plain,
% 2.34/2.56 (~r(s(s(s(s(z)))), s(z))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[12145, 12135, 12122, 12134, 10999, 204])).
% 2.34/2.56 tff(12147,plain,
% 2.34/2.56 (b(s(s(s(s(z)))), s(z))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[4490, 12146])).
% 2.34/2.56 tff(12148,plain,
% 2.34/2.56 (~r(s(s(s(z))), s(z))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[11022, 12119, 5, 3])).
% 2.34/2.56 tff(12149,plain,
% 2.34/2.56 (b(s(s(s(z))), s(z))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[113, 12148])).
% 2.34/2.56 tff(12150,plain,
% 2.34/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(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))))))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(12151,plain,
% 2.34/2.56 (((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(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))))))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(12152,plain,
% 2.34/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(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)))))))),
% 2.34/2.56 inference(monotonicity,[status(thm)],[12151])).
% 2.34/2.56 tff(12153,plain,
% 2.34/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(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))))))),
% 2.34/2.56 inference(transitivity,[status(thm)],[12152, 12150])).
% 2.34/2.56 tff(12154,plain,
% 2.34/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.34/2.56 inference(quant_inst,[status(thm)],[])).
% 2.34/2.56 tff(12155,plain,
% 2.34/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[12154, 12153])).
% 2.34/2.56 tff(12156,plain,
% 2.34/2.56 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[12155, 306, 12149, 12108, 12147])).
% 2.34/2.56 tff(12157,plain,
% 2.34/2.56 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[10146, 12156])).
% 2.34/2.56 tff(12158,plain,
% 2.34/2.56 (~r(s(s(s(s(z)))), elem!1)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[10153, 124, 3313, 1033])).
% 2.34/2.56 tff(12159,plain,
% 2.34/2.56 (b(s(s(s(s(z)))), elem!1)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[9832, 12158, 9815])).
% 2.34/2.56 tff(12160,plain,
% 2.34/2.56 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(12161,plain,
% 2.34/2.56 (((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(12162,plain,
% 2.34/2.56 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z))))),
% 2.34/2.56 inference(monotonicity,[status(thm)],[12161])).
% 2.34/2.56 tff(12163,plain,
% 2.34/2.56 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 2.34/2.56 inference(transitivity,[status(thm)],[12162, 12160])).
% 2.34/2.56 tff(12164,plain,
% 2.34/2.56 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 2.34/2.56 inference(quant_inst,[status(thm)],[])).
% 2.34/2.56 tff(12165,plain,
% 2.34/2.56 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[12164, 12163])).
% 2.34/2.56 tff(12166,plain,
% 2.34/2.56 (~r(s(s(s(s(z)))), z)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[12165, 124, 2518, 1033])).
% 2.34/2.56 tff(12167,plain,
% 2.34/2.56 (b(s(s(s(s(z)))), z)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[695, 12166])).
% 2.34/2.56 tff(12168,plain,
% 2.34/2.56 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(12169,plain,
% 2.34/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))))),
% 2.34/2.56 inference(monotonicity,[status(thm)],[12168])).
% 2.34/2.56 tff(12170,plain,
% 2.34/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.34/2.56 inference(transitivity,[status(thm)],[12169, 12136])).
% 2.34/2.56 tff(12171,plain,
% 2.34/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))),
% 2.34/2.56 inference(quant_inst,[status(thm)],[])).
% 2.34/2.56 tff(12172,plain,
% 2.34/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[12171, 12170])).
% 2.34/2.56 tff(12173,plain,
% 2.34/2.56 ($false),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[12172, 306, 838, 4012, 12167, 12159])).
% 2.34/2.56 tff(12174,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (s(s(s(s(z)))) = elem!1) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.56 tff(12175,plain,
% 2.34/2.56 (~r(z, s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[12174, 12157, 10999, 12135, 12134, 12131])).
% 2.34/2.56 tff(12176,plain,
% 2.34/2.56 (b(z, s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[11982, 12175])).
% 2.34/2.56 tff(12177,plain,
% 2.34/2.56 (~r(s(s(s(s(z)))), elem!1)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[10153, 124, 12131, 12157])).
% 2.34/2.56 tff(12178,plain,
% 2.34/2.56 (b(s(s(s(s(z)))), elem!1)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[9832, 12177, 12135])).
% 2.34/2.56 tff(12179,plain,
% 2.34/2.56 (~b(s(s(s(s(z)))), z)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[12172, 306, 12134, 10999, 12178])).
% 2.34/2.56 tff(12180,plain,
% 2.34/2.56 (r(s(s(s(s(z)))), z)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[695, 12179])).
% 2.34/2.56 tff(12181,plain,
% 2.34/2.56 (~r(s(s(s(z))), z)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[4737, 12180, 12157])).
% 2.34/2.56 tff(12182,plain,
% 2.34/2.56 (b(s(s(s(z))), z)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[2197, 12181])).
% 2.34/2.56 tff(12183,plain,
% 2.34/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(12184,plain,
% 2.34/2.56 (((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1))) <=> ((~b(elem!1, z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(12185,plain,
% 2.34/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z)))))))),
% 2.34/2.56 inference(monotonicity,[status(thm)],[12184])).
% 2.34/2.56 tff(12186,plain,
% 2.34/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))))),
% 2.34/2.56 inference(transitivity,[status(thm)],[12185, 12183])).
% 2.34/2.56 tff(12187,plain,
% 2.34/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 2.34/2.56 inference(quant_inst,[status(thm)],[])).
% 2.34/2.56 tff(12188,plain,
% 2.34/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z)))))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[12187, 12186])).
% 2.34/2.56 tff(12189,plain,
% 2.34/2.56 (~b(s(s(s(z))), elem!1)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[12188, 306, 10999, 12149, 12182, 12176])).
% 2.34/2.56 tff(12190,plain,
% 2.34/2.56 (r(s(s(s(z))), elem!1)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[1489, 12189, 12128])).
% 2.34/2.56 tff(12191,plain,
% 2.34/2.56 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), elem!1)))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(12192,plain,
% 2.34/2.56 (((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), elem!1)))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(12193,plain,
% 2.34/2.56 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), elem!1))))),
% 2.34/2.56 inference(monotonicity,[status(thm)],[12192])).
% 2.34/2.56 tff(12194,plain,
% 2.34/2.56 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), elem!1)))),
% 2.34/2.56 inference(transitivity,[status(thm)],[12193, 12191])).
% 2.34/2.56 tff(12195,plain,
% 2.34/2.56 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))))),
% 2.34/2.56 inference(quant_inst,[status(thm)],[])).
% 2.34/2.56 tff(12196,plain,
% 2.34/2.56 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), elem!1))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[12195, 12194])).
% 2.34/2.56 tff(12197,plain,
% 2.34/2.56 (~r(s(s(z)), s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[12196, 124, 2859, 2478])).
% 2.34/2.56 tff(12198,plain,
% 2.34/2.56 (b(s(s(z)), s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[2514, 12197])).
% 2.34/2.56 tff(12199,plain,
% 2.34/2.56 (~r(s(s(s(z))), s(z))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[1481, 359, 2859])).
% 2.34/2.56 tff(12200,plain,
% 2.34/2.56 (b(s(s(s(z))), s(z))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[113, 12199])).
% 2.34/2.56 tff(12201,plain,
% 2.34/2.56 ($false),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[10936, 306, 12200, 8, 12198, 7218])).
% 2.34/2.56 tff(12202,plain,((~r(s(s(z)), elem!1)) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.56 tff(12203,plain,
% 2.34/2.56 (~r(s(s(z)), elem!1)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[12202, 12190, 12108, 12122])).
% 2.34/2.56 tff(12204,plain,
% 2.34/2.56 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[4284, 12119])).
% 2.34/2.56 tff(12205,plain,
% 2.34/2.56 (b(s(s(s(s(s(s(z)))))), s(z))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[651, 43, 2844, 7175])).
% 2.34/2.56 tff(12206,plain,
% 2.34/2.56 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[4603, 43, 2863, 4577])).
% 2.34/2.56 tff(12207,plain,
% 2.34/2.56 (((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(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(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(12208,plain,
% 2.34/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[12207])).
% 2.34/2.57 tff(12209,plain,
% 2.34/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 2.34/2.57 inference(transitivity,[status(thm)],[12208, 2891])).
% 2.34/2.57 tff(12210,plain,
% 2.34/2.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 2.34/2.57 inference(quant_inst,[status(thm)],[])).
% 2.34/2.57 tff(12211,plain,
% 2.34/2.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[12210, 12209])).
% 2.34/2.57 tff(12212,plain,
% 2.34/2.57 ($false),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[12211, 306, 2284, 8, 12206, 12205])).
% 2.34/2.57 tff(12213,plain,((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.57 tff(12214,plain,
% 2.34/2.57 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[12213, 12190, 12112, 12149, 12108])).
% 2.34/2.57 tff(12215,plain,
% 2.34/2.57 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[1144, 12214, 12204])).
% 2.34/2.57 tff(12216,plain,
% 2.34/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.34/2.57 inference(rewrite,[status(thm)],[])).
% 2.34/2.57 tff(12217,plain,
% 2.34/2.57 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.34/2.57 inference(rewrite,[status(thm)],[])).
% 2.34/2.57 tff(12218,plain,
% 2.34/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[12217])).
% 2.34/2.57 tff(12219,plain,
% 2.34/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.34/2.57 inference(transitivity,[status(thm)],[12218, 12216])).
% 2.34/2.57 tff(12220,plain,
% 2.34/2.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.34/2.57 inference(quant_inst,[status(thm)],[])).
% 2.34/2.57 tff(12221,plain,
% 2.34/2.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[12220, 12219])).
% 2.34/2.57 tff(12222,plain,
% 2.34/2.57 (~b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[12221, 306, 838, 4012, 2812, 2811])).
% 2.34/2.57 tff(12223,plain,
% 2.34/2.57 (r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[2829, 43, 2826, 12222])).
% 2.34/2.57 tff(12224,plain,
% 2.34/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))),
% 2.34/2.57 inference(rewrite,[status(thm)],[])).
% 2.34/2.57 tff(12225,plain,
% 2.34/2.57 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))),
% 2.34/2.57 inference(rewrite,[status(thm)],[])).
% 2.34/2.57 tff(12226,plain,
% 2.34/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1))))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[12225])).
% 2.34/2.57 tff(12227,plain,
% 2.34/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))),
% 2.34/2.57 inference(transitivity,[status(thm)],[12226, 12224])).
% 2.34/2.57 tff(12228,plain,
% 2.34/2.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 2.34/2.57 inference(quant_inst,[status(thm)],[])).
% 2.34/2.57 tff(12229,plain,
% 2.34/2.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[12228, 12227])).
% 2.34/2.57 tff(12230,plain,
% 2.34/2.57 (~b(s(s(z)), z)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[12229, 306, 838, 4012, 2811])).
% 2.34/2.57 tff(12231,plain,
% 2.34/2.57 (r(s(s(z)), z)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[2531, 12230])).
% 2.34/2.57 tff(12232,plain,
% 2.34/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 2.34/2.57 inference(rewrite,[status(thm)],[])).
% 2.34/2.57 tff(12233,plain,
% 2.34/2.57 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), z))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 2.34/2.57 inference(rewrite,[status(thm)],[])).
% 2.34/2.57 tff(12234,plain,
% 2.34/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), elem!1))))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[12233])).
% 2.34/2.57 tff(12235,plain,
% 2.34/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 2.34/2.57 inference(transitivity,[status(thm)],[12234, 12232])).
% 2.34/2.57 tff(12236,plain,
% 2.34/2.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 2.34/2.57 inference(quant_inst,[status(thm)],[])).
% 2.34/2.57 tff(12237,plain,
% 2.34/2.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), elem!1))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[12236, 12235])).
% 2.34/2.57 tff(12238,plain,
% 2.34/2.57 (~b(s(s(s(s(s(s(z)))))), z)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[12237, 306, 838, 4012, 2812])).
% 2.34/2.57 tff(12239,plain,
% 2.34/2.57 (r(s(s(s(s(s(s(z)))))), z)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[4232, 12238])).
% 2.34/2.57 tff(12240,plain,
% 2.34/2.57 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.34/2.57 inference(rewrite,[status(thm)],[])).
% 2.34/2.57 tff(12241,plain,
% 2.34/2.57 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.34/2.57 inference(quant_inst,[status(thm)],[])).
% 2.34/2.57 tff(12242,plain,
% 2.34/2.57 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[12241, 12240])).
% 2.34/2.57 tff(12243,plain,
% 2.34/2.57 ($false),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[12242, 124, 12239, 12231, 12223])).
% 2.34/2.57 tff(12244,plain,((~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(z)))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.57 tff(12245,plain,
% 2.34/2.57 (~b(s(s(z)), elem!1)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[12244, 12215, 10999, 12134])).
% 2.34/2.57 tff(12246,plain,
% 2.34/2.57 (s(s(z)) = elem!1),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[2545, 12245, 12203])).
% 2.34/2.57 tff(12247,plain,
% 2.34/2.57 (s(s(z)) = s(s(elem!1))),
% 2.34/2.57 inference(transitivity,[status(thm)],[12246, 12120])).
% 2.34/2.57 tff(12248,plain,
% 2.34/2.57 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[12247])).
% 2.34/2.57 tff(12249,plain,
% 2.34/2.57 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 2.34/2.57 inference(symmetry,[status(thm)],[12248])).
% 2.34/2.57 tff(12250,plain,
% 2.34/2.57 (s(elem!1) = s(z)),
% 2.34/2.57 inference(transitivity,[status(thm)],[67, 12249, 546])).
% 2.34/2.57 tff(12251,plain,
% 2.34/2.57 ($false),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[12132, 12250])).
% 2.34/2.57 tff(12252,plain,((~r(s(z), z)) | b(elem!1, s(s(s(z)))) | b(elem!1, s(z)) | r(s(s(elem!1)), elem!1) | r(elem!1, z) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.34/2.57 tff(12253,plain,
% 2.34/2.57 (~r(s(z), z)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[12252, 2715, 5, 6, 3062, 3])).
% 2.34/2.57 tff(12254,plain,
% 2.34/2.57 (~(z = elem!1)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[1524, 12253, 12112])).
% 2.34/2.57 tff(12255,plain,
% 2.34/2.57 (~r(s(s(s(z))), s(z))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[11591, 12122, 12110])).
% 2.34/2.57 tff(12256,plain,
% 2.34/2.57 (b(s(s(s(z))), s(z))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[113, 12255])).
% 2.34/2.57 tff(12257,plain,
% 2.34/2.57 (~r(z, s(z))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[6096, 374, 4])).
% 2.34/2.57 tff(12258,plain,
% 2.34/2.57 (b(z, s(z))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[2263, 12257])).
% 2.34/2.57 tff(12259,plain,
% 2.34/2.57 (b(s(s(s(z))), elem!1)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[7148, 374, 8, 4, 2715])).
% 2.34/2.57 tff(12260,plain,
% 2.34/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))),
% 2.34/2.57 inference(rewrite,[status(thm)],[])).
% 2.34/2.57 tff(12261,plain,
% 2.34/2.57 (((~b(s(s(s(z))), elem!1)) | (~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(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))),
% 2.34/2.57 inference(rewrite,[status(thm)],[])).
% 2.34/2.57 tff(12262,plain,
% 2.34/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(z))), elem!1)) | (~b(z, s(z))) | (~b(z, s(s(s(z)))))))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[12261])).
% 2.34/2.57 tff(12263,plain,
% 2.34/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(z))), elem!1)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))),
% 2.34/2.57 inference(transitivity,[status(thm)],[12262, 12260])).
% 2.34/2.57 tff(12264,plain,
% 2.34/2.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))),
% 2.34/2.57 inference(quant_inst,[status(thm)],[])).
% 2.34/2.57 tff(12265,plain,
% 2.34/2.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(z))) | (~b(z, s(s(s(z)))))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[12264, 12263])).
% 2.34/2.57 tff(12266,plain,
% 2.34/2.57 (~b(z, s(s(s(z))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[12265, 306, 2284, 8, 12259, 12258])).
% 2.34/2.57 tff(12267,plain,
% 2.34/2.57 (r(z, s(s(s(z))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[11982, 12266])).
% 2.34/2.57 tff(12268,plain,
% 2.34/2.57 ($false),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[11991, 124, 374, 3313, 12267])).
% 2.34/2.57 tff(12269,plain,((~r(z, elem!1)) | (~r(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~r(s(z), elem!1)) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.34/2.57 tff(12270,plain,
% 2.34/2.57 (~r(z, elem!1)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[12269, 12110, 12256, 12108, 12112, 2715])).
% 2.34/2.57 tff(12271,plain,
% 2.34/2.57 (b(z, elem!1)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[835, 12270, 12254])).
% 2.34/2.57 tff(12272,plain,
% 2.34/2.57 (~(s(s(s(z))) = elem!1)),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[12109, 1538])).
% 2.34/2.57 tff(12273,plain,
% 2.34/2.57 (s(s(s(s(s(z))))) = s(elem!1)),
% 2.34/2.57 inference(monotonicity,[status(thm)],[9807])).
% 2.34/2.57 tff(12274,plain,
% 2.34/2.57 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[12273])).
% 2.34/2.57 tff(12275,plain,
% 2.34/2.57 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 2.34/2.57 inference(symmetry,[status(thm)],[12274])).
% 2.34/2.57 tff(12276,plain,
% 2.34/2.57 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.34/2.57 inference(monotonicity,[status(thm)],[12275])).
% 2.34/2.57 tff(12277,plain,
% 2.34/2.57 (~(s(s(elem!1)) = elem!1)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[9813, 9807])).
% 2.34/2.57 tff(12278,plain,
% 2.34/2.57 (b(s(s(elem!1)), elem!1)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[47, 12277, 6])).
% 2.34/2.57 tff(12279,plain,
% 2.34/2.57 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[12278, 12276])).
% 2.34/2.57 tff(12280,plain,
% 2.34/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 2.34/2.57 inference(rewrite,[status(thm)],[])).
% 2.34/2.57 tff(12281,plain,
% 2.34/2.57 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 2.34/2.57 inference(rewrite,[status(thm)],[])).
% 2.34/2.57 tff(12282,plain,
% 2.34/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1))))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[12281])).
% 2.34/2.57 tff(12283,plain,
% 2.34/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 2.34/2.57 inference(transitivity,[status(thm)],[12282, 12280])).
% 2.34/2.57 tff(12284,plain,
% 2.34/2.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))),
% 2.34/2.57 inference(quant_inst,[status(thm)],[])).
% 2.34/2.57 tff(12285,plain,
% 2.34/2.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[12284, 12283])).
% 2.34/2.57 tff(12286,plain,
% 2.34/2.57 (~b(s(s(s(z))), z)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[12285, 306, 838, 4012, 1967])).
% 2.34/2.57 tff(12287,plain,
% 2.34/2.57 (r(s(s(s(z))), z)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[2197, 12286])).
% 2.34/2.57 tff(12288,plain,
% 2.34/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(12289,plain,
% 2.34/2.58 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(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(s(z))))))))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(12290,plain,
% 2.34/2.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(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(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1))))),
% 2.34/2.58 inference(monotonicity,[status(thm)],[12289])).
% 2.34/2.58 tff(12291,plain,
% 2.34/2.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(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(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 2.34/2.58 inference(transitivity,[status(thm)],[12290, 12288])).
% 2.34/2.58 tff(12292,plain,
% 2.34/2.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(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(s(z)))))))))),
% 2.34/2.58 inference(quant_inst,[status(thm)],[])).
% 2.34/2.58 tff(12293,plain,
% 2.34/2.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1))),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[12292, 12291])).
% 2.34/2.58 tff(12294,plain,
% 2.34/2.58 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[12293, 306, 838, 4012, 1967, 2812])).
% 2.34/2.58 tff(12295,plain,
% 2.34/2.58 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[3207, 12294])).
% 2.34/2.58 tff(12296,plain,
% 2.34/2.58 (~r(s(s(s(s(s(s(z)))))), z)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[3203, 12295, 12287])).
% 2.34/2.58 tff(12297,plain,
% 2.34/2.58 ($false),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[856, 43, 554, 12238, 12296])).
% 2.34/2.58 tff(12298,plain,((~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.58 tff(12299,plain,
% 2.34/2.58 (~b(s(s(s(z))), elem!1)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[12298, 12279, 4012, 838])).
% 2.34/2.58 tff(12300,plain,
% 2.34/2.58 (r(s(s(s(z))), elem!1)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[1489, 12299, 1483])).
% 2.34/2.58 tff(12301,plain,
% 2.34/2.58 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(z)) = elem!1)),
% 2.34/2.58 inference(monotonicity,[status(thm)],[9807])).
% 2.34/2.58 tff(12302,plain,
% 2.34/2.58 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(z)) = elem!1))),
% 2.34/2.58 inference(monotonicity,[status(thm)],[12301])).
% 2.34/2.58 tff(12303,plain,
% 2.34/2.58 (~(s(s(z)) = elem!1)),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[1612, 12302])).
% 2.34/2.58 tff(12304,plain,
% 2.34/2.58 (~b(s(s(z)), elem!1)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[12244, 12279, 4012, 838])).
% 2.34/2.58 tff(12305,plain,
% 2.34/2.58 (r(s(s(z)), elem!1)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[2545, 12304, 12303])).
% 2.34/2.58 tff(12306,plain,
% 2.34/2.58 ($false),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[12202, 12305, 12300, 8, 359])).
% 2.34/2.58 tff(12307,plain,((~(s(s(s(s(z)))) = elem!1)) | (~b(s(z), s(s(s(z))))) | (~r(elem!1, s(z))) | (s(s(s(z))) = elem!1) | (~b(elem!1, z)) | (~b(z, elem!1)) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.34/2.58 tff(12308,plain,
% 2.34/2.58 (~(s(s(s(s(z)))) = elem!1)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[12307, 12108, 12122, 12272, 10999, 12271, 6])).
% 2.34/2.58 tff(12309,plain,
% 2.34/2.58 (b(s(z), z)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[221, 12253])).
% 2.34/2.58 tff(12310,plain,
% 2.34/2.58 ((z = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = z)),
% 2.34/2.58 inference(commutativity,[status(thm)],[])).
% 2.34/2.58 tff(12311,plain,
% 2.34/2.58 ((s(s(s(s(z)))) = z) <=> (z = s(s(s(s(z)))))),
% 2.34/2.58 inference(symmetry,[status(thm)],[12310])).
% 2.34/2.58 tff(12312,plain,
% 2.34/2.58 ((~(s(s(s(s(z)))) = z)) <=> (~(z = s(s(s(s(z))))))),
% 2.34/2.58 inference(monotonicity,[status(thm)],[12311])).
% 2.34/2.58 tff(12313,plain,
% 2.34/2.58 (~(z = s(s(s(s(z)))))),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[291, 12312])).
% 2.34/2.58 tff(12314,plain,
% 2.34/2.58 (~r(s(s(s(s(z)))), z)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[4737, 1033, 205])).
% 2.34/2.58 tff(12315,plain,
% 2.34/2.58 (b(s(s(s(s(z)))), z)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[695, 12314])).
% 2.34/2.58 tff(12316,plain,
% 2.34/2.58 (~b(s(s(s(s(z)))), elem!1)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[12141, 306, 838, 4012, 12315])).
% 2.34/2.58 tff(12317,plain,
% 2.34/2.58 ($false),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[9832, 12316, 12158, 9815])).
% 2.34/2.58 tff(12318,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (s(s(s(s(z)))) = elem!1) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.58 tff(12319,plain,
% 2.34/2.58 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[12318, 7239, 838, 4012, 3313, 9815])).
% 2.34/2.58 tff(12320,plain,
% 2.34/2.58 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[4471, 12319])).
% 2.34/2.58 tff(12321,plain,
% 2.34/2.58 (~r(s(s(s(z))), s(z))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[11591, 359, 3313])).
% 2.34/2.58 tff(12322,plain,
% 2.34/2.58 (b(s(s(s(z))), s(z))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[113, 12321])).
% 2.34/2.58 tff(12323,plain,
% 2.34/2.58 (((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~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))))))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(12324,plain,
% 2.34/2.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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)))))))),
% 2.34/2.58 inference(monotonicity,[status(thm)],[12323])).
% 2.34/2.58 tff(12325,plain,
% 2.34/2.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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))))))),
% 2.34/2.58 inference(transitivity,[status(thm)],[12324, 12150])).
% 2.34/2.58 tff(12326,plain,
% 2.34/2.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.34/2.58 inference(quant_inst,[status(thm)],[])).
% 2.34/2.58 tff(12327,plain,
% 2.34/2.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(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)))))),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[12326, 12325])).
% 2.34/2.58 tff(12328,plain,
% 2.34/2.58 (~b(s(s(s(s(z)))), s(z))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[12327, 306, 12322, 8, 12320])).
% 2.34/2.58 tff(12329,plain,
% 2.34/2.58 (r(s(s(s(s(z)))), s(z))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[4490, 12328])).
% 2.34/2.58 tff(12330,plain,
% 2.34/2.58 (~r(s(s(s(s(z)))), elem!1)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[9849, 124, 359, 12329])).
% 2.34/2.58 tff(12331,plain,
% 2.34/2.58 (b(s(s(s(s(z)))), elem!1)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[9832, 12330, 9815])).
% 2.34/2.58 tff(12332,plain,
% 2.34/2.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(12333,plain,
% 2.34/2.58 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(z))))))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(12334,plain,
% 2.34/2.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z))))))))),
% 2.34/2.58 inference(monotonicity,[status(thm)],[12333])).
% 2.34/2.58 tff(12335,plain,
% 2.34/2.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))))),
% 2.34/2.58 inference(transitivity,[status(thm)],[12334, 12332])).
% 2.34/2.58 tff(12336,plain,
% 2.34/2.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(z)))))))),
% 2.34/2.58 inference(quant_inst,[status(thm)],[])).
% 2.34/2.58 tff(12337,plain,
% 2.34/2.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z))))))),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[12336, 12335])).
% 2.34/2.58 tff(12338,plain,
% 2.34/2.58 (~b(z, s(s(s(s(z)))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[12337, 306, 838, 4012, 12331])).
% 2.34/2.58 tff(12339,plain,
% 2.34/2.58 (((~![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))))))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(12340,plain,
% 2.34/2.58 ((~![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))))))),
% 2.34/2.58 inference(quant_inst,[status(thm)],[])).
% 2.34/2.58 tff(12341,plain,
% 2.34/2.58 ((~![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)))))),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[12340, 12339])).
% 2.34/2.58 tff(12342,plain,
% 2.34/2.58 ((z = s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[12341, 43, 12338])).
% 2.34/2.58 tff(12343,plain,
% 2.34/2.58 (r(z, s(s(s(s(z)))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[12342, 12313])).
% 2.34/2.58 tff(12344,plain,
% 2.34/2.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(12345,plain,
% 2.34/2.58 (((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), 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(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(12346,plain,
% 2.34/2.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.34/2.58 inference(monotonicity,[status(thm)],[12345])).
% 2.34/2.58 tff(12347,plain,
% 2.34/2.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.34/2.58 inference(transitivity,[status(thm)],[12346, 12344])).
% 2.34/2.58 tff(12348,plain,
% 2.34/2.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~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)))))))),
% 2.34/2.58 inference(quant_inst,[status(thm)],[])).
% 2.34/2.58 tff(12349,plain,
% 2.34/2.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[12348, 12347])).
% 2.34/2.58 tff(12350,plain,
% 2.34/2.58 (~b(s(z), s(s(s(s(z)))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[12349, 306, 12322, 8, 12320])).
% 2.34/2.58 tff(12351,plain,
% 2.34/2.58 (r(s(z), s(s(s(s(z)))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[5135, 12350])).
% 2.34/2.58 tff(12352,plain,
% 2.34/2.58 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(12353,plain,
% 2.34/2.58 (((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(12354,plain,
% 2.34/2.58 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))))),
% 2.34/2.58 inference(monotonicity,[status(thm)],[12353])).
% 2.34/2.58 tff(12355,plain,
% 2.34/2.58 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 2.34/2.58 inference(transitivity,[status(thm)],[12354, 12352])).
% 2.34/2.58 tff(12356,plain,
% 2.34/2.58 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(z))))),
% 2.34/2.58 inference(quant_inst,[status(thm)],[])).
% 2.34/2.58 tff(12357,plain,
% 2.34/2.58 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[12356, 12355])).
% 2.34/2.58 tff(12358,plain,
% 2.34/2.58 (~r(z, s(z))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[12357, 124, 12351, 12343])).
% 2.34/2.58 tff(12359,plain,
% 2.34/2.58 (b(z, s(z))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[2263, 12358])).
% 2.34/2.58 tff(12360,plain,
% 2.34/2.58 ($false),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[2298, 306, 12322, 8, 859, 12359])).
% 2.34/2.58 tff(12361,plain,((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (s(s(s(s(z)))) = elem!1) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.58 tff(12362,plain,
% 2.34/2.58 (~b(z, s(s(s(z))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[12361, 12108, 12271, 10999, 12308, 12122, 12110, 12309])).
% 2.34/2.58 tff(12363,plain,
% 2.34/2.58 (r(z, s(s(s(z))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[11982, 12362])).
% 2.34/2.58 tff(12364,plain,
% 2.34/2.58 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[12174, 12363, 10999, 12308, 12271, 12110])).
% 2.34/2.58 tff(12365,plain,
% 2.34/2.58 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[4471, 12364])).
% 2.34/2.58 tff(12366,plain,
% 2.34/2.58 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[12155, 306, 2284, 8, 3620])).
% 2.34/2.58 tff(12367,plain,
% 2.34/2.58 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[10146, 12366])).
% 2.34/2.58 tff(12368,plain,
% 2.34/2.58 (s(s(s(s(z)))) = elem!1),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[12174, 12367, 4012, 2518, 838, 3313])).
% 2.34/2.58 tff(12369,plain,
% 2.34/2.58 (b(s(s(s(s(z)))), s(z)) <=> b(elem!1, s(z))),
% 2.34/2.58 inference(monotonicity,[status(thm)],[12368])).
% 2.34/2.58 tff(12370,plain,
% 2.34/2.58 (b(elem!1, s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 2.34/2.58 inference(symmetry,[status(thm)],[12369])).
% 2.34/2.58 tff(12371,plain,
% 2.34/2.58 ((~b(elem!1, s(z))) <=> (~b(s(s(s(s(z)))), s(z)))),
% 2.34/2.58 inference(monotonicity,[status(thm)],[12370])).
% 2.34/2.58 tff(12372,plain,
% 2.34/2.58 (~b(s(s(s(s(z)))), s(z))),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[5, 12371])).
% 2.34/2.58 tff(12373,plain,
% 2.34/2.58 ($false),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[3620, 12372])).
% 2.34/2.58 tff(12374,plain,((~b(s(s(s(s(z)))), s(z))) | b(elem!1, s(z)) | (~b(elem!1, z)) | (~r(z, s(s(s(z))))) | (~b(z, elem!1)) | (~r(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.58 tff(12375,plain,
% 2.34/2.58 (~b(s(s(s(s(z)))), s(z))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[12374, 12363, 10999, 5, 12271, 12110, 12256, 12108])).
% 2.34/2.58 tff(12376,plain,
% 2.34/2.58 (r(s(s(s(s(z)))), s(z))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[4490, 12375])).
% 2.34/2.58 tff(12377,plain,
% 2.34/2.58 (~r(s(s(s(s(z)))), elem!1)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[9849, 124, 12122, 12376])).
% 2.34/2.58 tff(12378,plain,
% 2.34/2.58 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(12379,plain,
% 2.34/2.58 (((~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(z))))))) <=> ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(12380,plain,
% 2.34/2.58 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z))))))))),
% 2.34/2.58 inference(monotonicity,[status(thm)],[12379])).
% 2.34/2.58 tff(12381,plain,
% 2.34/2.58 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))))),
% 2.34/2.58 inference(transitivity,[status(thm)],[12380, 12378])).
% 2.34/2.58 tff(12382,plain,
% 2.34/2.58 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(z)))))))),
% 2.34/2.58 inference(quant_inst,[status(thm)],[])).
% 2.34/2.58 tff(12383,plain,
% 2.34/2.58 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z))))))),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[12382, 12381])).
% 2.34/2.58 tff(12384,plain,
% 2.34/2.58 (~r(elem!1, s(s(s(s(z)))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[12383, 124, 12122, 12376])).
% 2.34/2.58 tff(12385,assumption,(~r(s(s(s(s(z)))), elem!1)), introduced(assumption)).
% 2.34/2.58 tff(12386,plain,
% 2.34/2.58 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 2.34/2.58 inference(monotonicity,[status(thm)],[9807])).
% 2.34/2.58 tff(12387,plain,
% 2.34/2.58 (b(elem!1, s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.58 inference(symmetry,[status(thm)],[12386])).
% 2.34/2.58 tff(12388,plain,
% 2.34/2.58 ((~b(elem!1, s(s(s(z))))) <=> (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.34/2.58 inference(monotonicity,[status(thm)],[12387])).
% 2.34/2.58 tff(12389,plain,
% 2.34/2.58 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[3, 12388])).
% 2.34/2.58 tff(12390,plain,
% 2.34/2.58 ($false),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[762, 12389])).
% 2.34/2.58 tff(12391,plain,((~(s(s(s(s(z)))) = elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | b(elem!1, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.58 tff(12392,plain,
% 2.34/2.58 (~(s(s(s(s(z)))) = elem!1)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[12391, 762, 3])).
% 2.34/2.58 tff(12393,plain,
% 2.34/2.58 (b(s(s(s(s(z)))), elem!1)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[9832, 12392, 12385])).
% 2.34/2.58 tff(12394,assumption,(~r(elem!1, s(s(s(s(z)))))), introduced(assumption)).
% 2.34/2.58 tff(12395,plain,
% 2.34/2.58 ((s(s(s(s(z)))) = elem!1) <=> (elem!1 = s(s(s(s(z)))))),
% 2.34/2.58 inference(symmetry,[status(thm)],[8778])).
% 2.34/2.58 tff(12396,plain,
% 2.34/2.58 ((~(s(s(s(s(z)))) = elem!1)) <=> (~(elem!1 = s(s(s(s(z))))))),
% 2.34/2.58 inference(monotonicity,[status(thm)],[12395])).
% 2.34/2.58 tff(12397,plain,
% 2.34/2.58 (~(elem!1 = s(s(s(s(z)))))),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[12392, 12396])).
% 2.34/2.58 tff(12398,plain,
% 2.34/2.58 (((~![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))))))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(12399,plain,
% 2.34/2.58 ((~![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))))))),
% 2.34/2.58 inference(quant_inst,[status(thm)],[])).
% 2.34/2.58 tff(12400,plain,
% 2.34/2.58 ((~![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)))))),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[12399, 12398])).
% 2.34/2.58 tff(12401,plain,
% 2.34/2.58 ((elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z)))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[12400, 43])).
% 2.34/2.58 tff(12402,plain,
% 2.34/2.58 (b(elem!1, s(s(s(s(z)))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[12401, 12397, 12394])).
% 2.34/2.58 tff(12403,plain,
% 2.34/2.58 (b(z, elem!1)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[835, 7, 2170])).
% 2.34/2.58 tff(12404,plain,
% 2.34/2.58 (~b(s(s(s(s(z)))), z)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[12172, 306, 12403, 4012, 12393])).
% 2.34/2.58 tff(12405,plain,
% 2.34/2.58 (r(s(s(s(s(z)))), z)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[695, 12404])).
% 2.34/2.58 tff(12406,plain,
% 2.34/2.58 (~b(z, s(s(s(s(z)))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[12337, 306, 12403, 4012, 12393])).
% 2.34/2.59 tff(12407,plain,
% 2.34/2.59 ((z = s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[12341, 43, 12406])).
% 2.34/2.59 tff(12408,plain,
% 2.34/2.59 (r(z, s(s(s(s(z)))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[12407, 12313])).
% 2.34/2.59 tff(12409,plain,
% 2.34/2.59 (~b(s(z), s(s(s(s(z)))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[12349, 306, 12322, 8, 762])).
% 2.34/2.59 tff(12410,plain,
% 2.34/2.59 (r(s(z), s(s(s(s(z)))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[5135, 12409])).
% 2.34/2.59 tff(12411,plain,
% 2.34/2.59 (~r(z, s(z))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[12357, 124, 12410, 12408])).
% 2.34/2.59 tff(12412,plain,
% 2.34/2.59 (b(z, s(z))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[2263, 12411])).
% 2.34/2.59 tff(12413,plain,
% 2.34/2.59 (~b(s(s(s(z))), z)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[4218, 12412, 8, 247])).
% 2.34/2.59 tff(12414,plain,
% 2.34/2.59 (r(s(s(s(z))), z)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[2197, 12413])).
% 2.34/2.59 tff(12415,plain,
% 2.34/2.59 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[4478, 124, 12414, 12405])).
% 2.34/2.59 tff(12416,plain,
% 2.34/2.59 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[4481, 12415])).
% 2.34/2.59 tff(12417,plain,
% 2.34/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))))),
% 2.34/2.59 inference(rewrite,[status(thm)],[])).
% 2.34/2.59 tff(12418,plain,
% 2.34/2.59 (((~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(elem!1, z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))))),
% 2.34/2.59 inference(rewrite,[status(thm)],[])).
% 2.34/2.59 tff(12419,plain,
% 2.34/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z))))))))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[12418])).
% 2.34/2.59 tff(12420,plain,
% 2.34/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))))),
% 2.34/2.59 inference(transitivity,[status(thm)],[12419, 12417])).
% 2.34/2.59 tff(12421,plain,
% 2.34/2.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)))),
% 2.34/2.59 inference(quant_inst,[status(thm)],[])).
% 2.34/2.59 tff(12422,plain,
% 2.34/2.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z))))))),
% 2.34/2.59 inference(modus_ponens,[status(thm)],[12421, 12420])).
% 2.34/2.59 tff(12423,plain,
% 2.34/2.59 (~b(s(s(s(z))), elem!1)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[12422, 306, 4012, 12416, 12393, 12402])).
% 2.34/2.59 tff(12424,plain,
% 2.34/2.59 (r(s(s(s(z))), elem!1)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[1489, 12423, 1483])).
% 2.34/2.59 tff(12425,plain,
% 2.34/2.59 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[12213, 12424, 4, 12322, 8])).
% 2.34/2.59 tff(12426,assumption,(b(s(s(s(s(z)))), elem!1)), introduced(assumption)).
% 2.34/2.59 tff(12427,plain,
% 2.34/2.59 (~b(s(s(s(s(z)))), z)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[12172, 306, 12403, 4012, 12426])).
% 2.34/2.59 tff(12428,plain,
% 2.34/2.59 (r(s(s(s(s(z)))), z)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[695, 12427])).
% 2.34/2.59 tff(12429,plain,
% 2.34/2.59 (~b(s(s(elem!1)), z)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[3976, 92, 3062, 7, 2170])).
% 2.34/2.59 tff(12430,plain,
% 2.34/2.59 (r(s(s(elem!1)), z)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[476, 12429])).
% 2.34/2.59 tff(12431,plain,
% 2.34/2.59 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.34/2.59 inference(rewrite,[status(thm)],[])).
% 2.34/2.59 tff(12432,plain,
% 2.34/2.59 (((~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.34/2.59 inference(rewrite,[status(thm)],[])).
% 2.34/2.59 tff(12433,plain,
% 2.34/2.59 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), s(s(s(s(z))))))))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[12432])).
% 2.34/2.59 tff(12434,plain,
% 2.34/2.59 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.34/2.59 inference(transitivity,[status(thm)],[12433, 12431])).
% 2.34/2.59 tff(12435,plain,
% 2.34/2.59 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.34/2.59 inference(quant_inst,[status(thm)],[])).
% 2.34/2.59 tff(12436,plain,
% 2.34/2.59 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), s(s(s(s(z))))))),
% 2.34/2.59 inference(modus_ponens,[status(thm)],[12435, 12434])).
% 2.34/2.59 tff(12437,plain,
% 2.34/2.59 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[12436, 124, 12430, 12428])).
% 2.34/2.59 tff(12438,plain,
% 2.34/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.34/2.59 inference(rewrite,[status(thm)],[])).
% 2.34/2.59 tff(12439,plain,
% 2.34/2.59 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.34/2.59 inference(rewrite,[status(thm)],[])).
% 2.34/2.59 tff(12440,plain,
% 2.34/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z))))))))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[12439])).
% 2.34/2.59 tff(12441,plain,
% 2.34/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.34/2.59 inference(transitivity,[status(thm)],[12440, 12438])).
% 2.34/2.59 tff(12442,plain,
% 2.34/2.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.34/2.59 inference(quant_inst,[status(thm)],[])).
% 2.34/2.59 tff(12443,plain,
% 2.34/2.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z))))))),
% 2.34/2.59 inference(modus_ponens,[status(thm)],[12442, 12441])).
% 2.34/2.59 tff(12444,plain,
% 2.34/2.59 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[12443, 306, 12403, 4012, 92, 12426])).
% 2.34/2.59 tff(12445,plain,
% 2.34/2.59 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(z))))) | b(s(s(elem!1)), s(s(s(s(z))))) | r(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(z))))) | b(s(s(elem!1)), s(s(s(s(z))))) | r(s(s(elem!1)), s(s(s(s(z))))))),
% 2.34/2.59 inference(rewrite,[status(thm)],[])).
% 2.34/2.59 tff(12446,plain,
% 2.34/2.59 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(z))))) | b(s(s(elem!1)), s(s(s(s(z))))) | r(s(s(elem!1)), s(s(s(s(z))))))),
% 2.34/2.59 inference(quant_inst,[status(thm)],[])).
% 2.34/2.59 tff(12447,plain,
% 2.34/2.59 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(z))))) | b(s(s(elem!1)), s(s(s(s(z))))) | r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.34/2.59 inference(modus_ponens,[status(thm)],[12446, 12445])).
% 2.34/2.59 tff(12448,plain,
% 2.34/2.59 (s(s(elem!1)) = s(s(s(s(z))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[12447, 43, 12444, 12437])).
% 2.34/2.59 tff(12449,plain,
% 2.34/2.59 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(z)))))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[12448])).
% 2.34/2.59 tff(12450,plain,
% 2.34/2.59 (s(elem!1) = s(s(s(z)))),
% 2.34/2.59 inference(transitivity,[status(thm)],[67, 12449, 320])).
% 2.34/2.59 tff(12451,plain,
% 2.34/2.59 (inj_0(s(elem!1)) = inj_0(s(s(s(z))))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[12450])).
% 2.34/2.59 tff(12452,plain,
% 2.34/2.59 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 2.34/2.59 inference(symmetry,[status(thm)],[12451])).
% 2.34/2.59 tff(12453,plain,
% 2.34/2.59 (s(s(z)) = elem!1),
% 2.34/2.59 inference(transitivity,[status(thm)],[103, 12452, 135])).
% 2.34/2.59 tff(12454,plain,
% 2.34/2.59 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[12448])).
% 2.34/2.59 tff(12455,plain,
% 2.34/2.59 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 2.34/2.59 inference(symmetry,[status(thm)],[12454])).
% 2.34/2.59 tff(12456,plain,
% 2.34/2.59 (r(s(s(s(s(s(z))))), s(s(z))) <=> r(s(s(s(elem!1))), elem!1)),
% 2.34/2.59 inference(monotonicity,[status(thm)],[12455, 12453])).
% 2.34/2.59 tff(12457,plain,
% 2.34/2.59 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(s(z))))), s(s(z)))),
% 2.34/2.59 inference(symmetry,[status(thm)],[12456])).
% 2.34/2.59 tff(12458,plain,
% 2.34/2.59 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(s(elem!1))) = elem!1)),
% 2.34/2.59 inference(monotonicity,[status(thm)],[12455, 12453])).
% 2.34/2.59 tff(12459,plain,
% 2.34/2.59 ((s(s(s(s(s(z))))) = s(s(z))) <=> (elem!1 = s(s(s(elem!1))))),
% 2.34/2.59 inference(transitivity,[status(thm)],[12458, 1554])).
% 2.34/2.59 tff(12460,plain,
% 2.34/2.59 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(s(elem!1))) = elem!1)),
% 2.34/2.59 inference(transitivity,[status(thm)],[12459, 1555])).
% 2.34/2.59 tff(12461,plain,
% 2.34/2.59 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[12460])).
% 2.34/2.59 tff(12462,plain,
% 2.34/2.59 (~(s(s(s(elem!1))) = elem!1)),
% 2.34/2.59 inference(modus_ponens,[status(thm)],[6464, 12461])).
% 2.34/2.59 tff(12463,plain,
% 2.34/2.59 (s(s(s(s(elem!1)))) = s(s(s(s(s(s(z))))))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[12454])).
% 2.34/2.59 tff(12464,plain,
% 2.34/2.59 (elem!1 = s(s(z))),
% 2.34/2.59 inference(transitivity,[status(thm)],[1651, 12451, 102])).
% 2.34/2.59 tff(12465,plain,
% 2.34/2.59 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(s(z)) = s(s(s(s(s(s(z)))))))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[12464, 12463])).
% 2.34/2.59 tff(12466,plain,
% 2.34/2.59 ((s(s(z)) = s(s(s(s(s(s(z))))))) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 2.34/2.59 inference(symmetry,[status(thm)],[12465])).
% 2.34/2.59 tff(12467,plain,
% 2.34/2.59 ((s(s(z)) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 2.34/2.59 inference(transitivity,[status(thm)],[12466, 1543])).
% 2.34/2.59 tff(12468,plain,
% 2.34/2.59 ((~(s(s(z)) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[12467])).
% 2.34/2.59 tff(12469,plain,
% 2.34/2.59 (~(s(s(s(s(elem!1)))) = elem!1)),
% 2.34/2.59 inference(modus_ponens,[status(thm)],[2826, 12468])).
% 2.34/2.59 tff(12470,plain,
% 2.34/2.59 (r(s(s(s(s(elem!1)))), elem!1) <=> r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.34/2.59 inference(monotonicity,[status(thm)],[12463])).
% 2.34/2.59 tff(12471,plain,
% 2.34/2.59 (r(s(s(s(s(s(s(z)))))), elem!1) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 2.34/2.59 inference(symmetry,[status(thm)],[12470])).
% 2.34/2.59 tff(12472,plain,
% 2.34/2.59 ((~r(s(s(s(s(s(s(z)))))), elem!1)) <=> (~r(s(s(s(s(elem!1)))), elem!1))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[12471])).
% 2.34/2.59 tff(12473,plain,
% 2.34/2.59 (~r(s(s(s(s(elem!1)))), elem!1)),
% 2.34/2.59 inference(modus_ponens,[status(thm)],[8026, 12472])).
% 2.34/2.59 tff(12474,plain,
% 2.34/2.59 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[1736, 12473, 12469])).
% 2.34/2.59 tff(12475,plain,
% 2.34/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.34/2.59 inference(rewrite,[status(thm)],[])).
% 2.34/2.59 tff(12476,plain,
% 2.34/2.59 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.34/2.59 inference(rewrite,[status(thm)],[])).
% 2.34/2.59 tff(12477,plain,
% 2.34/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1))))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[12476])).
% 2.34/2.59 tff(12478,plain,
% 2.34/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.34/2.59 inference(transitivity,[status(thm)],[12477, 12475])).
% 2.34/2.59 tff(12479,plain,
% 2.34/2.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~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))))))),
% 2.34/2.59 inference(quant_inst,[status(thm)],[])).
% 2.34/2.59 tff(12480,plain,
% 2.34/2.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1))),
% 2.34/2.59 inference(modus_ponens,[status(thm)],[12479, 12478])).
% 2.34/2.59 tff(12481,plain,
% 2.34/2.59 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[12480, 306, 838, 4012, 1664, 2076])).
% 2.34/2.59 tff(12482,plain,
% 2.34/2.59 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[1958, 43, 3476, 12481])).
% 2.34/2.59 tff(12483,plain,
% 2.34/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.34/2.59 inference(rewrite,[status(thm)],[])).
% 2.34/2.59 tff(12484,plain,
% 2.34/2.59 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z))) <=> ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.34/2.59 inference(rewrite,[status(thm)],[])).
% 2.34/2.59 tff(12485,plain,
% 2.34/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1))))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[12484])).
% 2.34/2.59 tff(12486,plain,
% 2.34/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.34/2.59 inference(transitivity,[status(thm)],[12485, 12483])).
% 2.34/2.59 tff(12487,plain,
% 2.34/2.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))),
% 2.34/2.59 inference(quant_inst,[status(thm)],[])).
% 2.34/2.59 tff(12488,plain,
% 2.34/2.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1))),
% 2.34/2.59 inference(modus_ponens,[status(thm)],[12487, 12486])).
% 2.34/2.59 tff(12489,plain,
% 2.34/2.59 (~b(s(s(s(elem!1))), z)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[12488, 306, 838, 4012, 1664])).
% 2.34/2.59 tff(12490,plain,
% 2.34/2.59 (r(s(s(s(elem!1))), z)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[3033, 43, 579, 12489])).
% 2.34/2.59 tff(12491,plain,
% 2.34/2.59 ($false),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[10778, 124, 12490, 6307, 12482])).
% 2.34/2.59 tff(12492,plain,((~b(s(s(s(s(elem!1)))), elem!1)) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.59 tff(12493,plain,
% 2.34/2.59 (~b(s(s(s(elem!1))), elem!1)),
% 2.34/2.60 inference(unit_resolution,[status(thm)],[12492, 12474, 4012, 12403, 6279])).
% 2.34/2.60 tff(12494,plain,
% 2.34/2.60 (r(s(s(s(elem!1))), elem!1)),
% 2.34/2.60 inference(unit_resolution,[status(thm)],[1636, 12493, 12462])).
% 2.34/2.60 tff(12495,plain,
% 2.34/2.60 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.34/2.60 inference(modus_ponens,[status(thm)],[12494, 12457])).
% 2.34/2.60 tff(12496,plain,
% 2.34/2.60 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.34/2.60 inference(monotonicity,[status(thm)],[12454, 12450])).
% 2.34/2.60 tff(12497,plain,
% 2.34/2.60 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(z))))),
% 2.34/2.60 inference(monotonicity,[status(thm)],[12450])).
% 2.34/2.60 tff(12498,plain,
% 2.34/2.60 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(elem!1))),
% 2.34/2.60 inference(symmetry,[status(thm)],[12497])).
% 2.34/2.60 tff(12499,plain,
% 2.34/2.60 (r(elem!1, s(elem!1))),
% 2.34/2.60 inference(modus_ponens,[status(thm)],[3313, 12498])).
% 2.34/2.60 tff(12500,plain,
% 2.34/2.60 (r(z, s(elem!1)) <=> r(z, s(s(s(z))))),
% 2.34/2.60 inference(monotonicity,[status(thm)],[12450])).
% 2.34/2.60 tff(12501,plain,
% 2.34/2.60 (r(z, s(s(s(z)))) <=> r(z, s(elem!1))),
% 2.34/2.60 inference(symmetry,[status(thm)],[12500])).
% 2.34/2.60 tff(12502,plain,
% 2.34/2.60 (r(z, s(elem!1))),
% 2.34/2.60 inference(modus_ponens,[status(thm)],[2518, 12501])).
% 2.34/2.60 tff(12503,plain,
% 2.34/2.60 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.34/2.60 inference(unit_resolution,[status(thm)],[6154, 12502, 12403, 12462, 12499, 4012])).
% 2.34/2.60 tff(12504,plain,
% 2.34/2.60 (b(s(s(s(elem!1))), s(elem!1))),
% 2.34/2.60 inference(unit_resolution,[status(thm)],[664, 12503, 144])).
% 2.34/2.60 tff(12505,plain,
% 2.34/2.60 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.34/2.60 inference(modus_ponens,[status(thm)],[12504, 12496])).
% 2.34/2.60 tff(12506,plain,
% 2.34/2.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), 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(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.34/2.60 inference(rewrite,[status(thm)],[])).
% 2.34/2.60 tff(12507,plain,
% 2.34/2.60 (((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.34/2.60 inference(rewrite,[status(thm)],[])).
% 2.34/2.60 tff(12508,plain,
% 2.34/2.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), 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(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), 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(z)))))),
% 2.34/2.60 inference(monotonicity,[status(thm)],[12507])).
% 2.34/2.60 tff(12509,plain,
% 2.34/2.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), 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(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), 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(z))))),
% 2.34/2.60 inference(transitivity,[status(thm)],[12508, 12506])).
% 2.34/2.60 tff(12510,plain,
% 2.34/2.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), 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(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.34/2.60 inference(quant_inst,[status(thm)],[])).
% 2.34/2.60 tff(12511,plain,
% 2.34/2.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), 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(z)))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[12510, 12509])).
% 2.44/2.60 tff(12512,plain,
% 2.44/2.60 (~b(s(s(s(s(s(z))))), s(z))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[12511, 306, 2284, 8, 12505])).
% 2.44/2.60 tff(12513,plain,
% 2.44/2.60 (r(s(s(s(s(s(z))))), s(z))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[503, 43, 500, 12512])).
% 2.44/2.60 tff(12514,plain,
% 2.44/2.60 (r(s(z), elem!1) <=> r(s(z), s(s(z)))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[12464])).
% 2.44/2.60 tff(12515,plain,
% 2.44/2.60 (r(s(z), s(s(z)))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[4, 12514])).
% 2.44/2.60 tff(12516,plain,
% 2.44/2.60 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.44/2.60 inference(rewrite,[status(thm)],[])).
% 2.44/2.60 tff(12517,plain,
% 2.44/2.60 (((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z)))) <=> ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.44/2.60 inference(rewrite,[status(thm)],[])).
% 2.44/2.60 tff(12518,plain,
% 2.44/2.60 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[12517])).
% 2.44/2.60 tff(12519,plain,
% 2.44/2.60 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.44/2.60 inference(transitivity,[status(thm)],[12518, 12516])).
% 2.44/2.60 tff(12520,plain,
% 2.44/2.60 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.44/2.60 inference(quant_inst,[status(thm)],[])).
% 2.44/2.60 tff(12521,plain,
% 2.44/2.60 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[12520, 12519])).
% 2.44/2.60 tff(12522,plain,
% 2.44/2.60 ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[12521, 124, 12515])).
% 2.44/2.60 tff(12523,plain,
% 2.44/2.60 ($false),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[12522, 12513, 12495])).
% 2.44/2.60 tff(12524,plain,((s(s(elem!1)) = elem!1) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, z)) | r(s(s(s(s(s(s(z)))))), elem!1) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | r(elem!1, z) | r(z, elem!1) | (z = elem!1) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.44/2.60 tff(12525,plain,
% 2.44/2.60 (s(s(elem!1)) = elem!1),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[12524, 12425, 8, 4012, 12322, 4, 3313, 2518, 12393, 3062, 7, 2170, 6])).
% 2.44/2.60 tff(12526,plain,
% 2.44/2.60 (elem!1 = s(s(elem!1))),
% 2.44/2.60 inference(symmetry,[status(thm)],[12525])).
% 2.44/2.60 tff(12527,plain,
% 2.44/2.60 (~r(s(s(z)), elem!1)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[12202, 12424, 8, 359])).
% 2.44/2.60 tff(12528,plain,
% 2.44/2.60 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[4284, 12525])).
% 2.44/2.60 tff(12529,plain,
% 2.44/2.60 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[1144, 12528, 12425])).
% 2.44/2.60 tff(12530,plain,
% 2.44/2.60 (~b(s(s(z)), elem!1)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[12244, 12529, 4012, 12403])).
% 2.44/2.60 tff(12531,plain,
% 2.44/2.60 (s(s(z)) = elem!1),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[2545, 12530, 12527])).
% 2.44/2.60 tff(12532,plain,
% 2.44/2.60 (s(s(z)) = s(s(elem!1))),
% 2.44/2.60 inference(transitivity,[status(thm)],[12531, 12526])).
% 2.44/2.60 tff(12533,plain,
% 2.44/2.60 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[12532])).
% 2.44/2.60 tff(12534,plain,
% 2.44/2.60 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 2.44/2.60 inference(symmetry,[status(thm)],[12533])).
% 2.44/2.60 tff(12535,plain,
% 2.44/2.60 (s(elem!1) = s(z)),
% 2.44/2.60 inference(transitivity,[status(thm)],[67, 12534, 546])).
% 2.44/2.60 tff(12536,plain,
% 2.44/2.60 ($false),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[3099, 12535])).
% 2.44/2.60 tff(12537,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, z)) | (~b(s(z), s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))) | r(elem!1, z) | r(z, elem!1) | (z = elem!1) | r(s(s(elem!1)), elem!1) | (~r(elem!1, s(z))) | (s(s(s(z))) = elem!1) | (~b(s(z), z)) | r(elem!1, s(s(s(s(z))))) | r(s(s(s(s(z)))), elem!1) | b(elem!1, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.60 tff(12538,plain,
% 2.44/2.60 ($false),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[12537, 12384, 12377, 12108, 12112, 12110, 10999, 3062, 12270, 12254, 6, 12122, 12272, 12309, 12363, 12365, 3])).
% 2.44/2.60 tff(12539,plain,(b(s(z), elem!1) | r(elem!1, z) | r(s(s(elem!1)), elem!1) | b(elem!1, s(s(s(z)))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.60 tff(12540,plain,
% 2.44/2.60 (r(s(s(elem!1)), elem!1)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[12539, 12106, 2715, 3, 5])).
% 2.44/2.60 tff(12541,plain,
% 2.44/2.60 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[12540, 11015])).
% 2.44/2.60 tff(12542,plain,
% 2.44/2.60 ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[11582, 124, 1034])).
% 2.44/2.60 tff(12543,plain,
% 2.44/2.60 (~r(s(z), s(s(s(s(s(z))))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[12542, 12541])).
% 2.44/2.60 tff(12544,plain,
% 2.44/2.60 (b(s(z), s(s(s(s(s(z))))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[626, 43, 12543, 11013])).
% 2.44/2.60 tff(12545,plain,
% 2.44/2.60 (b(s(elem!1), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[234])).
% 2.44/2.60 tff(12546,plain,
% 2.44/2.60 (b(s(s(s(s(z)))), s(z)) <=> b(s(elem!1), s(z))),
% 2.44/2.60 inference(symmetry,[status(thm)],[12545])).
% 2.44/2.60 tff(12547,plain,
% 2.44/2.60 ((s(s(s(s(z)))) = elem!1) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[231])).
% 2.44/2.60 tff(12548,plain,
% 2.44/2.60 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(s(z)))) = elem!1)),
% 2.44/2.60 inference(symmetry,[status(thm)],[12547])).
% 2.44/2.60 tff(12549,plain,
% 2.44/2.60 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[12548])).
% 2.44/2.60 tff(12550,plain,
% 2.44/2.60 (~(s(s(s(s(z)))) = elem!1)),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[4470, 12549])).
% 2.44/2.60 tff(12551,plain,
% 2.44/2.60 (~r(s(s(s(s(z)))), s(z))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[12145, 204, 12105, 359, 10999, 12550])).
% 2.44/2.60 tff(12552,plain,
% 2.44/2.60 (b(s(s(s(s(z)))), s(z))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[4490, 12551])).
% 2.44/2.60 tff(12553,plain,
% 2.44/2.60 (b(s(elem!1), s(z))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[12552, 12546])).
% 2.44/2.60 tff(12554,plain,
% 2.44/2.60 (~r(s(s(elem!1)), s(z))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[9725, 12540, 359])).
% 2.44/2.60 tff(12555,plain,
% 2.44/2.60 (b(s(s(elem!1)), s(z))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[3989, 12554])).
% 2.44/2.60 tff(12556,plain,
% 2.44/2.60 (b(s(z), s(s(elem!1)))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[12544, 11009])).
% 2.44/2.60 tff(12557,plain,
% 2.44/2.60 (~b(s(s(elem!1)), s(elem!1))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[4007, 12556, 12555, 12553])).
% 2.44/2.60 tff(12558,plain,
% 2.44/2.60 (r(s(s(elem!1)), s(elem!1))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[994, 12557, 196])).
% 2.44/2.60 tff(12559,plain,
% 2.44/2.60 (~r(s(elem!1), elem!1)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[7985, 12558, 12540])).
% 2.44/2.60 tff(12560,plain,
% 2.44/2.60 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[7090, 12559, 11006, 91])).
% 2.44/2.60 tff(12561,plain,
% 2.44/2.60 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[659, 12560, 12558])).
% 2.44/2.60 tff(12562,plain,
% 2.44/2.60 (b(s(s(s(elem!1))), s(elem!1))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[664, 12561, 144])).
% 2.44/2.60 tff(12563,plain,
% 2.44/2.60 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[12562, 11073])).
% 2.44/2.60 tff(12564,plain,
% 2.44/2.60 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[240, 231])).
% 2.44/2.60 tff(12565,plain,
% 2.44/2.60 (~(s(s(s(elem!1))) = elem!1)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[4105, 11016, 11007])).
% 2.44/2.60 tff(12566,plain,
% 2.44/2.60 (~r(s(s(s(elem!1))), elem!1)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[7780, 12560, 12540])).
% 2.44/2.60 tff(12567,plain,
% 2.44/2.60 (b(s(s(s(elem!1))), elem!1)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[1636, 12566, 12565])).
% 2.44/2.60 tff(12568,plain,
% 2.44/2.60 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[12567, 12564])).
% 2.44/2.60 tff(12569,plain,
% 2.44/2.60 (~r(elem!1, s(elem!1))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[5630, 12558, 12540])).
% 2.44/2.60 tff(12570,plain,
% 2.44/2.60 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[11127, 12569, 231])).
% 2.44/2.60 tff(12571,plain,
% 2.44/2.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.44/2.60 inference(rewrite,[status(thm)],[])).
% 2.44/2.60 tff(12572,plain,
% 2.44/2.60 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.44/2.60 inference(rewrite,[status(thm)],[])).
% 2.44/2.60 tff(12573,plain,
% 2.44/2.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[12572])).
% 2.44/2.60 tff(12574,plain,
% 2.44/2.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.44/2.60 inference(transitivity,[status(thm)],[12573, 12571])).
% 2.44/2.60 tff(12575,plain,
% 2.44/2.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 2.44/2.60 inference(quant_inst,[status(thm)],[])).
% 2.44/2.60 tff(12576,plain,
% 2.44/2.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[12575, 12574])).
% 2.44/2.60 tff(12577,plain,
% 2.44/2.60 ($false),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[12576, 306, 12570, 12568, 12552, 12563, 12544])).
% 2.44/2.60 tff(12578,plain,((~r(s(z), z)) | (~(elem!1 = s(s(s(z))))) | (s(s(elem!1)) = elem!1) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(z))) | b(s(z), elem!1) | b(elem!1, s(s(s(z)))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.60 tff(12579,plain,
% 2.44/2.60 (~r(s(z), z)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[12578, 231, 11023, 10943, 11017, 11018, 3, 5])).
% 2.44/2.60 tff(12580,plain,
% 2.44/2.60 (b(s(z), z)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[221, 12579])).
% 2.44/2.60 tff(12581,plain,
% 2.44/2.60 (b(s(s(s(s(z)))), z) <=> b(s(elem!1), z)),
% 2.44/2.60 inference(symmetry,[status(thm)],[11205])).
% 2.44/2.60 tff(12582,plain,
% 2.44/2.60 (r(s(s(s(z))), z)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[2204, 246, 11016])).
% 2.44/2.60 tff(12583,plain,
% 2.44/2.60 (~r(elem!1, s(elem!1))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[337, 246, 247, 231, 206])).
% 2.44/2.60 tff(12584,plain,
% 2.44/2.60 (b(elem!1, s(elem!1))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[372, 12583, 365])).
% 2.44/2.60 tff(12585,plain,
% 2.44/2.60 (~b(z, s(s(s(elem!1))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[11178, 247, 4012, 838, 1034, 231])).
% 2.44/2.60 tff(12586,plain,
% 2.44/2.60 (r(z, s(s(s(elem!1))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[585, 12585])).
% 2.44/2.60 tff(12587,plain,
% 2.44/2.60 (~(z = elem!1)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[11005, 4012])).
% 2.44/2.60 tff(12588,plain,
% 2.44/2.60 (~(s(elem!1) = s(z))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[2689, 12587])).
% 2.44/2.60 tff(12589,plain,
% 2.44/2.60 (~(s(s(s(elem!1))) = elem!1)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[4105, 11016, 12588])).
% 2.44/2.60 tff(12590,plain,
% 2.44/2.60 (~(elem!1 = s(s(s(elem!1))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[1641, 12589])).
% 2.44/2.60 tff(12591,plain,
% 2.44/2.60 (b(z, s(s(s(z))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[842, 231, 838])).
% 2.44/2.60 tff(12592,plain,
% 2.44/2.60 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[11127, 12583, 231])).
% 2.44/2.60 tff(12593,plain,
% 2.44/2.60 (~r(elem!1, s(s(s(elem!1))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[873, 12592, 206, 12591, 231, 247, 246])).
% 2.44/2.60 tff(12594,plain,
% 2.44/2.60 (b(elem!1, s(s(s(elem!1))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[3284, 12593, 12590])).
% 2.44/2.60 tff(12595,plain,
% 2.44/2.60 (~b(s(elem!1), elem!1)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[6993, 12594, 4012, 12586, 150, 12584])).
% 2.44/2.60 tff(12596,plain,
% 2.44/2.60 (r(s(elem!1), elem!1)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[813, 12595, 193])).
% 2.44/2.60 tff(12597,plain,
% 2.44/2.60 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[805, 12596, 231])).
% 2.44/2.60 tff(12598,plain,
% 2.44/2.60 (~r(s(s(s(s(z)))), z)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[4737, 12597, 12582])).
% 2.44/2.60 tff(12599,plain,
% 2.44/2.60 (b(s(s(s(s(z)))), z)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[695, 12598])).
% 2.44/2.60 tff(12600,plain,
% 2.44/2.60 (b(s(elem!1), z)),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[12599, 12581])).
% 2.44/2.60 tff(12601,plain,
% 2.44/2.60 (~(s(elem!1) = s(s(s(z))))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[193, 11288])).
% 2.44/2.60 tff(12602,plain,
% 2.44/2.60 (b(z, s(z))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[2281, 246, 5, 838])).
% 2.44/2.60 tff(12603,plain,
% 2.44/2.60 (~b(s(elem!1), z)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[8078, 12602, 247, 12588, 11090, 1034, 12601])).
% 2.44/2.60 tff(12604,plain,
% 2.44/2.60 ($false),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[12603, 12600])).
% 2.44/2.60 tff(12605,plain,((~r(elem!1, z)) | (~(elem!1 = s(s(s(z))))) | (s(elem!1) = elem!1) | (~b(elem!1, z)) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~r(s(z), s(s(s(z))))) | b(elem!1, s(z)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.60 tff(12606,plain,
% 2.44/2.60 (~r(elem!1, z)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[12605, 231, 11024, 10999, 11062, 206, 12580, 10943, 5, 12105])).
% 2.44/2.60 tff(12607,plain,
% 2.44/2.60 (r(s(s(elem!1)), elem!1)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[12539, 12606, 11018, 3, 5])).
% 2.44/2.60 tff(12608,plain,
% 2.44/2.60 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[12607, 11015])).
% 2.44/2.60 tff(12609,plain,
% 2.44/2.60 (~r(s(z), s(s(s(s(s(z))))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[11583, 12608])).
% 2.44/2.60 tff(12610,plain,
% 2.44/2.60 (b(s(z), s(s(s(s(s(z))))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[626, 43, 12609, 11013])).
% 2.44/2.60 tff(12611,plain,
% 2.44/2.60 (b(s(z), s(s(elem!1)))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[12610, 11009])).
% 2.44/2.60 tff(12612,plain,
% 2.44/2.60 (~r(s(s(elem!1)), s(z))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[9725, 12607, 11017])).
% 2.44/2.60 tff(12613,plain,
% 2.44/2.60 (b(s(s(elem!1)), s(z))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[3989, 12612])).
% 2.44/2.60 tff(12614,plain,
% 2.44/2.60 (r(s(elem!1), s(s(s(z)))) <=> r(s(elem!1), elem!1)),
% 2.44/2.60 inference(symmetry,[status(thm)],[11049])).
% 2.44/2.60 tff(12615,plain,
% 2.44/2.60 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(elem!1), s(s(s(z))))),
% 2.44/2.60 inference(symmetry,[status(thm)],[11048])).
% 2.44/2.60 tff(12616,plain,
% 2.44/2.60 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(elem!1), elem!1)),
% 2.44/2.60 inference(transitivity,[status(thm)],[12615, 12614])).
% 2.44/2.60 tff(12617,plain,
% 2.44/2.60 (r(s(z), elem!1)),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[10943, 1044])).
% 2.44/2.60 tff(12618,plain,
% 2.44/2.60 (~b(s(s(elem!1)), elem!1)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[11304, 12606, 10943, 10999, 206, 11023, 231, 12580, 12617])).
% 2.44/2.60 tff(12619,plain,
% 2.44/2.60 (~r(s(elem!1), elem!1)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[805, 709, 231])).
% 2.44/2.60 tff(12620,plain,
% 2.44/2.60 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[7090, 12619, 2170, 91])).
% 2.44/2.60 tff(12621,plain,
% 2.44/2.60 (~(s(z) = elem!1)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[7105, 2609, 3099, 808])).
% 2.44/2.60 tff(12622,plain,
% 2.44/2.60 (~(elem!1 = s(z))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[3096, 12621])).
% 2.44/2.60 tff(12623,plain,
% 2.44/2.60 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[2974, 12622])).
% 2.44/2.60 tff(12624,plain,
% 2.44/2.60 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[7090, 1175, 808, 2170])).
% 2.44/2.60 tff(12625,plain,
% 2.44/2.60 (r(s(s(elem!1)), elem!1)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[47, 1175, 6481])).
% 2.44/2.60 tff(12626,plain,
% 2.44/2.60 (~r(s(s(s(elem!1))), elem!1)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[7780, 12625, 12624])).
% 2.44/2.60 tff(12627,plain,
% 2.44/2.60 (b(s(elem!1), elem!1)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[813, 1176, 808])).
% 2.44/2.60 tff(12628,plain,
% 2.44/2.60 (b(s(s(s(elem!1))), s(elem!1))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[11573, 12627, 2170, 2609, 12624, 12625, 12621, 1, 150])).
% 2.44/2.60 tff(12629,plain,
% 2.44/2.60 (~r(elem!1, s(elem!1))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[5630, 244, 1730])).
% 2.44/2.60 tff(12630,plain,
% 2.44/2.60 (b(elem!1, s(elem!1))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[372, 12629, 366])).
% 2.44/2.60 tff(12631,plain,
% 2.44/2.60 (~b(s(s(s(elem!1))), elem!1)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[6962, 306, 759, 816, 12630])).
% 2.44/2.60 tff(12632,plain,
% 2.44/2.60 (s(s(s(elem!1))) = elem!1),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[1636, 12631, 11317])).
% 2.44/2.60 tff(12633,plain,
% 2.44/2.60 (~(s(s(s(z))) = elem!1)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[4105, 12632, 3099])).
% 2.44/2.60 tff(12634,plain,
% 2.44/2.60 (r(s(s(s(z))), elem!1)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[1489, 12633, 1])).
% 2.44/2.60 tff(12635,plain,
% 2.44/2.60 (~r(z, s(s(elem!1)))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[7671, 12630, 816, 759, 653, 244])).
% 2.44/2.60 tff(12636,plain,
% 2.44/2.60 (b(z, s(s(elem!1)))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[460, 12635])).
% 2.44/2.60 tff(12637,plain,
% 2.44/2.60 (~(s(s(s(z))) = s(elem!1))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[4128, 12632])).
% 2.44/2.60 tff(12638,plain,
% 2.44/2.60 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[11484, 124, 1730, 2859])).
% 2.44/2.60 tff(12639,plain,
% 2.44/2.60 (b(s(s(s(z))), s(s(elem!1)))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[2986, 43, 12638, 11319])).
% 2.44/2.60 tff(12640,plain,
% 2.44/2.60 (b(elem!1, z)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[174, 3062, 3103])).
% 2.44/2.60 tff(12641,plain,
% 2.44/2.60 (~b(z, s(elem!1))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[6367, 12640, 816, 815])).
% 2.44/2.60 tff(12642,plain,
% 2.44/2.60 (r(z, s(elem!1))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[275, 12641])).
% 2.44/2.60 tff(12643,plain,
% 2.44/2.60 (~r(s(s(elem!1)), z)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[6643, 124, 12642, 244])).
% 2.44/2.60 tff(12644,plain,
% 2.44/2.60 (b(s(s(elem!1)), z)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[476, 12643])).
% 2.44/2.60 tff(12645,plain,
% 2.44/2.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.44/2.60 inference(rewrite,[status(thm)],[])).
% 2.44/2.60 tff(12646,plain,
% 2.44/2.60 (((~b(z, s(s(elem!1)))) | (~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))) <=> ((~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)))))),
% 2.44/2.60 inference(rewrite,[status(thm)],[])).
% 2.44/2.60 tff(12647,plain,
% 2.44/2.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(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)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[12646])).
% 2.44/2.60 tff(12648,plain,
% 2.44/2.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(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)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.44/2.60 inference(transitivity,[status(thm)],[12647, 12645])).
% 2.44/2.60 tff(12649,plain,
% 2.44/2.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(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)))),
% 2.44/2.60 inference(quant_inst,[status(thm)],[])).
% 2.44/2.60 tff(12650,plain,
% 2.44/2.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1))))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[12649, 12648])).
% 2.44/2.60 tff(12651,plain,
% 2.44/2.60 (~b(s(s(s(z))), z)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[12650, 306, 1198, 12644, 12639])).
% 2.44/2.60 tff(12652,plain,
% 2.44/2.60 (r(s(s(s(z))), z)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[2197, 12651])).
% 2.44/2.60 tff(12653,plain,
% 2.44/2.60 (~r(z, elem!1)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[6831, 12652, 2859])).
% 2.44/2.60 tff(12654,plain,
% 2.44/2.60 (b(z, elem!1)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[835, 12653, 2170])).
% 2.44/2.60 tff(12655,plain,
% 2.44/2.60 (~b(s(elem!1), z)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[4020, 12654, 12640, 815])).
% 2.44/2.60 tff(12656,plain,
% 2.44/2.60 (r(s(elem!1), z)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[2380, 12655])).
% 2.44/2.60 tff(12657,plain,
% 2.44/2.60 (~r(s(s(s(z))), s(elem!1))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[6878, 124, 12656, 12652])).
% 2.44/2.60 tff(12658,plain,
% 2.44/2.60 (b(s(s(s(z))), s(elem!1))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[4132, 43, 6779, 12657])).
% 2.44/2.60 tff(12659,plain,
% 2.44/2.60 (~r(s(z), z)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[3113, 12653, 2609, 2170, 816, 3062])).
% 2.44/2.60 tff(12660,plain,
% 2.44/2.60 (b(s(z), z)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[221, 12659])).
% 2.44/2.60 tff(12661,plain,
% 2.44/2.60 ($false),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[6345, 306, 838, 4012, 2831, 247])).
% 2.44/2.60 tff(12662,plain,((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.60 tff(12663,plain,
% 2.44/2.60 (~b(s(z), elem!1)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[12662, 12660, 12640, 12654])).
% 2.44/2.60 tff(12664,plain,
% 2.44/2.60 (r(s(z), elem!1)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[1500, 43, 12663, 3094])).
% 2.44/2.60 tff(12665,plain,
% 2.44/2.61 (~r(s(s(elem!1)), s(z))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[8826, 12664, 1730])).
% 2.44/2.61 tff(12666,plain,
% 2.44/2.61 (b(s(s(elem!1)), s(z))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[3989, 12665])).
% 2.44/2.61 tff(12667,plain,
% 2.44/2.61 (~r(s(z), s(s(s(z))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[3790, 12664, 2859])).
% 2.44/2.61 tff(12668,plain,
% 2.44/2.61 (b(s(z), s(s(s(z))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[3302, 12667])).
% 2.44/2.61 tff(12669,plain,
% 2.44/2.61 (~b(elem!1, s(z))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[8234, 12660, 12640, 12654])).
% 2.44/2.61 tff(12670,plain,
% 2.44/2.61 (r(elem!1, s(z))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[96, 43, 12669, 5331])).
% 2.44/2.61 tff(12671,plain,
% 2.44/2.61 (~r(s(s(s(z))), s(z))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[1481, 12670, 2859])).
% 2.44/2.61 tff(12672,plain,
% 2.44/2.61 (b(s(s(s(z))), s(z))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[113, 12671])).
% 2.44/2.61 tff(12673,plain,
% 2.44/2.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(12674,plain,
% 2.44/2.61 (((~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(12675,plain,
% 2.44/2.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1)))))),
% 2.44/2.61 inference(monotonicity,[status(thm)],[12674])).
% 2.44/2.61 tff(12676,plain,
% 2.44/2.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))))),
% 2.44/2.61 inference(transitivity,[status(thm)],[12675, 12673])).
% 2.44/2.61 tff(12677,plain,
% 2.44/2.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.44/2.61 inference(quant_inst,[status(thm)],[])).
% 2.44/2.61 tff(12678,plain,
% 2.44/2.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1)))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[12677, 12676])).
% 2.44/2.61 tff(12679,plain,
% 2.44/2.61 ($false),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[12678, 306, 12672, 12668, 12639, 12666, 12658])).
% 2.44/2.61 tff(12680,plain,(r(elem!1, z) | (s(s(s(z))) = s(elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (s(z) = elem!1) | (~b(elem!1, s(elem!1))) | b(s(elem!1), s(z)) | (z = elem!1) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.61 tff(12681,plain,
% 2.44/2.61 (r(elem!1, z)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[12680, 12637, 12634, 1730, 3094, 12630, 2609, 2170, 816, 12636, 244])).
% 2.44/2.61 tff(12682,plain,
% 2.44/2.61 (~r(s(s(s(z))), z)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[2561, 12681, 12634])).
% 2.44/2.61 tff(12683,plain,
% 2.44/2.61 (b(s(s(s(z))), z)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[2197, 12682])).
% 2.44/2.61 tff(12684,plain,
% 2.44/2.61 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[11484, 124, 1730, 12634])).
% 2.44/2.61 tff(12685,plain,
% 2.44/2.61 (b(s(s(s(z))), s(s(elem!1)))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[2986, 43, 12684, 11319])).
% 2.44/2.61 tff(12686,assumption,(b(s(s(s(z))), s(s(elem!1)))), introduced(assumption)).
% 2.44/2.61 tff(12687,plain,
% 2.44/2.61 (((~b(s(s(elem!1)), z)) | (~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))))) <=> ((~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)))))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(12688,plain,
% 2.44/2.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 2.44/2.61 inference(monotonicity,[status(thm)],[12687])).
% 2.44/2.61 tff(12689,plain,
% 2.44/2.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.44/2.61 inference(transitivity,[status(thm)],[12688, 12645])).
% 2.44/2.61 tff(12690,plain,
% 2.44/2.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~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)))))),
% 2.44/2.61 inference(quant_inst,[status(thm)],[])).
% 2.44/2.61 tff(12691,plain,
% 2.44/2.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1))))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[12690, 12689])).
% 2.44/2.61 tff(12692,plain,
% 2.44/2.61 ($false),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[12691, 306, 1198, 3968, 12686, 1531])).
% 2.44/2.61 tff(12693,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,[]))).
% 2.44/2.61 tff(12694,plain,
% 2.44/2.61 (~b(s(s(elem!1)), z)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[12693, 12636, 12685, 12683])).
% 2.44/2.61 tff(12695,plain,
% 2.44/2.61 (r(s(s(elem!1)), z)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[476, 12694])).
% 2.44/2.61 tff(12696,plain,
% 2.44/2.61 ($false),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[7784, 124, 12681, 1730, 12695])).
% 2.44/2.61 tff(12697,plain,((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (s(z) = elem!1) | b(s(elem!1), s(z)) | (z = elem!1) | (~b(s(elem!1), elem!1)) | b(s(s(s(z))), elem!1) | (~b(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (elem!1 = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.61 tff(12698,plain,
% 2.44/2.61 (~r(s(s(elem!1)), s(elem!1))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[12697, 12625, 12621, 2609, 2170, 12627, 1, 12628, 12624, 11318])).
% 2.44/2.61 tff(12699,plain,
% 2.44/2.61 (b(s(s(elem!1)), s(elem!1))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[994, 12698, 1182])).
% 2.44/2.61 tff(12700,plain,
% 2.44/2.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), 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(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(12701,plain,
% 2.44/2.61 (((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), 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(elem!1))))))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(12702,plain,
% 2.44/2.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), 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(elem!1)))))))),
% 2.44/2.61 inference(monotonicity,[status(thm)],[12701])).
% 2.44/2.61 tff(12703,plain,
% 2.44/2.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), 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(elem!1))))))),
% 2.44/2.61 inference(transitivity,[status(thm)],[12702, 12700])).
% 2.44/2.61 tff(12704,plain,
% 2.44/2.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.44/2.61 inference(quant_inst,[status(thm)],[])).
% 2.44/2.61 tff(12705,plain,
% 2.44/2.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), 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(elem!1)))))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[12704, 12703])).
% 2.44/2.61 tff(12706,plain,
% 2.44/2.61 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[12705, 306, 4012, 759, 1005, 816])).
% 2.44/2.61 tff(12707,plain,
% 2.44/2.61 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[891, 12706, 157])).
% 2.44/2.61 tff(12708,plain,
% 2.44/2.61 (~r(elem!1, s(s(s(elem!1))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[5766, 12707, 1730])).
% 2.44/2.61 tff(12709,plain,
% 2.44/2.61 (s(s(s(elem!1))) = elem!1),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[7793, 12708, 759, 816, 7789])).
% 2.44/2.61 tff(12710,plain,
% 2.44/2.61 (~(s(s(s(z))) = elem!1)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[4105, 12709, 3099])).
% 2.44/2.61 tff(12711,plain,
% 2.44/2.61 (r(s(s(s(z))), elem!1)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[1489, 12710, 1])).
% 2.44/2.61 tff(12712,plain,
% 2.44/2.61 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[11484, 124, 1730, 12711])).
% 2.44/2.61 tff(12713,plain,
% 2.44/2.61 (b(s(s(s(z))), s(s(elem!1)))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[2986, 43, 12712, 11319])).
% 2.44/2.61 tff(12714,plain,
% 2.44/2.61 (~r(s(z), s(s(s(z))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[3790, 4, 2859])).
% 2.44/2.61 tff(12715,plain,
% 2.44/2.61 (b(s(z), s(s(s(z))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[3302, 12714])).
% 2.44/2.61 tff(12716,plain,
% 2.44/2.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(12717,plain,
% 2.44/2.61 (((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), 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(z), s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(12718,plain,
% 2.44/2.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 2.44/2.61 inference(monotonicity,[status(thm)],[12717])).
% 2.44/2.61 tff(12719,plain,
% 2.44/2.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.44/2.61 inference(transitivity,[status(thm)],[12718, 12716])).
% 2.44/2.61 tff(12720,plain,
% 2.44/2.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), 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))))))),
% 2.44/2.61 inference(quant_inst,[status(thm)],[])).
% 2.44/2.61 tff(12721,plain,
% 2.44/2.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1))))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[12720, 12719])).
% 2.44/2.61 tff(12722,plain,
% 2.44/2.61 ($false),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[12721, 306, 1005, 816, 6328, 12715, 12686])).
% 2.44/2.61 tff(12723,plain,((~r(s(z), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.61 tff(12724,plain,
% 2.44/2.61 (~r(s(z), elem!1)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[12723, 12713, 816, 1005, 1730, 12711])).
% 2.44/2.61 tff(12725,plain,
% 2.44/2.61 (b(s(z), elem!1)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[1500, 43, 12724, 3094])).
% 2.44/2.61 tff(12726,plain,
% 2.44/2.61 (s(s(s(s(elem!1)))) = s(elem!1)),
% 2.44/2.61 inference(monotonicity,[status(thm)],[12709])).
% 2.44/2.61 tff(12727,plain,
% 2.44/2.61 (b(s(z), s(s(s(s(elem!1))))) <=> b(s(z), s(elem!1))),
% 2.44/2.61 inference(monotonicity,[status(thm)],[12726])).
% 2.44/2.61 tff(12728,plain,
% 2.44/2.61 ((~b(s(z), s(s(s(s(elem!1)))))) <=> (~b(s(z), s(elem!1)))),
% 2.44/2.61 inference(monotonicity,[status(thm)],[12727])).
% 2.44/2.61 tff(12729,plain,
% 2.44/2.61 (b(elem!1, s(s(s(s(elem!1))))) <=> b(elem!1, s(elem!1))),
% 2.44/2.61 inference(monotonicity,[status(thm)],[12726])).
% 2.44/2.61 tff(12730,plain,
% 2.44/2.61 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 2.44/2.61 inference(symmetry,[status(thm)],[12729])).
% 2.44/2.61 tff(12731,plain,
% 2.44/2.61 (b(elem!1, s(elem!1))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[5902, 12709, 759])).
% 2.44/2.61 tff(12732,plain,
% 2.44/2.61 (b(elem!1, s(s(s(s(elem!1)))))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[12731, 12730])).
% 2.44/2.61 tff(12733,plain,
% 2.44/2.61 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(elem!1), elem!1)),
% 2.44/2.61 inference(monotonicity,[status(thm)],[12726])).
% 2.44/2.61 tff(12734,plain,
% 2.44/2.61 (b(s(elem!1), elem!1) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 2.44/2.61 inference(symmetry,[status(thm)],[12733])).
% 2.44/2.61 tff(12735,plain,
% 2.44/2.61 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[816, 12734])).
% 2.44/2.61 tff(12736,plain,
% 2.44/2.61 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[6716, 12725, 12735, 12732])).
% 2.44/2.61 tff(12737,plain,
% 2.44/2.61 (~b(s(z), s(elem!1))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[12736, 12728])).
% 2.44/2.61 tff(12738,plain,
% 2.44/2.61 ((s(z) = s(elem!1)) | r(s(z), s(elem!1))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[4047, 43, 12737])).
% 2.44/2.61 tff(12739,plain,
% 2.44/2.61 (r(s(z), s(elem!1))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[12738, 4040])).
% 2.44/2.61 tff(12740,plain,
% 2.44/2.61 (~b(z, s(elem!1))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[6367, 12731, 816, 4012])).
% 2.44/2.61 tff(12741,plain,
% 2.44/2.61 (r(z, s(elem!1))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[275, 12740])).
% 2.44/2.61 tff(12742,plain,
% 2.44/2.61 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(12743,plain,
% 2.44/2.61 (((~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))))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(12744,plain,
% 2.44/2.61 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(z), s(elem!1)))))),
% 2.44/2.61 inference(monotonicity,[status(thm)],[12743])).
% 2.44/2.61 tff(12745,plain,
% 2.44/2.61 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))),
% 2.44/2.61 inference(transitivity,[status(thm)],[12744, 12742])).
% 2.44/2.61 tff(12746,plain,
% 2.44/2.61 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), z)))),
% 2.44/2.61 inference(quant_inst,[status(thm)],[])).
% 2.44/2.61 tff(12747,plain,
% 2.44/2.61 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(z), s(elem!1)))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[12746, 12745])).
% 2.44/2.61 tff(12748,plain,
% 2.44/2.61 (~r(s(z), z)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[12747, 124, 12741, 12739])).
% 2.44/2.61 tff(12749,plain,
% 2.44/2.61 (b(s(z), z)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[221, 12748])).
% 2.44/2.61 tff(12750,plain,
% 2.44/2.61 (~b(z, elem!1)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[12662, 12749, 4012, 12725])).
% 2.44/2.61 tff(12751,plain,
% 2.44/2.61 (r(z, elem!1)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[835, 12750, 2170])).
% 2.44/2.61 tff(12752,plain,
% 2.44/2.61 (~r(s(s(s(z))), z)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[6831, 12751, 12711])).
% 2.44/2.61 tff(12753,plain,
% 2.44/2.61 (b(s(s(s(z))), z)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[2197, 12752])).
% 2.44/2.61 tff(12754,plain,
% 2.44/2.61 (~r(z, s(s(elem!1)))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[5837, 12751, 1730])).
% 2.44/2.61 tff(12755,plain,
% 2.44/2.61 (b(z, s(s(elem!1)))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[460, 12754])).
% 2.44/2.61 tff(12756,plain,
% 2.44/2.61 (~b(s(s(elem!1)), z)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[12693, 12755, 12713, 12753])).
% 2.44/2.61 tff(12757,plain,
% 2.44/2.61 (r(s(s(elem!1)), z)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[476, 12756])).
% 2.44/2.61 tff(12758,plain,
% 2.44/2.61 ($false),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[6539, 124, 12751, 1730, 12757])).
% 2.44/2.61 tff(12759,plain,((~b(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (z = elem!1) | (s(z) = elem!1) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | b(s(s(s(z))), elem!1) | (~b(s(s(s(elem!1))), s(elem!1))) | r(s(s(s(elem!1))), elem!1) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.61 tff(12760,plain,
% 2.44/2.61 (~b(elem!1, z)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[12759, 12625, 2170, 12621, 12627, 12699, 1, 12628, 12626, 232])).
% 2.44/2.61 tff(12761,plain,
% 2.44/2.61 (r(elem!1, z)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[174, 12760, 3103])).
% 2.44/2.61 tff(12762,plain,
% 2.44/2.61 (s(s(s(elem!1))) = elem!1),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[7812, 12628, 12627, 11318, 12761, 232, 12625, 12626])).
% 2.44/2.61 tff(12763,plain,
% 2.44/2.61 (~(s(s(s(z))) = elem!1)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[4105, 12762, 3099])).
% 2.44/2.61 tff(12764,plain,
% 2.44/2.61 (r(s(s(s(z))), elem!1)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[1489, 12763, 1])).
% 2.44/2.61 tff(12765,plain,
% 2.44/2.61 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[11484, 124, 12625, 12764])).
% 2.44/2.61 tff(12766,plain,
% 2.44/2.61 (~r(s(s(s(z))), z)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[2561, 12764, 12761])).
% 2.44/2.61 tff(12767,plain,
% 2.44/2.61 (b(s(s(s(z))), z)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[2197, 12766])).
% 2.44/2.61 tff(12768,plain,
% 2.44/2.61 (~r(s(s(elem!1)), z)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[7786, 12761, 12625])).
% 2.44/2.61 tff(12769,plain,
% 2.44/2.61 (b(s(s(elem!1)), z)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[476, 12768])).
% 2.44/2.61 tff(12770,plain,
% 2.44/2.61 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 2.44/2.61 inference(monotonicity,[status(thm)],[12762])).
% 2.44/2.61 tff(12771,plain,
% 2.44/2.61 (r(elem!1, s(s(elem!1)))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[12624, 12770])).
% 2.44/2.61 tff(12772,plain,
% 2.44/2.61 (~r(z, s(s(elem!1)))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[978, 12771, 12761])).
% 2.44/2.61 tff(12773,plain,
% 2.44/2.61 (b(z, s(s(elem!1)))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[460, 12772])).
% 2.44/2.61 tff(12774,plain,
% 2.44/2.61 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[12693, 12773, 12769, 12767])).
% 2.44/2.61 tff(12775,plain,
% 2.44/2.61 ($false),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[2986, 43, 12774, 12765, 12623])).
% 2.44/2.61 tff(12776,plain,((s(s(s(elem!1))) = s(elem!1)) | b(s(s(s(z))), elem!1) | (z = elem!1) | b(s(elem!1), s(z)) | r(s(elem!1), elem!1) | b(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.44/2.61 tff(12777,plain,
% 2.44/2.61 (b(s(elem!1), s(z))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[12776, 12619, 2170, 144, 11072, 6481])).
% 2.44/2.61 tff(12778,plain,
% 2.44/2.61 (~b(s(s(elem!1)), s(elem!1))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[4007, 12777, 24, 3999])).
% 2.44/2.61 tff(12779,plain,
% 2.44/2.61 (r(s(s(elem!1)), s(elem!1))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[994, 12778, 196])).
% 2.44/2.61 tff(12780,plain,
% 2.44/2.61 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[659, 12779, 12620])).
% 2.44/2.61 tff(12781,plain,
% 2.44/2.61 (b(s(s(s(elem!1))), s(elem!1))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[664, 12780, 144])).
% 2.44/2.61 tff(12782,plain,
% 2.44/2.61 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[12781, 11073])).
% 2.44/2.61 tff(12783,plain,
% 2.44/2.61 (~(s(s(s(elem!1))) = elem!1)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[4105, 11016, 3099])).
% 2.44/2.61 tff(12784,plain,
% 2.44/2.61 (~r(s(s(s(elem!1))), elem!1)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[7780, 12620, 1730])).
% 2.44/2.61 tff(12785,plain,
% 2.44/2.61 (b(s(s(s(elem!1))), elem!1)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[1636, 12784, 12783])).
% 2.44/2.61 tff(12786,plain,
% 2.44/2.61 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[12785, 12564])).
% 2.44/2.61 tff(12787,plain,
% 2.44/2.61 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[4471, 709])).
% 2.44/2.61 tff(12788,plain,
% 2.44/2.61 (~r(elem!1, s(elem!1))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[5630, 12779, 1730])).
% 2.44/2.61 tff(12789,plain,
% 2.44/2.61 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[11127, 12788, 231])).
% 2.44/2.61 tff(12790,plain,
% 2.44/2.61 ($false),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[11120, 306, 12789, 12787, 12786, 12782])).
% 2.44/2.62 tff(12791,plain,(r(s(s(s(s(z)))), s(s(s(z)))) | (~(elem!1 = s(s(s(z))))) | (~r(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (z = elem!1) | b(s(s(elem!1)), elem!1) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.44/2.62 tff(12792,plain,
% 2.44/2.62 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[12791, 231, 12607, 12613, 12611, 11006, 12618, 11023])).
% 2.44/2.62 tff(12793,plain,
% 2.44/2.62 (r(s(elem!1), elem!1)),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[12792, 12616])).
% 2.44/2.62 tff(12794,plain,
% 2.44/2.62 (~r(s(elem!1), s(z))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[2960, 12793, 11017])).
% 2.44/2.62 tff(12795,plain,
% 2.44/2.62 (b(s(elem!1), s(z))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[2964, 12794, 11007])).
% 2.44/2.62 tff(12796,plain,
% 2.44/2.62 (~r(s(s(elem!1)), s(elem!1))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[7985, 12793, 12607])).
% 2.44/2.62 tff(12797,plain,
% 2.44/2.62 (b(s(s(elem!1)), s(elem!1))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[994, 12796, 11025])).
% 2.44/2.62 tff(12798,plain,
% 2.44/2.62 ($false),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[4007, 12797, 12795, 12613, 12611])).
% 2.44/2.62 tff(12799,plain,((~(elem!1 = s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | b(elem!1, s(s(s(z)))) | b(elem!1, s(z)) | b(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.62 tff(12800,plain,
% 2.44/2.62 (~(elem!1 = s(s(s(z))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[12799, 114, 3, 5, 3300])).
% 2.44/2.62 tff(12801,plain,
% 2.44/2.62 (r(elem!1, s(s(s(z))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[2304, 12800, 3])).
% 2.44/2.62 tff(12802,plain,
% 2.44/2.62 (~r(elem!1, s(z))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[3293, 12801, 10943])).
% 2.44/2.62 tff(12803,plain,
% 2.44/2.62 (elem!1 = s(z)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[97, 12802])).
% 2.44/2.62 tff(12804,plain,
% 2.44/2.62 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(z))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[12803])).
% 2.44/2.62 tff(12805,plain,
% 2.44/2.62 (r(s(elem!1), s(z)) <=> r(s(elem!1), elem!1)),
% 2.44/2.62 inference(symmetry,[status(thm)],[12804])).
% 2.44/2.62 tff(12806,plain,
% 2.44/2.62 (s(elem!1) = s(s(z))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[12803])).
% 2.44/2.62 tff(12807,plain,
% 2.44/2.62 (r(s(elem!1), s(z)) <=> r(s(s(z)), s(z))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[12806])).
% 2.44/2.62 tff(12808,plain,
% 2.44/2.62 (r(s(s(z)), s(z)) <=> r(s(elem!1), s(z))),
% 2.44/2.62 inference(symmetry,[status(thm)],[12807])).
% 2.44/2.62 tff(12809,plain,
% 2.44/2.62 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(z))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[12803])).
% 2.44/2.62 tff(12810,plain,
% 2.44/2.62 (r(s(s(z)), elem!1) <=> r(s(elem!1), elem!1)),
% 2.44/2.62 inference(transitivity,[status(thm)],[12809, 12808, 12805])).
% 2.44/2.62 tff(12811,plain,
% 2.44/2.62 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(z))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[12803])).
% 2.44/2.62 tff(12812,plain,
% 2.44/2.62 ((s(s(z)) = s(z)) <=> (s(s(z)) = elem!1)),
% 2.44/2.62 inference(symmetry,[status(thm)],[12811])).
% 2.44/2.62 tff(12813,plain,
% 2.44/2.62 ((~(s(s(z)) = s(z))) <=> (~(s(s(z)) = elem!1))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[12812])).
% 2.44/2.62 tff(12814,plain,
% 2.44/2.62 (~(s(s(z)) = elem!1)),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[2470, 12813])).
% 2.44/2.62 tff(12815,plain,
% 2.44/2.62 ((s(s(s(s(s(s(z)))))) = elem!1) <=> (s(s(s(s(s(s(z)))))) = s(z))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[12803])).
% 2.44/2.62 tff(12816,plain,
% 2.44/2.62 ((s(s(s(s(s(s(z)))))) = s(z)) <=> (s(s(s(s(s(s(z)))))) = elem!1)),
% 2.44/2.62 inference(symmetry,[status(thm)],[12815])).
% 2.44/2.62 tff(12817,plain,
% 2.44/2.62 ((~(s(s(s(s(s(s(z)))))) = s(z))) <=> (~(s(s(s(s(s(s(z)))))) = elem!1))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[12816])).
% 2.44/2.62 tff(12818,plain,
% 2.44/2.62 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[2844, 12817])).
% 2.44/2.62 tff(12819,plain,
% 2.44/2.62 (r(s(s(elem!1)), elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[82, 12803, 9])).
% 2.44/2.62 tff(12820,plain,
% 2.44/2.62 (s(s(elem!1)) = s(s(s(z)))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[12806])).
% 2.44/2.62 tff(12821,plain,
% 2.44/2.62 ((s(s(s(s(s(s(z)))))) = s(s(elem!1))) <=> (s(s(s(s(s(s(z)))))) = s(s(s(z))))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[12820])).
% 2.44/2.62 tff(12822,plain,
% 2.44/2.62 ((s(s(s(s(s(s(z)))))) = s(s(elem!1))) <=> (s(s(s(z))) = s(s(s(s(s(s(z)))))))),
% 2.44/2.62 inference(transitivity,[status(thm)],[12821, 1122])).
% 2.44/2.62 tff(12823,plain,
% 2.44/2.62 ((s(s(s(z))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = s(s(elem!1)))),
% 2.44/2.62 inference(symmetry,[status(thm)],[12822])).
% 2.44/2.62 tff(12824,plain,
% 2.44/2.62 ((~(s(s(s(z))) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(s(s(s(s(z)))))) = s(s(elem!1))))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[12823])).
% 2.44/2.62 tff(12825,plain,
% 2.44/2.62 (~(s(s(s(s(s(s(z)))))) = s(s(elem!1)))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[556, 12824])).
% 2.44/2.62 tff(12826,plain,
% 2.44/2.62 (~(elem!1 = s(elem!1))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[364, 11598])).
% 2.44/2.62 tff(12827,plain,
% 2.44/2.62 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[1284, 11614])).
% 2.44/2.62 tff(12828,plain,
% 2.44/2.62 (r(elem!1, s(s(elem!1))) <=> r(s(z), s(s(elem!1)))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[12803])).
% 2.44/2.62 tff(12829,plain,
% 2.44/2.62 (r(s(z), s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 2.44/2.62 inference(symmetry,[status(thm)],[12828])).
% 2.44/2.62 tff(12830,plain,
% 2.44/2.62 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(s(z))))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[12820])).
% 2.44/2.62 tff(12831,plain,
% 2.44/2.62 (r(s(z), s(s(s(z)))) <=> r(s(z), s(s(elem!1)))),
% 2.44/2.62 inference(symmetry,[status(thm)],[12830])).
% 2.44/2.62 tff(12832,plain,
% 2.44/2.62 (r(s(z), s(s(s(z)))) <=> r(elem!1, s(s(elem!1)))),
% 2.44/2.62 inference(transitivity,[status(thm)],[12831, 12829])).
% 2.44/2.62 tff(12833,plain,
% 2.44/2.62 (r(elem!1, s(s(elem!1)))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[10943, 12832])).
% 2.44/2.62 tff(12834,plain,
% 2.44/2.62 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[12820])).
% 2.44/2.62 tff(12835,plain,
% 2.44/2.62 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[12834])).
% 2.44/2.62 tff(12836,plain,
% 2.44/2.62 ((s(s(s(s(elem!1)))) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(s(z)))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[12835, 12806])).
% 2.44/2.62 tff(12837,plain,
% 2.44/2.62 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 2.44/2.62 inference(symmetry,[status(thm)],[12836])).
% 2.44/2.62 tff(12838,plain,
% 2.44/2.62 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(s(s(elem!1)))) = s(elem!1)))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[12837])).
% 2.44/2.62 tff(12839,plain,
% 2.44/2.62 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[6464, 12838])).
% 2.44/2.62 tff(12840,plain,
% 2.44/2.62 (~(s(s(s(s(elem!1)))) = elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[6321, 12803])).
% 2.44/2.62 tff(12841,plain,
% 2.44/2.62 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[152, 11614])).
% 2.44/2.62 tff(12842,plain,
% 2.44/2.62 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[3437, 12841])).
% 2.44/2.62 tff(12843,plain,
% 2.44/2.62 ((elem!1 = s(s(s(elem!1)))) <=> (s(z) = s(s(s(elem!1))))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[12803])).
% 2.44/2.62 tff(12844,plain,
% 2.44/2.62 ((s(z) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 2.44/2.62 inference(symmetry,[status(thm)],[12843])).
% 2.44/2.62 tff(12845,plain,
% 2.44/2.62 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 2.44/2.62 inference(transitivity,[status(thm)],[12844, 1555])).
% 2.44/2.62 tff(12846,plain,
% 2.44/2.62 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[12845])).
% 2.44/2.62 tff(12847,plain,
% 2.44/2.62 (~(s(s(s(elem!1))) = elem!1)),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[645, 12846])).
% 2.44/2.62 tff(12848,plain,
% 2.44/2.62 (~b(s(s(elem!1)), elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[32, 12803, 9])).
% 2.44/2.62 tff(12849,plain,
% 2.44/2.62 (~b(s(elem!1), elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[7044, 601, 4012, 12587, 91])).
% 2.44/2.62 tff(12850,plain,
% 2.44/2.62 (r(s(elem!1), elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[813, 12849, 181])).
% 2.44/2.62 tff(12851,plain,
% 2.44/2.62 (~r(s(s(elem!1)), s(elem!1))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[7985, 12850, 1730])).
% 2.44/2.62 tff(12852,plain,
% 2.44/2.62 (b(s(s(elem!1)), s(elem!1))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[994, 12851, 196])).
% 2.44/2.62 tff(12853,plain,
% 2.44/2.62 (~r(s(elem!1), s(s(s(elem!1))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[3187, 124, 802, 1627])).
% 2.44/2.62 tff(12854,plain,
% 2.44/2.62 ((s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[1881, 43, 12853])).
% 2.44/2.62 tff(12855,plain,
% 2.44/2.62 (b(s(elem!1), s(s(s(elem!1))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[12854, 3181])).
% 2.44/2.62 tff(12856,plain,
% 2.44/2.62 (~(s(elem!1) = s(s(elem!1)))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[1182, 1658])).
% 2.44/2.62 tff(12857,plain,
% 2.44/2.62 (b(s(elem!1), s(s(elem!1)))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[10789, 12856])).
% 2.44/2.62 tff(12858,plain,
% 2.44/2.62 ($false),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[1877, 306, 1005, 601, 12857, 12855])).
% 2.44/2.62 tff(12859,plain,((~r(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.62 tff(12860,plain,
% 2.44/2.62 (~r(s(s(s(elem!1))), elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[12859, 12852, 1730, 601, 144, 12850])).
% 2.44/2.62 tff(12861,plain,
% 2.44/2.62 (~r(s(s(s(s(elem!1)))), elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[10803, 12850, 1730, 196, 1516, 970, 6278])).
% 2.44/2.62 tff(12862,plain,
% 2.44/2.62 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[1736, 12861, 1731])).
% 2.44/2.62 tff(12863,plain,
% 2.44/2.62 (~b(s(s(s(elem!1))), elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[12492, 12862, 4012, 838, 6279])).
% 2.44/2.62 tff(12864,plain,
% 2.44/2.62 ($false),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[1636, 12863, 12860, 1526])).
% 2.44/2.62 tff(12865,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(s(elem!1))) = elem!1) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (s(s(s(s(elem!1)))) = elem!1) | (s(s(s(s(elem!1)))) = s(elem!1)) | (~r(elem!1, s(s(elem!1)))) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.44/2.62 tff(12866,plain,
% 2.44/2.62 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[12865, 12847, 10999, 12105, 12819, 12840, 12839, 12833, 11597])).
% 2.44/2.62 tff(12867,plain,
% 2.44/2.62 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[610, 233, 8175])).
% 2.44/2.62 tff(12868,plain,
% 2.44/2.62 ($false),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[7780, 12625, 12867, 1627])).
% 2.44/2.62 tff(12869,plain,((s(s(s(elem!1))) = s(elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | b(s(s(elem!1)), elem!1) | b(s(s(s(elem!1))), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.62 tff(12870,plain,
% 2.44/2.62 (~r(s(s(s(elem!1))), elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[12869, 12866, 11614, 12848])).
% 2.44/2.62 tff(12871,plain,
% 2.44/2.62 (b(s(s(s(elem!1))), elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[1636, 12870, 12847])).
% 2.44/2.62 tff(12872,plain,
% 2.44/2.62 (~b(s(s(s(s(elem!1)))), elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[12492, 12871, 10999, 12105, 12842])).
% 2.44/2.62 tff(12873,plain,
% 2.44/2.62 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[1736, 12872, 12840])).
% 2.44/2.62 tff(12874,plain,
% 2.44/2.62 (~r(s(elem!1), elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[10803, 12873, 12819, 11599, 12839, 12833, 12827])).
% 2.44/2.62 tff(12875,plain,
% 2.44/2.62 (b(s(elem!1), elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[813, 12874, 11598])).
% 2.44/2.62 tff(12876,plain,
% 2.44/2.62 (~b(z, s(s(s(elem!1))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[6150, 12871, 10999, 12105])).
% 2.44/2.62 tff(12877,plain,
% 2.44/2.62 (r(z, s(s(s(elem!1))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[585, 12876])).
% 2.44/2.62 tff(12878,plain,
% 2.44/2.62 (b(elem!1, s(s(s(elem!1)))) <=> b(s(z), s(s(s(s(z)))))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[12803, 12834])).
% 2.44/2.62 tff(12879,plain,
% 2.44/2.62 (b(s(z), s(s(s(s(z))))) <=> b(elem!1, s(s(s(elem!1))))),
% 2.44/2.62 inference(symmetry,[status(thm)],[12878])).
% 2.44/2.62 tff(12880,plain,
% 2.44/2.62 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[12834, 12820])).
% 2.44/2.62 tff(12881,plain,
% 2.44/2.62 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[159, 12841])).
% 2.44/2.62 tff(12882,plain,
% 2.44/2.62 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[610, 12866, 12881])).
% 2.44/2.62 tff(12883,plain,
% 2.44/2.62 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[12882, 12880])).
% 2.44/2.62 tff(12884,plain,
% 2.44/2.62 (~r(s(z), s(s(s(s(z)))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[3585, 124, 10943, 12883])).
% 2.44/2.62 tff(12885,plain,
% 2.44/2.62 (b(s(z), s(s(s(s(z)))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[5135, 12884])).
% 2.44/2.62 tff(12886,plain,
% 2.44/2.62 (b(elem!1, s(s(s(elem!1))))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[12885, 12879])).
% 2.44/2.62 tff(12887,plain,
% 2.44/2.62 (~b(elem!1, s(elem!1))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[6993, 12886, 10999, 12877, 11614, 12875])).
% 2.44/2.62 tff(12888,plain,
% 2.44/2.62 (r(elem!1, s(elem!1))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[372, 12887, 12826])).
% 2.44/2.62 tff(12889,plain,
% 2.44/2.62 ((s(s(s(s(s(s(z)))))) = s(elem!1)) <=> (s(s(s(s(s(s(z)))))) = s(s(z)))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[12806])).
% 2.44/2.62 tff(12890,plain,
% 2.44/2.62 ((s(s(s(s(s(s(z)))))) = s(elem!1)) <=> (s(s(z)) = s(s(s(s(s(s(z)))))))),
% 2.44/2.62 inference(transitivity,[status(thm)],[12889, 4307])).
% 2.44/2.62 tff(12891,plain,
% 2.44/2.62 ((s(s(z)) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = s(elem!1))),
% 2.44/2.62 inference(symmetry,[status(thm)],[12890])).
% 2.44/2.62 tff(12892,plain,
% 2.44/2.62 ((~(s(s(z)) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(s(s(s(s(z)))))) = s(elem!1)))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[12891])).
% 2.44/2.62 tff(12893,plain,
% 2.44/2.62 (~(s(s(s(s(s(s(z)))))) = s(elem!1))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[2826, 12892])).
% 2.44/2.62 tff(12894,plain,
% 2.44/2.62 (r(elem!1, s(s(s(elem!1)))) <=> r(s(z), s(s(s(elem!1))))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[12803])).
% 2.44/2.62 tff(12895,plain,
% 2.44/2.62 (r(s(z), s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 2.44/2.62 inference(symmetry,[status(thm)],[12894])).
% 2.44/2.62 tff(12896,plain,
% 2.44/2.62 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(s(s(s(z)))))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[12834])).
% 2.44/2.62 tff(12897,plain,
% 2.44/2.62 (r(s(z), s(s(s(s(z))))) <=> r(s(z), s(s(s(elem!1))))),
% 2.44/2.62 inference(symmetry,[status(thm)],[12896])).
% 2.44/2.62 tff(12898,plain,
% 2.44/2.62 (r(s(z), s(s(s(s(z))))) <=> r(elem!1, s(s(s(elem!1))))),
% 2.44/2.62 inference(transitivity,[status(thm)],[12897, 12895])).
% 2.44/2.62 tff(12899,plain,
% 2.44/2.62 ((~r(s(z), s(s(s(s(z)))))) <=> (~r(elem!1, s(s(s(elem!1)))))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[12898])).
% 2.44/2.62 tff(12900,plain,
% 2.44/2.62 (~r(elem!1, s(s(s(elem!1))))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[12884, 12899])).
% 2.44/2.62 tff(12901,plain,
% 2.44/2.62 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[7793, 12900, 12875, 12870, 12847])).
% 2.44/2.62 tff(12902,plain,
% 2.44/2.62 (r(s(s(s(elem!1))), s(elem!1))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[664, 12901, 11614])).
% 2.44/2.62 tff(12903,plain,
% 2.44/2.62 (~r(s(s(elem!1)), s(elem!1))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[659, 12902, 12882])).
% 2.44/2.62 tff(12904,plain,
% 2.44/2.62 (b(s(s(elem!1)), s(elem!1))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[994, 12903, 11599])).
% 2.44/2.62 tff(12905,plain,
% 2.44/2.62 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[9431, 12904, 12875, 12893, 12886, 12888, 12825, 12819])).
% 2.44/2.62 tff(12906,plain,
% 2.44/2.62 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[1144, 12905, 12818])).
% 2.44/2.62 tff(12907,plain,
% 2.44/2.62 (~b(s(s(z)), elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[12244, 12906, 10999, 12105])).
% 2.44/2.62 tff(12908,plain,
% 2.44/2.62 (r(s(s(z)), elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[2545, 12907, 12814])).
% 2.44/2.62 tff(12909,plain,
% 2.44/2.62 (r(s(elem!1), elem!1)),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[12908, 12810])).
% 2.44/2.62 tff(12910,plain,
% 2.44/2.62 ($false),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[12874, 12909])).
% 2.44/2.62 tff(12911,plain,(b(s(s(s(z))), s(z)) | b(elem!1, s(z)) | b(elem!1, s(s(s(z)))) | b(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.62 tff(12912,plain,
% 2.44/2.62 (b(s(s(s(z))), s(z))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[12911, 3300, 3, 5])).
% 2.44/2.62 tff(12913,plain,
% 2.44/2.62 (~(elem!1 = s(s(s(z))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[5016, 12912, 5])).
% 2.44/2.62 tff(12914,plain,
% 2.44/2.62 (r(elem!1, s(s(s(z))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[2304, 12913, 3])).
% 2.44/2.62 tff(12915,plain,
% 2.44/2.62 (~r(elem!1, s(z))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[3293, 12914, 10943])).
% 2.44/2.62 tff(12916,plain,
% 2.44/2.62 (elem!1 = s(z)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[97, 12915])).
% 2.44/2.62 tff(12917,plain,
% 2.44/2.62 (b(elem!1, z) <=> b(s(z), z)),
% 2.44/2.62 inference(monotonicity,[status(thm)],[12916])).
% 2.44/2.62 tff(12918,plain,
% 2.44/2.62 (b(s(z), z) <=> b(elem!1, z)),
% 2.44/2.62 inference(symmetry,[status(thm)],[12917])).
% 2.44/2.62 tff(12919,plain,
% 2.44/2.62 ((~b(s(z), z)) <=> (~b(elem!1, z))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[12918])).
% 2.44/2.62 tff(12920,plain,
% 2.44/2.62 (~b(s(z), z)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[11897, 12916, 12105, 12912, 10943, 10999])).
% 2.44/2.62 tff(12921,plain,
% 2.44/2.62 (~b(elem!1, z)),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[12920, 12919])).
% 2.44/2.62 tff(12922,plain,
% 2.44/2.62 ($false),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[10999, 12921])).
% 2.44/2.62 tff(12923,plain,(b(s(z), s(s(s(z)))) | b(elem!1, s(z)) | b(elem!1, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.62 tff(12924,plain,
% 2.44/2.62 (b(s(z), s(s(s(z))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[12923, 3, 5])).
% 2.44/2.62 tff(12925,plain,
% 2.44/2.62 (~(s(z) = elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[10431, 12924, 3])).
% 2.44/2.62 tff(12926,plain,
% 2.44/2.62 (~(elem!1 = s(z))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[3096, 12925])).
% 2.44/2.62 tff(12927,plain,
% 2.44/2.62 (r(elem!1, s(z))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[97, 12926])).
% 2.44/2.62 tff(12928,plain,
% 2.44/2.62 (~r(s(s(s(z))), s(z))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[11591, 11008, 12927])).
% 2.44/2.62 tff(12929,plain,
% 2.44/2.62 (b(s(s(s(z))), s(z))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[113, 12928])).
% 2.44/2.62 tff(12930,plain,
% 2.44/2.62 (~r(z, elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[11993, 12929, 3, 5])).
% 2.44/2.62 tff(12931,plain,
% 2.44/2.62 (b(z, s(z))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[2281, 246, 5, 12105])).
% 2.44/2.62 tff(12932,plain,
% 2.44/2.62 ($false),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[2314, 12931, 246, 3, 12105, 12924, 2284])).
% 2.44/2.62 tff(12933,plain,((~r(elem!1, z)) | b(elem!1, s(s(s(z)))) | (~b(s(s(s(z))), s(z))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.62 tff(12934,plain,
% 2.44/2.62 (~r(elem!1, z)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[12933, 12929, 3, 5])).
% 2.44/2.62 tff(12935,plain,
% 2.44/2.62 (elem!1 = s(s(s(z)))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[1430, 6881])).
% 2.44/2.62 tff(12936,plain,
% 2.44/2.62 ($false),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[2301, 12935])).
% 2.44/2.62 tff(12937,plain,((~(s(s(s(z))) = elem!1)) | (elem!1 = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.62 tff(12938,plain,
% 2.44/2.62 (~(s(s(s(z))) = elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[12937, 2301])).
% 2.44/2.62 tff(12939,plain,
% 2.44/2.62 (~r(s(s(s(z))), s(z))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[11591, 3313, 12927])).
% 2.44/2.62 tff(12940,plain,
% 2.44/2.62 (b(s(s(s(z))), s(z))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[113, 12939])).
% 2.44/2.62 tff(12941,plain,
% 2.44/2.62 (~r(elem!1, z)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[12933, 12940, 3, 5])).
% 2.44/2.62 tff(12942,plain,
% 2.44/2.62 (b(s(z), elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[12539, 6, 12941, 3, 5])).
% 2.44/2.62 tff(12943,plain,
% 2.44/2.62 (~b(s(z), z)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[12662, 12942, 10999, 12105])).
% 2.44/2.62 tff(12944,plain,
% 2.44/2.62 (r(s(z), z)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[221, 12943])).
% 2.44/2.62 tff(12945,plain,
% 2.44/2.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 2.44/2.62 inference(rewrite,[status(thm)],[])).
% 2.44/2.62 tff(12946,plain,
% 2.44/2.62 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z)))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 2.44/2.62 inference(rewrite,[status(thm)],[])).
% 2.44/2.62 tff(12947,plain,
% 2.44/2.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1))))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[12946])).
% 2.44/2.62 tff(12948,plain,
% 2.44/2.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 2.44/2.62 inference(transitivity,[status(thm)],[12947, 12945])).
% 2.44/2.62 tff(12949,plain,
% 2.44/2.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 2.44/2.62 inference(quant_inst,[status(thm)],[])).
% 2.44/2.62 tff(12950,plain,
% 2.44/2.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[12949, 12948])).
% 2.44/2.62 tff(12951,plain,
% 2.44/2.62 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[12950, 306, 838, 4012, 2831, 2812])).
% 2.44/2.62 tff(12952,plain,
% 2.44/2.62 (r(s(s(s(s(s(s(z)))))), s(z))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[651, 43, 2844, 12951])).
% 2.44/2.62 tff(12953,plain,
% 2.44/2.62 ($false),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[4322, 124, 204, 12239, 12952])).
% 2.44/2.62 tff(12954,plain,((~b(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.62 tff(12955,plain,
% 2.44/2.62 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[12954, 12944, 10999, 12105, 12942])).
% 2.44/2.62 tff(12956,plain,
% 2.44/2.62 (~r(z, elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[11993, 12940, 3, 5])).
% 2.44/2.62 tff(12957,plain,
% 2.44/2.62 (~(s(s(s(s(z)))) = elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[12307, 6, 12927, 12924, 10999, 12105, 1483])).
% 2.44/2.62 tff(12958,plain,
% 2.44/2.62 (~r(s(s(s(s(z)))), s(z))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[12145, 12392, 838, 359, 4012, 204])).
% 2.44/2.62 tff(12959,plain,
% 2.44/2.62 (b(s(s(s(s(z)))), s(z))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[4490, 12958])).
% 2.44/2.62 tff(12960,plain,
% 2.44/2.62 ($false),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[12327, 306, 2284, 8, 762, 12959])).
% 2.44/2.62 tff(12961,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, elem!1)) | (~r(elem!1, s(z))) | (~b(elem!1, z)) | (~r(s(z), z)) | b(elem!1, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.62 tff(12962,plain,
% 2.44/2.62 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[12961, 12944, 12924, 12105, 12927, 10999, 12940, 3])).
% 2.44/2.62 tff(12963,plain,
% 2.44/2.62 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[10146, 12962])).
% 2.44/2.62 tff(12964,plain,
% 2.44/2.62 (~r(s(s(s(s(z)))), elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[10153, 124, 3313, 12963])).
% 2.44/2.62 tff(12965,plain,
% 2.44/2.62 (b(s(s(s(s(z)))), elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[9832, 12964, 12957])).
% 2.44/2.62 tff(12966,plain,
% 2.44/2.62 (~r(z, s(s(s(z))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[12174, 12963, 10999, 12105, 12957, 3313])).
% 2.44/2.62 tff(12967,plain,
% 2.44/2.62 (b(z, s(s(s(z))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[11982, 12966])).
% 2.44/2.62 tff(12968,plain,
% 2.44/2.62 (~r(s(s(s(z))), z)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[12318, 12963, 12105, 10999, 3313, 12957])).
% 2.44/2.62 tff(12969,plain,
% 2.44/2.62 (b(s(s(s(z))), z)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[2197, 12968])).
% 2.44/2.62 tff(12970,plain,
% 2.44/2.62 (~b(s(s(s(z))), elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[12188, 306, 10999, 12940, 12969, 12967])).
% 2.44/2.62 tff(12971,plain,
% 2.44/2.62 (~b(s(s(s(s(z)))), z)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[12172, 306, 12105, 10999, 12426])).
% 2.44/2.62 tff(12972,plain,
% 2.44/2.62 (r(s(s(s(s(z)))), z)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[695, 12971])).
% 2.44/2.62 tff(12973,plain,
% 2.44/2.62 (~b(s(s(elem!1)), z)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[3976, 92, 11006, 7, 3062])).
% 2.44/2.62 tff(12974,plain,
% 2.44/2.62 (r(s(s(elem!1)), z)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[476, 12973])).
% 2.44/2.62 tff(12975,plain,
% 2.44/2.62 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[12436, 124, 12974, 12972])).
% 2.44/2.62 tff(12976,plain,
% 2.44/2.62 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[12443, 306, 12105, 10999, 92, 12426])).
% 2.44/2.62 tff(12977,plain,
% 2.44/2.62 (s(s(elem!1)) = s(s(s(s(z))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[12447, 43, 12976, 12975])).
% 2.44/2.62 tff(12978,plain,
% 2.44/2.62 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(z)))))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[12977])).
% 2.44/2.62 tff(12979,plain,
% 2.44/2.62 (s(elem!1) = s(s(s(z)))),
% 2.44/2.62 inference(transitivity,[status(thm)],[67, 12978, 320])).
% 2.44/2.62 tff(12980,plain,
% 2.44/2.62 (b(s(z), s(elem!1)) <=> b(s(z), s(s(s(z))))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[12979])).
% 2.44/2.62 tff(12981,plain,
% 2.44/2.62 (b(s(z), s(s(s(z)))) <=> b(s(z), s(elem!1))),
% 2.44/2.62 inference(symmetry,[status(thm)],[12980])).
% 2.44/2.62 tff(12982,plain,
% 2.44/2.62 (b(s(z), s(elem!1))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[12924, 12981])).
% 2.44/2.62 tff(12983,plain,
% 2.44/2.62 (~b(z, s(s(elem!1)))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[4030, 306, 12105, 10999, 92])).
% 2.44/2.62 tff(12984,plain,
% 2.44/2.62 (r(z, s(s(elem!1)))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[460, 12983])).
% 2.44/2.62 tff(12985,plain,
% 2.44/2.62 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[7090, 808, 11006, 91])).
% 2.44/2.62 tff(12986,plain,
% 2.44/2.62 (~r(z, s(s(s(elem!1))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[950, 12985, 12984])).
% 2.44/2.62 tff(12987,plain,
% 2.44/2.62 (b(z, s(s(s(elem!1))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[585, 12986])).
% 2.44/2.62 tff(12988,plain,
% 2.44/2.62 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))))),
% 2.44/2.62 inference(rewrite,[status(thm)],[])).
% 2.44/2.62 tff(12989,plain,
% 2.44/2.62 (((~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))))),
% 2.44/2.62 inference(rewrite,[status(thm)],[])).
% 2.44/2.62 tff(12990,plain,
% 2.44/2.62 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1))))))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[12989])).
% 2.44/2.62 tff(12991,plain,
% 2.44/2.62 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))))),
% 2.44/2.62 inference(transitivity,[status(thm)],[12990, 12988])).
% 2.44/2.62 tff(12992,plain,
% 2.44/2.62 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))),
% 2.44/2.62 inference(quant_inst,[status(thm)],[])).
% 2.44/2.62 tff(12993,plain,
% 2.44/2.62 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1))))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[12992, 12991])).
% 2.44/2.62 tff(12994,plain,
% 2.44/2.62 (~r(s(s(s(elem!1))), z)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[12993, 124, 12984, 12985])).
% 2.44/2.62 tff(12995,plain,
% 2.44/2.62 (b(s(s(s(elem!1))), z)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[3033, 43, 579, 12994])).
% 2.44/2.62 tff(12996,plain,
% 2.44/2.62 (~b(s(s(elem!1)), z)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[3974, 306, 12105, 10999, 92])).
% 2.44/2.62 tff(12997,plain,
% 2.44/2.62 (r(s(s(elem!1)), z)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[476, 12996])).
% 2.44/2.62 tff(12998,plain,
% 2.44/2.62 (~(elem!1 = z)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[2172, 11006])).
% 2.44/2.62 tff(12999,plain,
% 2.44/2.62 (b(s(elem!1), elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[813, 808, 181])).
% 2.44/2.62 tff(13000,plain,
% 2.44/2.62 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[659, 244, 653])).
% 2.44/2.62 tff(13001,plain,
% 2.44/2.62 (b(s(s(s(elem!1))), s(elem!1))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[664, 13000, 150])).
% 2.44/2.62 tff(13002,plain,
% 2.44/2.62 (~b(elem!1, s(elem!1))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[7671, 13001, 437, 653, 816, 244])).
% 2.44/2.62 tff(13003,plain,
% 2.44/2.62 (r(elem!1, s(elem!1))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[372, 13002, 366])).
% 2.44/2.62 tff(13004,plain,
% 2.44/2.62 (~r(z, s(elem!1))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[799, 244, 437])).
% 2.44/2.62 tff(13005,plain,
% 2.44/2.62 (b(z, s(elem!1))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[275, 13004])).
% 2.44/2.62 tff(13006,plain,
% 2.44/2.62 (~b(elem!1, s(s(elem!1)))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[2341, 13005, 838, 816, 30])).
% 2.44/2.62 tff(13007,plain,
% 2.44/2.62 (r(elem!1, s(s(elem!1)))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[516, 13006, 360])).
% 2.44/2.62 tff(13008,plain,
% 2.44/2.62 ($false),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[1238, 13007, 13003, 244])).
% 2.44/2.62 tff(13009,plain,((~r(s(s(elem!1)), s(elem!1))) | (elem!1 = s(s(elem!1))) | (elem!1 = s(elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.62 tff(13010,plain,
% 2.44/2.62 (~r(s(s(elem!1)), s(elem!1))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[13009, 12999, 5621, 12105, 187, 92, 12984, 12985, 144])).
% 2.44/2.62 tff(13011,plain,
% 2.44/2.62 (b(s(s(elem!1)), s(elem!1))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[994, 13010, 196])).
% 2.44/2.62 tff(13012,plain,
% 2.44/2.62 (~b(elem!1, s(s(elem!1)))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[1024, 13011, 92, 12999])).
% 2.44/2.62 tff(13013,plain,
% 2.44/2.62 (r(elem!1, s(s(elem!1)))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[516, 13012, 187])).
% 2.44/2.62 tff(13014,plain,
% 2.44/2.62 (elem!1 = s(s(s(elem!1)))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[11524, 13013, 12998, 12997, 12995, 12987, 12985])).
% 2.44/2.62 tff(13015,plain,
% 2.44/2.62 (s(s(s(elem!1))) = elem!1),
% 2.44/2.62 inference(symmetry,[status(thm)],[13014])).
% 2.44/2.62 tff(13016,plain,
% 2.44/2.62 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 2.44/2.62 inference(monotonicity,[status(thm)],[13015])).
% 2.44/2.62 tff(13017,plain,
% 2.44/2.62 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.44/2.62 inference(symmetry,[status(thm)],[13016])).
% 2.44/2.62 tff(13018,plain,
% 2.44/2.62 (s(elem!1) = s(s(s(s(elem!1))))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[13014])).
% 2.44/2.62 tff(13019,plain,
% 2.44/2.62 (s(s(s(s(elem!1)))) = s(elem!1)),
% 2.44/2.62 inference(symmetry,[status(thm)],[13018])).
% 2.44/2.62 tff(13020,plain,
% 2.44/2.62 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(elem!1), s(s(s(elem!1))))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[13019, 13014])).
% 2.44/2.62 tff(13021,plain,
% 2.44/2.62 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 2.44/2.62 inference(symmetry,[status(thm)],[13020])).
% 2.44/2.62 tff(13022,plain,
% 2.44/2.62 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(elem!1))))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[13014])).
% 2.44/2.62 tff(13023,plain,
% 2.44/2.62 (b(s(elem!1), s(s(s(elem!1))))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[12999, 13022])).
% 2.44/2.62 tff(13024,plain,
% 2.44/2.62 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[13023, 13021])).
% 2.44/2.62 tff(13025,plain,
% 2.44/2.62 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[13024, 13017])).
% 2.44/2.62 tff(13026,plain,
% 2.44/2.62 (b(s(elem!1), z) <=> b(s(s(s(s(elem!1)))), z)),
% 2.44/2.62 inference(monotonicity,[status(thm)],[13018])).
% 2.44/2.62 tff(13027,plain,
% 2.44/2.62 (~r(elem!1, z)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[978, 13013, 12984])).
% 2.44/2.62 tff(13028,plain,
% 2.44/2.62 (b(s(z), elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[12539, 13027, 6, 3, 5])).
% 2.44/2.62 tff(13029,plain,
% 2.44/2.62 (~r(s(elem!1), z)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[7030, 13028, 10999, 12105, 11007, 12999])).
% 2.44/2.63 tff(13030,plain,
% 2.44/2.63 (b(s(elem!1), z)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[2380, 13029])).
% 2.44/2.63 tff(13031,plain,
% 2.44/2.63 (b(s(s(s(s(elem!1)))), z)),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[13030, 13026])).
% 2.44/2.63 tff(13032,plain,
% 2.44/2.63 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[6451, 306, 12987, 12995, 13031])).
% 2.44/2.63 tff(13033,plain,
% 2.44/2.63 ($false),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[13032, 13025])).
% 2.44/2.63 tff(13034,plain,(r(s(elem!1), elem!1) | r(s(s(elem!1)), elem!1) | b(elem!1, s(s(s(z)))) | b(elem!1, s(z)) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.44/2.63 tff(13035,plain,
% 2.44/2.63 (r(s(elem!1), elem!1)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[13034, 91, 3, 5, 6])).
% 2.44/2.63 tff(13036,plain,
% 2.44/2.63 (~r(s(elem!1), s(z))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[2960, 13035, 12927])).
% 2.44/2.63 tff(13037,plain,
% 2.44/2.63 (b(s(elem!1), s(z))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[2964, 13036, 11007])).
% 2.44/2.63 tff(13038,plain,
% 2.44/2.63 (b(s(z), elem!1)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[12539, 6, 3062, 3, 5])).
% 2.44/2.63 tff(13039,plain,
% 2.44/2.63 (~b(s(z), z)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[12662, 13038, 10999, 12105])).
% 2.44/2.63 tff(13040,plain,
% 2.44/2.63 (r(s(z), z)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[221, 13039])).
% 2.44/2.63 tff(13041,plain,
% 2.44/2.63 (~r(s(s(elem!1)), s(z))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[3981, 124, 12974, 13040])).
% 2.44/2.63 tff(13042,plain,
% 2.44/2.63 (b(s(s(elem!1)), s(z))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[3989, 13041])).
% 2.44/2.63 tff(13043,plain,
% 2.44/2.63 (~r(s(z), s(s(elem!1)))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[3993, 124, 12974, 13040])).
% 2.44/2.63 tff(13044,plain,
% 2.44/2.63 (b(s(z), s(s(elem!1)))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[3997, 43, 79, 13043])).
% 2.44/2.63 tff(13045,plain,
% 2.44/2.63 (~b(s(s(elem!1)), s(elem!1))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[4007, 13044, 13042, 13037])).
% 2.44/2.63 tff(13046,plain,
% 2.44/2.63 (r(s(s(elem!1)), s(elem!1))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[994, 13045, 196])).
% 2.44/2.63 tff(13047,plain,
% 2.44/2.63 (~r(z, s(elem!1))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[799, 13046, 12984])).
% 2.44/2.63 tff(13048,plain,
% 2.44/2.63 (b(z, s(elem!1))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[275, 13047])).
% 2.44/2.63 tff(13049,plain,
% 2.44/2.63 (~r(s(elem!1), z)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[471, 13046, 12974])).
% 2.44/2.63 tff(13050,plain,
% 2.44/2.63 (b(s(elem!1), z)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[2380, 13049])).
% 2.44/2.63 tff(13051,plain,
% 2.44/2.63 (~(s(s(s(elem!1))) = elem!1)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[4134, 13044, 13035, 1, 13037, 12927, 92, 11007])).
% 2.44/2.63 tff(13052,plain,
% 2.44/2.63 (~b(elem!1, s(elem!1))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[4020, 13050, 10999, 12105])).
% 2.44/2.63 tff(13053,plain,
% 2.44/2.63 (r(elem!1, s(elem!1))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[372, 13052, 5621])).
% 2.44/2.63 tff(13054,plain,
% 2.44/2.63 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[4095, 13053, 92, 13046, 160, 13051])).
% 2.44/2.63 tff(13055,plain,
% 2.44/2.63 (b(s(s(s(elem!1))), s(elem!1))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[664, 13054, 144])).
% 2.44/2.63 tff(13056,plain,
% 2.44/2.63 (~b(s(z), s(elem!1))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[4077, 13055, 12105, 13040, 13050, 13048])).
% 2.44/2.63 tff(13057,plain,
% 2.44/2.63 ($false),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[13056, 12982])).
% 2.44/2.63 tff(13058,plain,((s(s(elem!1)) = elem!1) | b(s(s(s(z))), elem!1) | (~b(s(s(s(s(z)))), elem!1)) | r(z, elem!1) | r(elem!1, z) | b(elem!1, s(s(s(z)))) | b(elem!1, s(z)) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.44/2.63 tff(13059,plain,
% 2.44/2.63 (s(s(elem!1)) = elem!1),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[13058, 12970, 12965, 12956, 12941, 3, 5, 6])).
% 2.44/2.63 tff(13060,plain,
% 2.44/2.63 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[4284, 13059])).
% 2.44/2.63 tff(13061,plain,
% 2.44/2.63 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[1144, 13060, 12955])).
% 2.44/2.63 tff(13062,plain,
% 2.44/2.63 (r(s(s(s(z))), elem!1)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[1489, 12970, 1483])).
% 2.44/2.63 tff(13063,plain,
% 2.44/2.63 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[2862, 124, 13062, 13061])).
% 2.44/2.63 tff(13064,plain,
% 2.44/2.63 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[4599, 12969, 12105, 12924, 12967])).
% 2.44/2.63 tff(13065,plain,
% 2.44/2.63 ($false),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[4603, 43, 13064, 13063, 4577])).
% 2.44/2.63 tff(13066,plain,(r(s(s(elem!1)), elem!1) | b(elem!1, s(s(s(z)))) | b(elem!1, s(z)) | (s(s(s(z))) = elem!1) | (~r(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.63 tff(13067,plain,
% 2.44/2.63 (r(s(s(elem!1)), elem!1)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[13066, 12938, 5, 3, 11008])).
% 2.44/2.63 tff(13068,plain,
% 2.44/2.63 (~r(s(s(elem!1)), s(z))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[9725, 1730, 359])).
% 2.44/2.63 tff(13069,plain,
% 2.44/2.63 (b(s(s(elem!1)), s(z))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[3989, 13068])).
% 2.44/2.63 tff(13070,plain,
% 2.44/2.63 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[7090, 808, 12587, 91])).
% 2.44/2.63 tff(13071,plain,
% 2.44/2.63 (~r(s(s(s(elem!1))), s(z))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[9146, 124, 653, 8211])).
% 2.44/2.63 tff(13072,plain,
% 2.44/2.63 ((s(s(s(elem!1))) = s(z)) | b(s(s(s(elem!1))), s(z))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[5924, 43, 13071])).
% 2.44/2.63 tff(13073,plain,
% 2.44/2.63 (b(s(s(s(elem!1))), s(z))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[13072, 5909])).
% 2.44/2.63 tff(13074,plain,
% 2.44/2.63 ($false),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[6326, 124, 1730, 4, 8211])).
% 2.44/2.63 tff(13075,plain,((~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.63 tff(13076,plain,
% 2.44/2.63 (~r(s(z), elem!1)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[13075, 8211, 1730])).
% 2.44/2.63 tff(13077,plain,
% 2.44/2.63 (b(s(z), elem!1)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[1500, 43, 13076, 3094])).
% 2.44/2.63 tff(13078,plain,
% 2.44/2.63 (~r(s(s(s(elem!1))), elem!1)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[7780, 653, 1730])).
% 2.44/2.63 tff(13079,plain,
% 2.44/2.63 (r(s(s(s(elem!1))), s(z)) <=> r(elem!1, s(z))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[2184])).
% 2.44/2.63 tff(13080,plain,
% 2.44/2.63 (r(elem!1, s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 2.44/2.63 inference(symmetry,[status(thm)],[13079])).
% 2.44/2.63 tff(13081,plain,
% 2.44/2.63 (r(s(s(s(elem!1))), s(z))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[359, 13080])).
% 2.44/2.63 tff(13082,assumption,(~r(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 2.44/2.63 tff(13083,plain,
% 2.44/2.63 ($false),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[13082, 13081])).
% 2.44/2.63 tff(13084,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,[]))).
% 2.44/2.63 tff(13085,plain,
% 2.44/2.63 (~(s(s(s(elem!1))) = elem!1)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[13084, 13071, 359])).
% 2.44/2.63 tff(13086,plain,
% 2.44/2.63 (b(s(s(s(elem!1))), elem!1)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[1636, 13085, 13078])).
% 2.44/2.63 tff(13087,plain,
% 2.44/2.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(13088,plain,
% 2.44/2.63 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(13089,plain,
% 2.44/2.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z)))))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[13088])).
% 2.44/2.63 tff(13090,plain,
% 2.44/2.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 2.44/2.63 inference(transitivity,[status(thm)],[13089, 13087])).
% 2.44/2.63 tff(13091,plain,
% 2.44/2.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 2.44/2.63 inference(quant_inst,[status(thm)],[])).
% 2.44/2.63 tff(13092,plain,
% 2.44/2.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z)))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[13091, 13090])).
% 2.44/2.63 tff(13093,plain,
% 2.44/2.63 ($false),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[13092, 306, 838, 4012, 13086, 13077, 13073])).
% 2.44/2.63 tff(13094,plain,((~r(s(z), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~r(elem!1, s(z))) | (s(z) = elem!1) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.63 tff(13095,plain,
% 2.44/2.63 (~r(s(z), s(s(elem!1)))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[13094, 13070, 4012, 359, 3094, 1730, 838])).
% 2.44/2.63 tff(13096,plain,
% 2.44/2.63 (b(s(z), s(s(elem!1)))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[3997, 43, 79, 13095])).
% 2.44/2.63 tff(13097,plain,
% 2.44/2.63 (~r(s(s(s(z))), s(z))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[11591, 3313, 359])).
% 2.44/2.63 tff(13098,plain,
% 2.44/2.63 (b(s(s(s(z))), s(z))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[113, 13097])).
% 2.44/2.63 tff(13099,plain,
% 2.44/2.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(13100,plain,
% 2.44/2.63 (((~b(s(s(elem!1)), s(z))) | (~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))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(13101,plain,
% 2.44/2.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[13100])).
% 2.44/2.63 tff(13102,plain,
% 2.44/2.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.44/2.63 inference(transitivity,[status(thm)],[13101, 13099])).
% 2.44/2.63 tff(13103,plain,
% 2.44/2.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(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)))))),
% 2.44/2.63 inference(quant_inst,[status(thm)],[])).
% 2.44/2.63 tff(13104,plain,
% 2.44/2.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1))))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[13103, 13102])).
% 2.44/2.63 tff(13105,plain,
% 2.44/2.63 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[13104, 306, 13098, 13096, 13069])).
% 2.44/2.63 tff(13106,plain,
% 2.44/2.63 (r(s(s(s(z))), s(s(elem!1)))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[2986, 43, 13105, 11319])).
% 2.44/2.63 tff(13107,plain,
% 2.44/2.63 (~b(elem!1, s(s(elem!1)))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[6655, 12630, 4012, 816, 244])).
% 2.44/2.63 tff(13108,plain,
% 2.44/2.63 (r(elem!1, s(s(elem!1)))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[516, 13107, 360])).
% 2.44/2.63 tff(13109,plain,
% 2.44/2.63 (r(elem!1, s(s(s(elem!1))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[7793, 13001, 816, 13078, 1526])).
% 2.44/2.63 tff(13110,plain,
% 2.44/2.63 ($false),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[1256, 124, 13109, 13108, 653])).
% 2.44/2.63 tff(13111,plain,((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (elem!1 = s(s(elem!1))) | (~b(s(elem!1), elem!1)) | (s(s(s(elem!1))) = elem!1) | (~b(elem!1, z)) | (s(s(s(elem!1))) = s(elem!1)) | (elem!1 = s(elem!1)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.63 tff(13112,plain,
% 2.44/2.63 (~r(s(s(elem!1)), s(elem!1))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[13111, 1526, 360, 816, 653, 4012, 150, 366, 1730])).
% 2.44/2.63 tff(13113,plain,
% 2.44/2.63 (b(s(s(elem!1)), s(elem!1))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[994, 13112, 403])).
% 2.44/2.63 tff(13114,plain,
% 2.44/2.63 (~b(s(elem!1), s(z))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[4007, 13113, 24, 3999])).
% 2.44/2.63 tff(13115,plain,
% 2.44/2.63 (~r(s(z), z)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[3113, 13114, 3062, 12587, 816, 7])).
% 2.44/2.63 tff(13116,plain,
% 2.44/2.63 (b(s(z), z)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[221, 13115])).
% 2.44/2.63 tff(13117,plain,
% 2.44/2.63 (b(s(s(s(elem!1))), elem!1)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[1636, 1526, 13078])).
% 2.44/2.63 tff(13118,plain,
% 2.44/2.63 (r(s(elem!1), s(z))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[2964, 13114, 12588])).
% 2.44/2.63 tff(13119,plain,
% 2.44/2.63 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[11414, 13116, 838, 87, 366, 816, 13118, 13117])).
% 2.44/2.63 tff(13120,plain,
% 2.44/2.63 (b(s(s(s(elem!1))), s(elem!1))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[664, 13119, 150])).
% 2.44/2.63 tff(13121,plain,
% 2.44/2.63 (r(elem!1, s(s(s(elem!1))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[7793, 13120, 816, 13078, 1526])).
% 2.44/2.63 tff(13122,plain,
% 2.44/2.63 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[5766, 13121, 1730])).
% 2.44/2.63 tff(13123,plain,
% 2.44/2.63 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[891, 13122, 232])).
% 2.44/2.63 tff(13124,plain,
% 2.44/2.63 (~b(z, s(s(s(elem!1))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[6150, 13117, 4012, 838])).
% 2.44/2.63 tff(13125,plain,
% 2.44/2.63 (r(z, s(s(s(elem!1))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[585, 13124])).
% 2.44/2.63 tff(13126,plain,
% 2.44/2.63 (~r(z, s(s(elem!1)))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[950, 13125, 653])).
% 2.44/2.63 tff(13127,plain,
% 2.44/2.63 (b(z, s(s(elem!1)))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[460, 13126])).
% 2.44/2.63 tff(13128,plain,
% 2.44/2.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), z)))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(13129,plain,
% 2.44/2.63 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), z)))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(13130,plain,
% 2.44/2.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), z))))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[13129])).
% 2.44/2.63 tff(13131,plain,
% 2.44/2.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), z)))),
% 2.44/2.63 inference(transitivity,[status(thm)],[13130, 13128])).
% 2.44/2.63 tff(13132,plain,
% 2.44/2.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~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)))),
% 2.44/2.63 inference(quant_inst,[status(thm)],[])).
% 2.44/2.63 tff(13133,plain,
% 2.44/2.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), z))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[13132, 13131])).
% 2.44/2.63 tff(13134,plain,
% 2.44/2.63 ($false),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[13133, 306, 13120, 13127, 13123, 3999, 13116])).
% 2.44/2.63 tff(13135,plain,((s(s(s(elem!1))) = elem!1) | (~b(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (~b(z, elem!1)) | (elem!1 = s(z)) | (elem!1 = s(elem!1)) | r(elem!1, z) | r(z, elem!1) | (~b(s(s(elem!1)), s(z))) | (s(s(elem!1)) = s(elem!1)) | (elem!1 = s(s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.63 tff(13136,plain,
% 2.44/2.63 (s(s(s(elem!1))) = elem!1),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[13135, 13096, 1730, 12999, 144, 838, 5331, 5621, 3062, 7, 13069, 196, 187, 13070, 4012])).
% 2.44/2.63 tff(13137,plain,
% 2.44/2.63 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[13136])).
% 2.44/2.63 tff(13138,plain,
% 2.44/2.63 (r(elem!1, s(s(elem!1)))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[13070, 13137])).
% 2.44/2.63 tff(13139,plain,
% 2.44/2.63 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(13140,plain,
% 2.44/2.63 (((~r(s(s(s(z))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(z)))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(13141,plain,
% 2.44/2.63 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1))))))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[13140])).
% 2.44/2.63 tff(13142,plain,
% 2.44/2.63 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.44/2.63 inference(transitivity,[status(thm)],[13141, 13139])).
% 2.44/2.63 tff(13143,plain,
% 2.44/2.63 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(z))))))),
% 2.44/2.63 inference(quant_inst,[status(thm)],[])).
% 2.44/2.63 tff(13144,plain,
% 2.44/2.63 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1))))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[13143, 13142])).
% 2.44/2.63 tff(13145,plain,
% 2.44/2.63 ($false),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[13144, 124, 13138, 3313, 13106])).
% 2.44/2.63 tff(13146,plain,(r(s(elem!1), elem!1) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | r(elem!1, z) | r(z, elem!1) | (~b(elem!1, z)) | (~r(elem!1, s(z))) | (s(z) = elem!1) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.44/2.63 tff(13147,plain,
% 2.44/2.63 (r(s(elem!1), elem!1)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[13146, 91, 1730, 838, 3062, 7, 4012, 359, 3094, 3313])).
% 2.44/2.63 tff(13148,plain,
% 2.44/2.63 (~r(s(elem!1), s(z))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[2960, 13147, 359])).
% 2.44/2.63 tff(13149,plain,
% 2.44/2.63 (b(s(elem!1), s(z))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[2964, 13148, 12588])).
% 2.44/2.63 tff(13150,plain,
% 2.44/2.63 (~r(s(s(elem!1)), s(elem!1))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[7985, 13147, 1730])).
% 2.44/2.63 tff(13151,plain,
% 2.44/2.63 (b(s(s(elem!1)), s(elem!1))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[994, 13150, 196])).
% 2.44/2.63 tff(13152,plain,
% 2.44/2.63 (~b(s(z), s(s(elem!1)))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[4007, 13151, 13069, 13149])).
% 2.44/2.63 tff(13153,plain,
% 2.44/2.63 (r(s(z), s(s(elem!1)))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[3997, 43, 13152, 79])).
% 2.44/2.63 tff(13154,plain,
% 2.44/2.63 (~r(s(z), elem!1)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[13075, 13153, 1730])).
% 2.44/2.63 tff(13155,plain,
% 2.44/2.63 ($false),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[1500, 43, 2715, 8966, 3094])).
% 2.44/2.63 tff(13156,plain,(b(s(z), elem!1) | r(s(z), elem!1) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.44/2.63 tff(13157,plain,
% 2.44/2.63 (b(s(z), elem!1)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[13156, 13154, 3094])).
% 2.44/2.63 tff(13158,plain,
% 2.44/2.63 (~b(s(z), z)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[12662, 13157, 4012, 838])).
% 2.44/2.63 tff(13159,plain,
% 2.44/2.63 (r(s(z), z)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[221, 13158])).
% 2.44/2.63 tff(13160,plain,
% 2.44/2.63 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[13094, 13153, 4012, 359, 3094, 1730, 838])).
% 2.44/2.63 tff(13161,plain,
% 2.44/2.63 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[610, 13160, 160])).
% 2.44/2.63 tff(13162,plain,
% 2.44/2.63 (~r(s(s(s(elem!1))), elem!1)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[12859, 13161, 1730, 13151, 144, 13147])).
% 2.44/2.63 tff(13163,plain,
% 2.44/2.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(13164,plain,
% 2.44/2.64 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(13165,plain,
% 2.44/2.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1)))))))),
% 2.44/2.64 inference(monotonicity,[status(thm)],[13164])).
% 2.44/2.64 tff(13166,plain,
% 2.44/2.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 2.44/2.64 inference(transitivity,[status(thm)],[13165, 13163])).
% 2.44/2.64 tff(13167,plain,
% 2.44/2.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 2.44/2.64 inference(quant_inst,[status(thm)],[])).
% 2.44/2.64 tff(13168,plain,
% 2.44/2.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1)))))),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[13167, 13166])).
% 2.44/2.64 tff(13169,plain,
% 2.44/2.64 (~b(s(z), s(s(s(elem!1))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[13168, 306, 838, 4012, 1664, 2831])).
% 2.44/2.64 tff(13170,plain,
% 2.44/2.64 (~b(s(z), z)),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[12662, 2831, 4012, 838])).
% 2.44/2.64 tff(13171,plain,
% 2.44/2.64 (r(s(z), z)),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[221, 13170])).
% 2.44/2.64 tff(13172,plain,
% 2.44/2.64 (~b(z, s(s(s(elem!1))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[6150, 1664, 4012, 838])).
% 2.44/2.64 tff(13173,plain,
% 2.44/2.64 (r(z, s(s(s(elem!1))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[585, 13172])).
% 2.44/2.64 tff(13174,plain,
% 2.44/2.64 (~r(s(z), s(s(s(elem!1))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[4074, 13173, 13171])).
% 2.44/2.64 tff(13175,plain,
% 2.44/2.64 ($false),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[3017, 43, 645, 13174, 13169])).
% 2.44/2.64 tff(13176,plain,((~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.64 tff(13177,plain,
% 2.44/2.64 (~b(s(s(s(elem!1))), elem!1)),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[13176, 13157, 4012, 838])).
% 2.44/2.64 tff(13178,plain,
% 2.44/2.64 (s(s(s(elem!1))) = elem!1),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[1636, 13177, 13162])).
% 2.44/2.64 tff(13179,plain,
% 2.44/2.64 (b(s(s(s(elem!1))), z) <=> b(elem!1, z)),
% 2.44/2.64 inference(monotonicity,[status(thm)],[13178])).
% 2.44/2.64 tff(13180,plain,
% 2.44/2.64 (b(elem!1, z) <=> b(s(s(s(elem!1))), z)),
% 2.44/2.64 inference(symmetry,[status(thm)],[13179])).
% 2.44/2.64 tff(13181,plain,
% 2.44/2.64 (b(s(s(s(elem!1))), z)),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[4012, 13180])).
% 2.44/2.64 tff(13182,plain,
% 2.44/2.64 (~(s(s(s(z))) = s(elem!1))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[4128, 13178])).
% 2.44/2.64 tff(13183,plain,
% 2.44/2.64 (~r(s(elem!1), s(z))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[2634, 13171, 466])).
% 2.44/2.64 tff(13184,plain,
% 2.44/2.64 (b(s(elem!1), s(z))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[2612, 43, 13183, 2249])).
% 2.44/2.64 tff(13185,plain,
% 2.44/2.64 (~r(s(s(s(z))), s(elem!1))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[4110, 124, 802, 2859])).
% 2.44/2.64 tff(13186,plain,
% 2.44/2.64 (b(s(s(s(z))), s(elem!1))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[4132, 43, 6779, 13185])).
% 2.44/2.64 tff(13187,plain,
% 2.44/2.64 (b(s(s(s(z))), s(s(elem!1)))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[2986, 43, 12638, 2976])).
% 2.44/2.64 tff(13188,plain,
% 2.44/2.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(13189,plain,
% 2.44/2.64 (((~b(s(z), elem!1)) | (~b(s(elem!1), s(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))))) <=> ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(13190,plain,
% 2.44/2.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1)))))),
% 2.44/2.64 inference(monotonicity,[status(thm)],[13189])).
% 2.44/2.64 tff(13191,plain,
% 2.44/2.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))))),
% 2.44/2.64 inference(transitivity,[status(thm)],[13190, 13188])).
% 2.44/2.64 tff(13192,plain,
% 2.44/2.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), s(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)))))),
% 2.44/2.64 inference(quant_inst,[status(thm)],[])).
% 2.44/2.64 tff(13193,plain,
% 2.44/2.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1)))),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[13192, 13191])).
% 2.44/2.64 tff(13194,plain,
% 2.44/2.64 ($false),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[13193, 306, 1005, 2831, 13187, 2647, 13186])).
% 2.44/2.64 tff(13195,plain,((~r(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (s(s(s(z))) = s(s(elem!1))) | (s(s(s(z))) = s(elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.64 tff(13196,plain,
% 2.44/2.64 (~r(s(s(s(z))), elem!1)),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[13195, 2831, 1005, 13184, 2976, 6779, 1730, 802])).
% 2.44/2.64 tff(13197,plain,
% 2.44/2.64 (b(s(s(s(z))), elem!1)),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[1489, 13196, 1483])).
% 2.44/2.64 tff(13198,plain,
% 2.44/2.64 (~b(s(s(s(z))), z)),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[12285, 306, 838, 4012, 13197])).
% 2.44/2.64 tff(13199,plain,
% 2.44/2.64 (r(s(s(s(z))), z)),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[2197, 13198])).
% 2.44/2.64 tff(13200,plain,
% 2.44/2.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(13201,plain,
% 2.44/2.64 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(13202,plain,
% 2.44/2.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1))))),
% 2.44/2.64 inference(monotonicity,[status(thm)],[13201])).
% 2.44/2.64 tff(13203,plain,
% 2.44/2.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)))),
% 2.44/2.64 inference(transitivity,[status(thm)],[13202, 13200])).
% 2.44/2.64 tff(13204,plain,
% 2.44/2.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 2.44/2.64 inference(quant_inst,[status(thm)],[])).
% 2.44/2.64 tff(13205,plain,
% 2.44/2.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1))),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[13204, 13203])).
% 2.44/2.64 tff(13206,plain,
% 2.44/2.64 (~b(s(s(s(z))), s(z))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[13205, 306, 838, 4012, 2831, 13197])).
% 2.44/2.64 tff(13207,plain,
% 2.44/2.64 (r(s(s(s(z))), s(z))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[113, 13206])).
% 2.44/2.64 tff(13208,plain,
% 2.44/2.64 ($false),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[211, 13207, 13199, 13171])).
% 2.44/2.64 tff(13209,plain,((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (s(s(s(z))) = elem!1) | (~b(s(s(elem!1)), s(elem!1))) | (s(s(s(z))) = s(s(elem!1))) | (s(s(s(z))) = s(elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (s(elem!1) = s(z)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.64 tff(13210,plain,
% 2.44/2.64 (~r(s(elem!1), z)),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[13209, 13182, 4012, 1483, 13147, 11319, 13151, 1730, 838, 12588, 13157])).
% 2.44/2.64 tff(13211,plain,
% 2.44/2.64 (b(s(elem!1), z)),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[2380, 13210])).
% 2.44/2.64 tff(13212,plain,
% 2.44/2.64 (b(z, s(s(s(elem!1)))) <=> b(z, elem!1)),
% 2.44/2.64 inference(monotonicity,[status(thm)],[13178])).
% 2.44/2.64 tff(13213,plain,
% 2.44/2.64 (b(z, elem!1) <=> b(z, s(s(s(elem!1))))),
% 2.44/2.64 inference(symmetry,[status(thm)],[13212])).
% 2.44/2.64 tff(13214,plain,
% 2.44/2.64 (b(z, s(s(s(elem!1))))),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[838, 13213])).
% 2.44/2.64 tff(13215,plain,
% 2.44/2.64 (~b(s(s(elem!1)), z)),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[9394, 13214, 13151, 13211, 13181])).
% 2.44/2.64 tff(13216,plain,
% 2.44/2.64 (r(s(s(elem!1)), z)),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[476, 13215])).
% 2.44/2.64 tff(13217,plain,
% 2.44/2.64 ($false),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[3993, 124, 13216, 13159, 13153])).
% 2.44/2.64 tff(13218,plain,((s(s(elem!1)) = elem!1) | (~b(elem!1, z)) | (~b(z, elem!1)) | (s(s(s(z))) = elem!1) | (~r(s(s(elem!1)), elem!1)) | (s(z) = elem!1) | (~r(elem!1, s(z))) | r(elem!1, z) | r(z, elem!1) | (~r(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.64 tff(13219,plain,
% 2.44/2.64 (s(s(elem!1)) = elem!1),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[13218, 12938, 12105, 10999, 13067, 12925, 12927, 12934, 12930, 11008])).
% 2.44/2.64 tff(13220,plain,
% 2.44/2.64 (elem!1 = s(s(elem!1))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[1174, 13219])).
% 2.44/2.64 tff(13221,plain,
% 2.44/2.64 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), s(s(elem!1)))),
% 2.44/2.64 inference(monotonicity,[status(thm)],[13220])).
% 2.44/2.64 tff(13222,plain,
% 2.44/2.64 (r(s(s(elem!1)), s(s(elem!1))) <=> r(s(s(elem!1)), elem!1)),
% 2.44/2.64 inference(symmetry,[status(thm)],[13221])).
% 2.44/2.64 tff(13223,plain,
% 2.44/2.64 ((~r(s(s(elem!1)), s(s(elem!1)))) <=> (~r(s(s(elem!1)), elem!1))),
% 2.44/2.64 inference(monotonicity,[status(thm)],[13222])).
% 2.44/2.64 tff(13224,plain,
% 2.44/2.64 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(elem!1)))))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(13225,plain,
% 2.44/2.64 (((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(elem!1)))))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(13226,plain,
% 2.44/2.64 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(elem!1))))))),
% 2.44/2.64 inference(monotonicity,[status(thm)],[13225])).
% 2.44/2.64 tff(13227,plain,
% 2.44/2.64 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(elem!1)))))),
% 2.44/2.64 inference(transitivity,[status(thm)],[13226, 13224])).
% 2.44/2.64 tff(13228,plain,
% 2.44/2.64 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(elem!1)))))),
% 2.44/2.64 inference(quant_inst,[status(thm)],[])).
% 2.44/2.64 tff(13229,plain,
% 2.44/2.64 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(elem!1))))),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[13228, 13227])).
% 2.44/2.64 tff(13230,plain,
% 2.44/2.64 (~r(s(s(elem!1)), s(s(elem!1)))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[13229, 124, 13067])).
% 2.44/2.64 tff(13231,plain,
% 2.44/2.64 (~r(s(s(elem!1)), elem!1)),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[13230, 13223])).
% 2.44/2.64 tff(13232,plain,
% 2.44/2.64 ($false),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[13067, 13231])).
% 2.44/2.64 tff(13233,plain,((elem!1 = s(s(s(z)))) | b(elem!1, s(z)) | b(elem!1, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.64 tff(13234,plain,
% 2.44/2.64 (elem!1 = s(s(s(z)))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[13233, 3, 5])).
% 2.44/2.64 tff(13235,plain,
% 2.44/2.64 (s(s(s(z))) = elem!1),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[4555, 13234])).
% 2.44/2.64 tff(13236,plain,
% 2.44/2.64 (~(s(s(s(elem!1))) = elem!1)),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[4105, 13235, 11007])).
% 2.44/2.64 tff(13237,plain,
% 2.44/2.64 (~(s(s(elem!1)) = s(elem!1))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[1564, 13236])).
% 2.44/2.64 tff(13238,plain,
% 2.44/2.64 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[2974, 12926])).
% 2.44/2.64 tff(13239,plain,
% 2.44/2.64 (~(s(s(elem!1)) = elem!1)),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[10068, 13234, 13238])).
% 2.44/2.64 tff(13240,plain,
% 2.44/2.64 (~b(s(s(s(z))), s(z))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[5016, 13234, 5])).
% 2.44/2.64 tff(13241,plain,
% 2.44/2.64 (r(s(s(s(z))), s(z))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[113, 13240])).
% 2.44/2.64 tff(13242,plain,
% 2.44/2.64 (b(s(z), elem!1)),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[12031, 13234, 12924])).
% 2.44/2.64 tff(13243,plain,
% 2.44/2.64 (~b(s(z), z)),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[12662, 13242, 10999, 12105])).
% 2.44/2.64 tff(13244,plain,
% 2.44/2.64 (r(s(z), z)),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[221, 13243])).
% 2.44/2.64 tff(13245,plain,
% 2.44/2.64 (~r(s(s(s(z))), z)),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[211, 13244, 13241])).
% 2.44/2.64 tff(13246,plain,
% 2.44/2.64 (~r(elem!1, z)),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[2204, 13245, 13235])).
% 2.44/2.64 tff(13247,plain,
% 2.44/2.64 (b(z, s(s(s(z))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[842, 13234, 12105])).
% 2.44/2.64 tff(13248,plain,
% 2.44/2.64 (b(s(s(s(z))), z)),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[2197, 13245])).
% 2.44/2.64 tff(13249,plain,
% 2.44/2.64 (~b(z, s(z))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[10960, 306, 12924, 13248, 13247])).
% 2.44/2.64 tff(13250,plain,
% 2.44/2.64 (r(z, s(z))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[2263, 13249])).
% 2.44/2.64 tff(13251,plain,
% 2.44/2.64 (~r(z, elem!1)),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[385, 13250, 12927])).
% 2.44/2.64 tff(13252,plain,
% 2.44/2.64 (~b(s(s(elem!1)), z)),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[3976, 30, 2170, 7, 3062])).
% 2.44/2.64 tff(13253,plain,
% 2.44/2.64 (r(s(s(elem!1)), z)),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[476, 13252])).
% 2.44/2.64 tff(13254,plain,
% 2.44/2.64 (r(s(s(s(s(s(z))))), z)),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[13253, 1075])).
% 2.44/2.64 tff(13255,plain,
% 2.44/2.64 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.44/2.64 inference(transitivity,[status(thm)],[1014, 1013])).
% 2.44/2.64 tff(13256,plain,
% 2.44/2.64 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[30, 13255])).
% 2.44/2.64 tff(13257,plain,
% 2.44/2.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(13258,plain,
% 2.44/2.64 (((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(13259,plain,
% 2.44/2.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.44/2.64 inference(monotonicity,[status(thm)],[13258])).
% 2.44/2.64 tff(13260,plain,
% 2.44/2.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.44/2.64 inference(transitivity,[status(thm)],[13259, 13257])).
% 2.44/2.64 tff(13261,plain,
% 2.44/2.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), 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))))),
% 2.44/2.64 inference(quant_inst,[status(thm)],[])).
% 2.44/2.64 tff(13262,plain,
% 2.44/2.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[13261, 13260])).
% 2.44/2.64 tff(13263,plain,
% 2.44/2.64 (~b(s(s(s(s(s(z))))), s(z))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[13262, 306, 8, 1531, 859, 13256])).
% 2.44/2.64 tff(13264,plain,
% 2.44/2.64 (r(s(s(s(s(s(z))))), s(z))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[503, 43, 500, 13263])).
% 2.44/2.64 tff(13265,plain,
% 2.44/2.64 ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z)))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[1110, 124, 204])).
% 2.44/2.64 tff(13266,plain,
% 2.44/2.64 ($false),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[13265, 13264, 13254])).
% 2.44/2.64 tff(13267,plain,((~b(s(s(elem!1)), elem!1)) | (~r(s(z), z)) | (~(elem!1 = s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (z = elem!1) | r(z, elem!1) | r(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 2.44/2.64 tff(13268,plain,
% 2.44/2.64 (~b(s(s(elem!1)), elem!1)),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[13267, 13244, 13234, 12924, 13248, 13247, 11006, 13251, 13246])).
% 2.44/2.64 tff(13269,plain,
% 2.44/2.64 (r(s(s(elem!1)), elem!1)),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[47, 13268, 13239])).
% 2.44/2.64 tff(13270,plain,
% 2.44/2.64 (~b(s(s(s(elem!1))), elem!1)),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[13176, 13242, 10999, 12105])).
% 2.44/2.64 tff(13271,plain,
% 2.44/2.64 (r(s(s(s(elem!1))), elem!1)),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[1636, 13270, 13236])).
% 2.44/2.64 tff(13272,plain,
% 2.44/2.64 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[7780, 13269, 13271])).
% 2.44/2.64 tff(13273,plain,
% 2.44/2.64 (r(s(elem!1), elem!1)),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[7090, 13272, 11006, 13239])).
% 2.44/2.64 tff(13274,plain,
% 2.44/2.64 (~r(s(s(elem!1)), s(elem!1))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[7985, 13273, 13269])).
% 2.44/2.64 tff(13275,plain,
% 2.44/2.64 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[143, 13239])).
% 2.44/2.64 tff(13276,plain,
% 2.44/2.64 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[12869, 13268, 13275, 13271])).
% 2.44/2.64 tff(13277,plain,
% 2.44/2.64 (~b(s(s(elem!1)), s(elem!1))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[12859, 13273, 13271, 13269, 13275, 13276])).
% 2.44/2.64 tff(13278,plain,
% 2.44/2.64 ($false),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[994, 13277, 13274, 13237])).
% 2.44/2.64 tff(13279,plain,(b(elem!1, s(s(s(z)))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.64 tff(13280,plain,
% 2.44/2.64 (b(elem!1, s(s(s(z))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[13279, 5])).
% 2.44/2.64 tff(13281,plain,
% 2.44/2.64 (~(s(s(s(z))) = elem!1)),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[1472, 13280])).
% 2.44/2.64 tff(13282,plain,
% 2.44/2.64 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.44/2.64 inference(monotonicity,[status(thm)],[5311])).
% 2.44/2.64 tff(13283,plain,
% 2.44/2.64 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(z)))),
% 2.44/2.64 inference(monotonicity,[status(thm)],[13282, 5311])).
% 2.44/2.64 tff(13284,plain,
% 2.44/2.64 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.44/2.64 inference(symmetry,[status(thm)],[13283])).
% 2.44/2.64 tff(13285,plain,
% 2.44/2.64 ((~b(s(s(s(z))), s(s(z)))) <=> (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 2.44/2.64 inference(monotonicity,[status(thm)],[13284])).
% 2.44/2.64 tff(13286,plain,
% 2.44/2.64 ((elem!1 = s(z)) <=> (z = s(z))),
% 2.44/2.64 inference(monotonicity,[status(thm)],[3063])).
% 2.44/2.64 tff(13287,plain,
% 2.44/2.64 ((elem!1 = s(z)) <=> (s(z) = z)),
% 2.44/2.64 inference(transitivity,[status(thm)],[13286, 375])).
% 2.44/2.64 tff(13288,plain,
% 2.44/2.64 ((s(z) = z) <=> (elem!1 = s(z))),
% 2.44/2.64 inference(symmetry,[status(thm)],[13287])).
% 2.44/2.64 tff(13289,plain,
% 2.44/2.64 ((~(s(z) = z)) <=> (~(elem!1 = s(z)))),
% 2.44/2.64 inference(monotonicity,[status(thm)],[13288])).
% 2.44/2.64 tff(13290,plain,
% 2.44/2.64 (~(elem!1 = s(z))),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[216, 13289])).
% 2.44/2.64 tff(13291,plain,
% 2.44/2.64 (r(elem!1, s(z))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[97, 13290])).
% 2.44/2.64 tff(13292,plain,
% 2.44/2.64 (r(s(s(z)), elem!1) <=> r(s(s(z)), z)),
% 2.44/2.64 inference(monotonicity,[status(thm)],[3063])).
% 2.44/2.64 tff(13293,plain,
% 2.44/2.64 (r(s(s(z)), z) <=> r(s(s(z)), elem!1)),
% 2.44/2.64 inference(symmetry,[status(thm)],[13292])).
% 2.44/2.64 tff(13294,plain,
% 2.44/2.64 (r(s(s(elem!1)), z) <=> r(s(s(z)), elem!1)),
% 2.44/2.64 inference(transitivity,[status(thm)],[10484, 13293])).
% 2.44/2.64 tff(13295,plain,
% 2.44/2.64 (b(s(s(s(z))), s(z))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[82, 10, 6])).
% 2.44/2.64 tff(13296,plain,
% 2.44/2.64 (b(s(s(elem!1)), elem!1)),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[13295, 5072])).
% 2.44/2.64 tff(13297,plain,
% 2.44/2.64 (~b(s(z), z)),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[4298, 10, 2])).
% 2.44/2.64 tff(13298,plain,
% 2.44/2.64 (r(s(z), z)),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[221, 13297])).
% 2.44/2.64 tff(13299,plain,
% 2.44/2.64 (~(s(elem!1) = elem!1)),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[2654, 13298, 10451, 5])).
% 2.44/2.64 tff(13300,plain,
% 2.44/2.64 (~(s(s(elem!1)) = s(elem!1))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[195, 13299])).
% 2.44/2.64 tff(13301,plain,
% 2.44/2.64 (b(s(s(elem!1)), s(elem!1))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[994, 13300, 3149])).
% 2.44/2.64 tff(13302,plain,
% 2.44/2.64 (~(z = elem!1)),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[1618, 10450])).
% 2.44/2.64 tff(13303,plain,
% 2.44/2.64 (~(s(elem!1) = s(z))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[2689, 13302])).
% 2.44/2.64 tff(13304,plain,
% 2.44/2.64 (~b(s(elem!1), elem!1)),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[9665, 91, 6, 10425, 808, 10451, 181, 2, 13303])).
% 2.44/2.64 tff(13305,plain,
% 2.44/2.64 ($false),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[813, 13304, 181, 808])).
% 2.44/2.64 tff(13306,plain,((s(s(elem!1)) = elem!1) | r(s(elem!1), elem!1) | r(s(s(elem!1)), elem!1) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 2.44/2.64 tff(13307,plain,
% 2.44/2.64 (r(s(elem!1), elem!1)),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[13306, 11840, 2, 6])).
% 2.44/2.64 tff(13308,plain,
% 2.44/2.64 (~r(s(elem!1), z)),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[416, 13307, 10425])).
% 2.44/2.64 tff(13309,plain,
% 2.44/2.64 (b(s(elem!1), z)),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[2380, 13308])).
% 2.44/2.64 tff(13310,plain,
% 2.44/2.64 (~b(z, s(s(elem!1)))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[1228, 13309, 10425, 13301, 13299, 13296])).
% 2.44/2.64 tff(13311,plain,
% 2.44/2.64 (r(z, s(s(elem!1)))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[460, 13310])).
% 2.44/2.64 tff(13312,plain,
% 2.44/2.64 (s(z) = elem!1),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[3096, 10])).
% 2.44/2.64 tff(13313,plain,
% 2.44/2.64 (b(s(z), s(s(s(z))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[9887, 13312, 13280])).
% 2.44/2.64 tff(13314,plain,
% 2.44/2.64 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(s(z)))))),
% 2.44/2.64 inference(monotonicity,[status(thm)],[14, 3589])).
% 2.44/2.64 tff(13315,plain,
% 2.44/2.64 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 2.44/2.64 inference(symmetry,[status(thm)],[13314])).
% 2.44/2.64 tff(13316,plain,
% 2.44/2.64 (~b(s(z), s(s(s(s(z)))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[12349, 306, 2284, 8, 762])).
% 2.44/2.64 tff(13317,plain,
% 2.44/2.64 (r(s(z), s(s(s(s(z)))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[5135, 13316])).
% 2.44/2.64 tff(13318,plain,
% 2.44/2.64 (r(elem!1, s(s(s(elem!1))))),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[13317, 11728])).
% 2.44/2.64 tff(13319,plain,
% 2.44/2.64 (~r(z, s(s(s(elem!1))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[573, 13318, 374])).
% 2.44/2.64 tff(13320,plain,
% 2.44/2.64 (b(z, s(s(s(elem!1))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[585, 13319])).
% 2.44/2.64 tff(13321,plain,
% 2.44/2.64 (b(z, s(s(s(s(z)))))),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[13320, 11654])).
% 2.44/2.64 tff(13322,plain,
% 2.44/2.64 (r(s(elem!1), z) <=> r(s(s(z)), z)),
% 2.44/2.64 inference(monotonicity,[status(thm)],[14])).
% 2.44/2.64 tff(13323,plain,
% 2.44/2.64 ((~r(s(elem!1), z)) <=> (~r(s(s(z)), z))),
% 2.44/2.64 inference(monotonicity,[status(thm)],[13322])).
% 2.44/2.64 tff(13324,plain,
% 2.44/2.64 (~r(s(s(z)), z)),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[7920, 13323])).
% 2.44/2.64 tff(13325,plain,
% 2.44/2.64 (b(s(s(z)), z)),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[2529, 43, 106, 13324])).
% 2.44/2.64 tff(13326,plain,
% 2.44/2.64 (~b(s(s(s(s(z)))), s(z))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[12327, 306, 2284, 8, 762])).
% 2.44/2.64 tff(13327,plain,
% 2.44/2.64 (r(s(s(s(s(z)))), s(z))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[4490, 13326])).
% 2.44/2.64 tff(13328,plain,
% 2.44/2.64 (~r(s(s(s(s(z)))), z)),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[10160, 13327, 204])).
% 2.44/2.64 tff(13329,plain,
% 2.44/2.64 (b(s(s(s(s(z)))), z)),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[695, 13328])).
% 2.44/2.65 tff(13330,plain,
% 2.44/2.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.44/2.65 inference(rewrite,[status(thm)],[])).
% 2.44/2.65 tff(13331,plain,
% 2.44/2.65 (((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.44/2.65 inference(rewrite,[status(thm)],[])).
% 2.44/2.65 tff(13332,plain,
% 2.44/2.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z))))))))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[13331])).
% 2.44/2.65 tff(13333,plain,
% 2.44/2.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.44/2.65 inference(transitivity,[status(thm)],[13332, 13330])).
% 2.44/2.65 tff(13334,plain,
% 2.44/2.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 2.44/2.65 inference(quant_inst,[status(thm)],[])).
% 2.44/2.65 tff(13335,plain,
% 2.44/2.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z))))))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[13334, 13333])).
% 2.44/2.65 tff(13336,plain,
% 2.44/2.65 ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[13335, 306, 13329, 13325])).
% 2.44/2.65 tff(13337,plain,
% 2.44/2.65 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[13336, 13321])).
% 2.44/2.65 tff(13338,plain,
% 2.44/2.65 (r(s(s(z)), s(s(s(s(z)))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[4510, 13337])).
% 2.44/2.65 tff(13339,plain,
% 2.44/2.65 (r(s(elem!1), s(s(s(elem!1))))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[13338, 13315])).
% 2.44/2.65 tff(13340,plain,
% 2.44/2.65 (~r(s(elem!1), s(s(s(elem!1))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[3447, 13318, 802])).
% 2.44/2.65 tff(13341,plain,
% 2.44/2.65 ($false),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[13340, 13339])).
% 2.44/2.65 tff(13342,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~(elem!1 = s(z))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.65 tff(13343,plain,
% 2.44/2.65 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[13342, 10, 10425, 13307, 13298, 13295, 13313])).
% 2.44/2.65 tff(13344,plain,
% 2.44/2.65 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[10146, 13343])).
% 2.44/2.65 tff(13345,plain,
% 2.44/2.65 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[13344, 11698])).
% 2.44/2.65 tff(13346,plain,
% 2.44/2.65 (~r(z, s(s(s(elem!1))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[950, 13345, 13311])).
% 2.44/2.65 tff(13347,plain,
% 2.44/2.65 (b(z, s(s(s(elem!1))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[585, 13346])).
% 2.44/2.65 tff(13348,plain,
% 2.44/2.65 (b(z, s(s(s(s(z)))))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[13347, 11654])).
% 2.44/2.65 tff(13349,plain,
% 2.44/2.65 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(s(s(z))))), z)),
% 2.44/2.65 inference(monotonicity,[status(thm)],[3590])).
% 2.44/2.65 tff(13350,plain,
% 2.44/2.65 (r(s(s(s(s(s(z))))), z) <=> r(s(s(s(s(elem!1)))), z)),
% 2.44/2.65 inference(monotonicity,[status(thm)],[3591])).
% 2.44/2.65 tff(13351,plain,
% 2.44/2.65 ((~r(s(s(s(s(s(z))))), z)) <=> (~r(s(s(s(s(elem!1)))), z))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[13350])).
% 2.44/2.65 tff(13352,plain,
% 2.44/2.65 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[1284, 11704])).
% 2.44/2.65 tff(13353,plain,
% 2.44/2.65 (s(s(s(z))) = s(s(elem!1))),
% 2.44/2.65 inference(symmetry,[status(thm)],[15])).
% 2.44/2.65 tff(13354,plain,
% 2.44/2.65 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[3591, 13353])).
% 2.44/2.65 tff(13355,plain,
% 2.44/2.65 ((~r(s(s(s(s(s(z))))), s(s(s(z))))) <=> (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[13354])).
% 2.44/2.65 tff(13356,plain,
% 2.44/2.65 (r(z, s(s(elem!1))) <=> r(z, s(s(s(z))))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[15])).
% 2.44/2.65 tff(13357,plain,
% 2.44/2.65 (r(z, s(s(s(z))))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[13311, 13356])).
% 2.44/2.65 tff(13358,plain,
% 2.44/2.65 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[3591, 5225])).
% 2.44/2.65 tff(13359,plain,
% 2.44/2.65 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 2.44/2.65 inference(symmetry,[status(thm)],[13358])).
% 2.44/2.65 tff(13360,plain,
% 2.44/2.65 ((~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))) <=> (~(s(s(s(s(s(z))))) = s(s(s(s(z))))))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[13359])).
% 2.44/2.65 tff(13361,plain,
% 2.44/2.65 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[11870])).
% 2.44/2.65 tff(13362,plain,
% 2.44/2.65 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[4470, 13361])).
% 2.44/2.65 tff(13363,plain,
% 2.44/2.65 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[3437, 13362])).
% 2.44/2.65 tff(13364,plain,
% 2.44/2.65 (~(s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[13363, 13360])).
% 2.44/2.65 tff(13365,assumption,(b(z, s(s(s(s(z)))))), introduced(assumption)).
% 2.44/2.65 tff(13366,assumption,(r(s(s(s(s(s(z))))), s(s(s(z))))), introduced(assumption)).
% 2.44/2.65 tff(13367,plain,
% 2.44/2.65 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(z))))))),
% 2.44/2.65 inference(rewrite,[status(thm)],[])).
% 2.44/2.65 tff(13368,plain,
% 2.44/2.65 (((~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(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(z))))))),
% 2.44/2.65 inference(rewrite,[status(thm)],[])).
% 2.44/2.65 tff(13369,plain,
% 2.44/2.65 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(z)))))))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[13368])).
% 2.44/2.65 tff(13370,plain,
% 2.44/2.65 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(z))))))),
% 2.44/2.65 inference(transitivity,[status(thm)],[13369, 13367])).
% 2.44/2.65 tff(13371,plain,
% 2.44/2.65 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)))),
% 2.44/2.65 inference(quant_inst,[status(thm)],[])).
% 2.44/2.65 tff(13372,plain,
% 2.44/2.65 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(z)))))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[13371, 13370])).
% 2.44/2.65 tff(13373,plain,
% 2.44/2.65 ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[13372, 124, 2518])).
% 2.44/2.65 tff(13374,plain,
% 2.44/2.65 (~r(s(s(s(s(s(z))))), z)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[13373, 13366])).
% 2.44/2.65 tff(13375,plain,
% 2.44/2.65 (~r(s(s(s(s(elem!1)))), z)),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[13374, 13351])).
% 2.44/2.65 tff(13376,plain,
% 2.44/2.65 (b(s(s(s(s(elem!1)))), z)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[5723, 13375])).
% 2.44/2.65 tff(13377,plain,
% 2.44/2.65 (b(s(s(s(s(s(z))))), z)),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[13376, 13349])).
% 2.44/2.65 tff(13378,plain,
% 2.44/2.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.44/2.65 inference(rewrite,[status(thm)],[])).
% 2.44/2.65 tff(13379,plain,
% 2.44/2.65 (((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.44/2.65 inference(rewrite,[status(thm)],[])).
% 2.44/2.65 tff(13380,plain,
% 2.44/2.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z))))))))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[13379])).
% 2.44/2.65 tff(13381,plain,
% 2.44/2.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.44/2.65 inference(transitivity,[status(thm)],[13380, 13378])).
% 2.44/2.65 tff(13382,plain,
% 2.44/2.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(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)))))))),
% 2.44/2.65 inference(quant_inst,[status(thm)],[])).
% 2.44/2.65 tff(13383,plain,
% 2.44/2.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z))))))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[13382, 13381])).
% 2.44/2.65 tff(13384,plain,
% 2.44/2.65 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[13383, 306, 12167, 13377, 13365])).
% 2.44/2.65 tff(13385,plain,
% 2.44/2.65 ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[3661, 124, 1033])).
% 2.44/2.65 tff(13386,plain,
% 2.44/2.65 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[13385, 13366])).
% 2.44/2.65 tff(13387,plain,
% 2.44/2.65 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) | b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[3665, 43, 13386])).
% 2.44/2.65 tff(13388,plain,
% 2.44/2.65 ($false),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[13387, 13384, 13364])).
% 2.44/2.65 tff(13389,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~(elem!1 = s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.65 tff(13390,plain,
% 2.44/2.65 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[13389, 13348, 10, 13344, 13357])).
% 2.44/2.65 tff(13391,plain,
% 2.44/2.65 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[13390, 13355])).
% 2.44/2.65 tff(13392,plain,
% 2.44/2.65 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[1302, 13391, 13352])).
% 2.44/2.65 tff(13393,plain,
% 2.44/2.65 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[5264, 13392, 10])).
% 2.44/2.65 tff(13394,plain,
% 2.44/2.65 (~b(s(s(s(s(s(z))))), s(z))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[12511, 306, 13295, 13313, 13393])).
% 2.44/2.65 tff(13395,plain,
% 2.44/2.65 (r(s(s(s(s(s(z))))), s(z))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[503, 43, 500, 13394])).
% 2.44/2.65 tff(13396,plain,
% 2.44/2.65 (r(z, elem!1) <=> r(z, s(z))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[10])).
% 2.44/2.65 tff(13397,plain,
% 2.44/2.65 (r(z, s(z))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[10425, 13396])).
% 2.44/2.65 tff(13398,plain,
% 2.44/2.65 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)))),
% 2.44/2.65 inference(rewrite,[status(thm)],[])).
% 2.44/2.65 tff(13399,plain,
% 2.44/2.65 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)))),
% 2.44/2.65 inference(quant_inst,[status(thm)],[])).
% 2.44/2.65 tff(13400,plain,
% 2.44/2.65 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[13399, 13398])).
% 2.44/2.65 tff(13401,plain,
% 2.44/2.65 (~r(s(s(s(s(s(z))))), z)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[13400, 124, 13397, 13395])).
% 2.44/2.65 tff(13402,plain,
% 2.44/2.65 (~r(s(s(s(s(elem!1)))), z)),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[13401, 13351])).
% 2.44/2.65 tff(13403,plain,
% 2.44/2.65 (b(s(s(s(s(elem!1)))), z)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[5723, 13402])).
% 2.44/2.65 tff(13404,plain,
% 2.44/2.65 (b(s(s(s(s(s(z))))), z)),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[13403, 13349])).
% 2.44/2.65 tff(13405,plain,
% 2.44/2.65 (~r(s(s(z)), z)),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[13308, 13323])).
% 2.44/2.65 tff(13406,plain,
% 2.44/2.65 (b(s(s(z)), z)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[2529, 43, 106, 13405])).
% 2.44/2.65 tff(13407,plain,
% 2.44/2.65 (~r(s(s(s(s(z)))), z)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[12165, 124, 13357, 13344])).
% 2.44/2.65 tff(13408,plain,
% 2.44/2.65 (b(s(s(s(s(z)))), z)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[695, 13407])).
% 2.44/2.65 tff(13409,plain,
% 2.44/2.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.44/2.65 inference(rewrite,[status(thm)],[])).
% 2.44/2.65 tff(13410,plain,
% 2.44/2.65 (((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.44/2.65 inference(rewrite,[status(thm)],[])).
% 2.44/2.65 tff(13411,plain,
% 2.44/2.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[13410])).
% 2.44/2.65 tff(13412,plain,
% 2.44/2.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.44/2.65 inference(transitivity,[status(thm)],[13411, 13409])).
% 2.44/2.65 tff(13413,plain,
% 2.44/2.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.44/2.65 inference(quant_inst,[status(thm)],[])).
% 2.44/2.65 tff(13414,plain,
% 2.44/2.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[13413, 13412])).
% 2.44/2.65 tff(13415,plain,
% 2.44/2.65 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[13414, 306, 13408, 13406, 13404, 13348])).
% 2.44/2.65 tff(13416,plain,
% 2.44/2.65 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(z))) | b(s(s(s(s(s(z))))), s(s(z))) | r(s(s(s(s(s(z))))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(z))) | b(s(s(s(s(s(z))))), s(s(z))) | r(s(s(s(s(s(z))))), s(s(z))))),
% 2.44/2.65 inference(rewrite,[status(thm)],[])).
% 2.44/2.65 tff(13417,plain,
% 2.44/2.65 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(z))) | b(s(s(s(s(s(z))))), s(s(z))) | r(s(s(s(s(s(z))))), s(s(z))))),
% 2.44/2.65 inference(quant_inst,[status(thm)],[])).
% 2.44/2.65 tff(13418,plain,
% 2.44/2.65 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(z))) | b(s(s(s(s(s(z))))), s(s(z))) | r(s(s(s(s(s(z))))), s(s(z)))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[13417, 13416])).
% 2.44/2.65 tff(13419,plain,
% 2.44/2.65 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[13418, 43, 6464, 13415])).
% 2.44/2.65 tff(13420,plain,
% 2.44/2.65 (b(s(s(s(elem!1))), z) <=> b(s(s(s(s(z)))), z)),
% 2.44/2.65 inference(monotonicity,[status(thm)],[3589])).
% 2.44/2.65 tff(13421,plain,
% 2.44/2.65 (b(s(s(s(s(z)))), z) <=> b(s(s(s(elem!1))), z)),
% 2.44/2.65 inference(symmetry,[status(thm)],[13420])).
% 2.44/2.65 tff(13422,plain,
% 2.44/2.65 (b(s(s(s(elem!1))), z)),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[13408, 13421])).
% 2.44/2.65 tff(13423,plain,
% 2.44/2.65 (~(s(s(s(s(elem!1)))) = elem!1)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[6321, 10])).
% 2.44/2.65 tff(13424,plain,
% 2.44/2.65 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 2.44/2.65 inference(symmetry,[status(thm)],[3594])).
% 2.44/2.65 tff(13425,plain,
% 2.44/2.65 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 2.44/2.65 inference(transitivity,[status(thm)],[3592, 13424])).
% 2.44/2.65 tff(13426,plain,
% 2.44/2.65 ((~b(s(s(s(s(s(z))))), s(z))) <=> (~b(s(s(s(s(elem!1)))), elem!1))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[13425])).
% 2.44/2.65 tff(13427,plain,
% 2.44/2.65 (~b(s(s(s(s(elem!1)))), elem!1)),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[13394, 13426])).
% 2.44/2.65 tff(13428,plain,
% 2.44/2.65 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[1736, 13427, 13423])).
% 2.44/2.65 tff(13429,plain,
% 2.44/2.65 (~r(s(s(s(elem!1))), elem!1)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[6453, 13428, 13363, 13347, 13422, 10425])).
% 2.44/2.65 tff(13430,plain,
% 2.44/2.65 (b(s(s(s(elem!1))), elem!1)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[1636, 13429, 5076])).
% 2.44/2.66 tff(13431,plain,
% 2.44/2.66 (b(s(s(s(s(z)))), s(z))),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[13430, 5220])).
% 2.44/2.66 tff(13432,plain,
% 2.44/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.44/2.66 inference(rewrite,[status(thm)],[])).
% 2.44/2.66 tff(13433,plain,
% 2.44/2.66 (((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.44/2.66 inference(rewrite,[status(thm)],[])).
% 2.44/2.66 tff(13434,plain,
% 2.44/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z)))))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[13433])).
% 2.44/2.66 tff(13435,plain,
% 2.44/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.44/2.66 inference(transitivity,[status(thm)],[13434, 13432])).
% 2.44/2.66 tff(13436,plain,
% 2.44/2.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.44/2.66 inference(quant_inst,[status(thm)],[])).
% 2.44/2.66 tff(13437,plain,
% 2.44/2.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z)))),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[13436, 13435])).
% 2.44/2.66 tff(13438,plain,
% 2.44/2.66 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[13437, 306, 13295, 13313, 13431])).
% 2.44/2.66 tff(13439,plain,
% 2.44/2.66 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[10124, 13438])).
% 2.44/2.66 tff(13440,plain,
% 2.44/2.66 ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[13335, 306, 13408, 13406])).
% 2.44/2.66 tff(13441,plain,
% 2.44/2.66 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[13440, 13348])).
% 2.44/2.66 tff(13442,plain,
% 2.44/2.66 (r(s(s(z)), s(s(s(s(z)))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[4510, 13441])).
% 2.44/2.66 tff(13443,plain,
% 2.44/2.66 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.44/2.66 inference(rewrite,[status(thm)],[])).
% 2.44/2.66 tff(13444,plain,
% 2.44/2.66 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.44/2.66 inference(rewrite,[status(thm)],[])).
% 2.44/2.66 tff(13445,plain,
% 2.44/2.66 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[13444])).
% 2.44/2.66 tff(13446,plain,
% 2.44/2.66 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.44/2.66 inference(transitivity,[status(thm)],[13445, 13443])).
% 2.44/2.66 tff(13447,plain,
% 2.44/2.66 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.44/2.66 inference(quant_inst,[status(thm)],[])).
% 2.44/2.66 tff(13448,plain,
% 2.44/2.66 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[13447, 13446])).
% 2.44/2.66 tff(13449,plain,
% 2.44/2.66 (~r(s(s(z)), s(s(s(z))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[13448, 124, 13442, 13439])).
% 2.44/2.66 tff(13450,plain,
% 2.44/2.66 (b(s(s(z)), s(s(s(z))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[2514, 13449])).
% 2.44/2.66 tff(13451,plain,
% 2.44/2.66 (~b(s(z), s(s(z)))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[10499, 306, 13295, 13313, 13450])).
% 2.44/2.66 tff(13452,plain,
% 2.44/2.66 (r(s(z), s(s(z)))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[4434, 13451])).
% 2.44/2.66 tff(13453,plain,
% 2.44/2.66 ($false),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[12521, 124, 13452, 13395, 13419])).
% 2.44/2.66 tff(13454,plain,((~(elem!1 = s(z))) | b(elem!1, z) | r(s(s(elem!1)), elem!1) | r(s(s(elem!1)), s(elem!1)) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.66 tff(13455,plain,
% 2.44/2.66 (~(elem!1 = s(z))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[13454, 3149, 6, 2, 5])).
% 2.44/2.66 tff(13456,plain,
% 2.44/2.66 (r(elem!1, s(z))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[97, 13455])).
% 2.44/2.66 tff(13457,plain,
% 2.44/2.66 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[7480, 247, 10425, 13456])).
% 2.44/2.66 tff(13458,plain,
% 2.44/2.66 (~(s(z) = elem!1)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[89, 13455])).
% 2.44/2.66 tff(13459,plain,
% 2.44/2.66 (~r(z, s(z))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[385, 359, 10425])).
% 2.44/2.66 tff(13460,plain,
% 2.44/2.66 (b(z, s(z))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[2263, 13459])).
% 2.44/2.66 tff(13461,plain,
% 2.44/2.66 (~b(s(s(s(z))), z)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[7398, 306, 2284, 247, 13460])).
% 2.44/2.66 tff(13462,plain,
% 2.44/2.66 (r(s(s(s(z))), z)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[2197, 13461])).
% 2.44/2.66 tff(13463,plain,
% 2.44/2.66 (~b(s(z), elem!1)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[9090, 13462, 10425, 10451, 2284, 4198])).
% 2.44/2.66 tff(13464,plain,
% 2.44/2.66 (r(s(z), elem!1)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[13156, 13463, 3094])).
% 2.44/2.66 tff(13465,plain,
% 2.44/2.66 (~r(s(elem!1), elem!1)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[9508, 13464, 10425, 247, 13303])).
% 2.44/2.66 tff(13466,plain,
% 2.44/2.66 (s(s(elem!1)) = elem!1),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[13306, 13465, 2, 6])).
% 2.44/2.66 tff(13467,plain,
% 2.44/2.66 (~(s(s(s(s(z)))) = elem!1)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[9813, 13466])).
% 2.44/2.66 tff(13468,plain,
% 2.44/2.66 (~r(s(s(s(z))), elem!1)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[6831, 13462, 10425])).
% 2.44/2.66 tff(13469,plain,
% 2.44/2.66 (b(s(s(s(z))), elem!1)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[1489, 13468, 4198])).
% 2.44/2.66 tff(13470,plain,
% 2.44/2.66 (~r(s(s(s(s(z)))), z)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[9834, 13467, 1470, 10451, 13462, 13469])).
% 2.44/2.66 tff(13471,plain,
% 2.44/2.66 (b(s(s(s(s(z)))), z)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[695, 13470])).
% 2.44/2.66 tff(13472,plain,
% 2.44/2.66 (~b(s(s(s(s(z)))), s(z))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[702, 306, 13471, 247, 13460])).
% 2.44/2.66 tff(13473,plain,
% 2.44/2.66 (r(s(s(s(s(z)))), s(z))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[4490, 13472])).
% 2.44/2.66 tff(13474,plain,
% 2.44/2.66 (~r(s(s(s(s(z)))), elem!1)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[9849, 124, 359, 13473])).
% 2.44/2.66 tff(13475,plain,
% 2.44/2.66 (b(s(s(s(s(z)))), elem!1)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[9832, 13474, 13467])).
% 2.44/2.66 tff(13476,plain,
% 2.44/2.66 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[7480, 247, 10425, 359])).
% 2.44/2.66 tff(13477,plain,
% 2.44/2.66 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[4284, 13466])).
% 2.44/2.66 tff(13478,plain,
% 2.44/2.66 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[1144, 13477, 13476])).
% 2.44/2.66 tff(13479,plain,
% 2.44/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 2.44/2.66 inference(rewrite,[status(thm)],[])).
% 2.44/2.66 tff(13480,plain,
% 2.44/2.66 (((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 2.44/2.66 inference(rewrite,[status(thm)],[])).
% 2.44/2.66 tff(13481,plain,
% 2.44/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1))))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[13480])).
% 2.44/2.66 tff(13482,plain,
% 2.44/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 2.44/2.66 inference(transitivity,[status(thm)],[13481, 13479])).
% 2.44/2.66 tff(13483,plain,
% 2.44/2.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 2.44/2.66 inference(quant_inst,[status(thm)],[])).
% 2.44/2.66 tff(13484,plain,
% 2.44/2.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1))),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[13483, 13482])).
% 2.44/2.66 tff(13485,plain,
% 2.44/2.66 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[13484, 306, 2284, 13478, 1470, 13475])).
% 2.44/2.66 tff(13486,plain,
% 2.44/2.66 (b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[4864, 10660])).
% 2.44/2.66 tff(13487,plain,
% 2.44/2.66 (r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[13486, 13485])).
% 2.44/2.66 tff(13488,plain,
% 2.44/2.66 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[4239, 306, 2284, 13469, 13478, 1470])).
% 2.44/2.66 tff(13489,plain,
% 2.44/2.66 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[3207, 13488])).
% 2.44/2.66 tff(13490,plain,
% 2.44/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.44/2.66 inference(rewrite,[status(thm)],[])).
% 2.44/2.66 tff(13491,plain,
% 2.44/2.66 (((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.44/2.66 inference(rewrite,[status(thm)],[])).
% 2.44/2.66 tff(13492,plain,
% 2.44/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1))))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[13491])).
% 2.44/2.66 tff(13493,plain,
% 2.44/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.44/2.66 inference(transitivity,[status(thm)],[13492, 13490])).
% 2.44/2.66 tff(13494,plain,
% 2.44/2.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.44/2.66 inference(quant_inst,[status(thm)],[])).
% 2.44/2.66 tff(13495,plain,
% 2.44/2.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1))),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[13494, 13493])).
% 2.44/2.66 tff(13496,plain,
% 2.44/2.66 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[13495, 306, 2284, 13469, 1470, 13475])).
% 2.44/2.66 tff(13497,plain,
% 2.44/2.66 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[10124, 13496])).
% 2.44/2.66 tff(13498,plain,
% 2.44/2.66 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(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(s(z)))))))))),
% 2.44/2.66 inference(rewrite,[status(thm)],[])).
% 2.44/2.66 tff(13499,plain,
% 2.44/2.66 (((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(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(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 2.44/2.66 inference(rewrite,[status(thm)],[])).
% 2.44/2.66 tff(13500,plain,
% 2.44/2.66 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(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(s(z))))))))))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[13499])).
% 2.44/2.66 tff(13501,plain,
% 2.44/2.66 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(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(s(z)))))))))),
% 2.44/2.66 inference(transitivity,[status(thm)],[13500, 13498])).
% 2.44/2.66 tff(13502,plain,
% 2.44/2.66 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 2.44/2.66 inference(quant_inst,[status(thm)],[])).
% 2.44/2.66 tff(13503,plain,
% 2.44/2.66 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[13502, 13501])).
% 2.44/2.66 tff(13504,plain,
% 2.44/2.66 ($false),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[13503, 124, 13497, 13489, 13487])).
% 2.44/2.66 tff(13505,plain,((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~r(elem!1, s(z))) | (~b(s(z), z)) | b(elem!1, z) | r(s(s(elem!1)), elem!1) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.44/2.66 tff(13506,plain,
% 2.44/2.66 (~b(s(s(s(z))), s(z))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[13505, 247, 13456, 13280, 2, 6, 13458])).
% 2.44/2.66 tff(13507,plain,
% 2.44/2.66 (~r(s(z), s(s(s(z))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[9853, 13506, 2, 5, 6])).
% 2.44/2.66 tff(13508,plain,
% 2.44/2.66 (b(s(z), s(s(s(z))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[3302, 13507])).
% 2.44/2.66 tff(13509,plain,
% 2.44/2.66 (~r(z, s(z))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[385, 1474, 10425])).
% 2.44/2.66 tff(13510,plain,
% 2.44/2.66 (b(z, s(z))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[2263, 13509])).
% 2.44/2.66 tff(13511,plain,
% 2.44/2.66 (r(s(z), elem!1)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[4192, 90])).
% 2.44/2.66 tff(13512,plain,
% 2.44/2.66 (~r(s(z), z)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[1049, 13511, 10451])).
% 2.44/2.66 tff(13513,plain,
% 2.44/2.66 (b(s(z), z)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[221, 13512])).
% 2.44/2.66 tff(13514,plain,
% 2.44/2.66 (~b(s(s(s(z))), z)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[4218, 13513, 8, 13510])).
% 2.44/2.66 tff(13515,plain,
% 2.44/2.66 (r(s(s(s(z))), z)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[2197, 13514])).
% 2.44/2.66 tff(13516,plain,
% 2.44/2.66 (b(elem!1, s(s(s(z))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[10460, 5, 6, 2])).
% 2.44/2.66 tff(13517,plain,
% 2.44/2.66 (b(s(s(s(z))), elem!1)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[7148, 13511, 10425, 8, 2715])).
% 2.44/2.66 tff(13518,plain,
% 2.44/2.66 (~r(s(elem!1), elem!1)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[9508, 13513, 10425, 13303, 13511])).
% 2.44/2.66 tff(13519,plain,
% 2.44/2.66 (s(s(elem!1)) = elem!1),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[13306, 13518, 6, 2])).
% 2.44/2.66 tff(13520,plain,
% 2.44/2.66 (~(s(s(s(s(z)))) = elem!1)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[9813, 13519])).
% 2.44/2.66 tff(13521,plain,
% 2.44/2.66 (~r(s(s(s(s(z)))), z)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[9834, 13520, 13517, 10451, 13516, 13515])).
% 2.44/2.66 tff(13522,plain,
% 2.44/2.66 (b(s(s(s(s(z)))), z)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[695, 13521])).
% 2.44/2.66 tff(13523,plain,
% 2.44/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)))),
% 2.44/2.66 inference(rewrite,[status(thm)],[])).
% 2.44/2.66 tff(13524,plain,
% 2.44/2.66 (((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)))),
% 2.44/2.66 inference(rewrite,[status(thm)],[])).
% 2.44/2.66 tff(13525,plain,
% 2.44/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z))))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[13524])).
% 2.44/2.66 tff(13526,plain,
% 2.44/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)))),
% 2.44/2.66 inference(transitivity,[status(thm)],[13525, 13523])).
% 2.44/2.66 tff(13527,plain,
% 2.44/2.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 2.44/2.66 inference(quant_inst,[status(thm)],[])).
% 2.44/2.66 tff(13528,plain,
% 2.44/2.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z))),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[13527, 13526])).
% 2.44/2.66 tff(13529,plain,
% 2.44/2.66 (~b(s(s(s(s(z)))), s(z))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[13528, 306, 8, 13522, 13513, 13510])).
% 2.44/2.66 tff(13530,plain,
% 2.44/2.66 (r(s(s(s(s(z)))), s(z))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[4490, 13529])).
% 2.44/2.66 tff(13531,plain,
% 2.44/2.66 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[707, 124, 114, 13530])).
% 2.44/2.66 tff(13532,plain,
% 2.44/2.66 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[4471, 13531])).
% 2.44/2.66 tff(13533,plain,
% 2.44/2.66 (~r(s(s(s(s(z)))), elem!1)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[9849, 124, 1474, 13530])).
% 2.44/2.66 tff(13534,plain,
% 2.44/2.66 (b(s(s(s(s(z)))), elem!1)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[9832, 13533, 13520])).
% 2.44/2.66 tff(13535,plain,
% 2.44/2.66 ($false),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[9823, 306, 13517, 13516, 13534, 13532])).
% 2.44/2.66 tff(13536,plain,(b(s(s(s(z))), s(z)) | (~b(s(z), s(s(s(z))))) | r(s(s(elem!1)), elem!1) | b(elem!1, z) | b(s(z), elem!1) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.66 tff(13537,plain,
% 2.44/2.66 (b(s(z), elem!1)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[13536, 13508, 2, 6, 13506, 5])).
% 2.44/2.66 tff(13538,plain,
% 2.44/2.66 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[7520, 13537, 13280, 10425, 13281, 13456])).
% 2.44/2.66 tff(13539,plain,
% 2.44/2.66 (s(s(s(s(s(s(z)))))) = elem!1),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[1144, 13538, 13457])).
% 2.44/2.66 tff(13540,plain,
% 2.44/2.66 (~(s(s(elem!1)) = elem!1)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[4284, 13539])).
% 2.44/2.66 tff(13541,plain,
% 2.44/2.66 (~(elem!1 = s(s(elem!1)))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[186, 13540])).
% 2.44/2.66 tff(13542,plain,
% 2.44/2.66 (r(s(s(s(z))), s(z))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[113, 13506])).
% 2.44/2.66 tff(13543,plain,
% 2.44/2.66 (~(s(elem!1) = elem!1)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[9225, 13538, 10425, 13542, 2, 13456])).
% 2.44/2.66 tff(13544,plain,
% 2.44/2.66 (~(s(s(elem!1)) = s(elem!1))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[195, 13543])).
% 2.44/2.66 tff(13545,plain,
% 2.44/2.66 (b(s(s(elem!1)), s(elem!1))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[994, 13544, 3149])).
% 2.44/2.66 tff(13546,plain,
% 2.44/2.66 (b(s(elem!1), elem!1)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[9534, 13537, 10425, 247, 13456, 13303, 13542, 2, 13281, 13280])).
% 2.44/2.66 tff(13547,plain,
% 2.44/2.66 (b(s(s(elem!1)), elem!1)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[47, 13540, 6])).
% 2.44/2.66 tff(13548,plain,
% 2.44/2.66 (~b(elem!1, s(s(elem!1)))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[1024, 13547, 13546, 13545])).
% 2.44/2.66 tff(13549,plain,
% 2.44/2.66 (r(elem!1, s(s(elem!1)))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[516, 13548, 13541])).
% 2.44/2.66 tff(13550,plain,
% 2.44/2.66 (~r(z, s(s(elem!1)))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[978, 13549, 10451])).
% 2.44/2.66 tff(13551,plain,
% 2.44/2.66 (r(s(elem!1), elem!1)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[13306, 13540, 2, 6])).
% 2.44/2.67 tff(13552,plain,
% 2.44/2.67 (~r(s(elem!1), z)),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[416, 13551, 10425])).
% 2.44/2.67 tff(13553,plain,
% 2.44/2.67 (b(s(elem!1), z)),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[2380, 13552])).
% 2.44/2.67 tff(13554,plain,
% 2.44/2.67 (~b(z, s(s(elem!1)))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[1228, 13553, 10425, 13545, 13543, 13547])).
% 2.44/2.67 tff(13555,plain,
% 2.44/2.67 ($false),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[460, 13554, 13550])).
% 2.44/2.67 tff(13556,plain,((~b(s(z), z)) | b(elem!1, z) | r(s(s(elem!1)), elem!1) | r(s(s(elem!1)), s(elem!1)) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.67 tff(13557,plain,
% 2.44/2.67 (~b(s(z), z)),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[13556, 3149, 6, 2, 5])).
% 2.44/2.67 tff(13558,plain,
% 2.44/2.67 (r(s(z), z)),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[221, 13557])).
% 2.44/2.67 tff(13559,plain,
% 2.44/2.67 ($false),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[2180, 124, 10451, 13456, 13558])).
% 2.44/2.67 tff(13560,plain,(r(s(s(elem!1)), s(elem!1)) | r(s(s(elem!1)), elem!1) | b(elem!1, z) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.67 tff(13561,plain,
% 2.44/2.67 (r(s(s(elem!1)), s(elem!1))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[13560, 6, 2, 5])).
% 2.44/2.67 tff(13562,plain,
% 2.44/2.67 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(s(z))), s(s(z)))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[15, 14])).
% 2.44/2.67 tff(13563,plain,
% 2.44/2.67 (r(s(s(s(z))), s(s(z)))),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[244, 13562])).
% 2.44/2.67 tff(13564,plain,
% 2.44/2.67 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(z)))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[3589, 14])).
% 2.44/2.67 tff(13565,plain,
% 2.44/2.67 (b(s(z), s(s(s(z))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[9887, 13312, 1470])).
% 2.44/2.67 tff(13566,plain,
% 2.44/2.67 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[13342, 13307, 10425, 10, 13298, 13295, 13565])).
% 2.44/2.67 tff(13567,plain,
% 2.44/2.67 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[10146, 13566])).
% 2.44/2.67 tff(13568,plain,
% 2.44/2.67 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[13567, 11698])).
% 2.44/2.67 tff(13569,plain,
% 2.44/2.67 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[659, 13568, 244])).
% 2.44/2.67 tff(13570,plain,
% 2.44/2.67 (b(s(s(s(elem!1))), s(elem!1))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[664, 13569, 11704])).
% 2.44/2.67 tff(13571,plain,
% 2.44/2.67 (b(s(s(s(s(z)))), s(s(z)))),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[13570, 13564])).
% 2.44/2.67 tff(13572,plain,
% 2.44/2.67 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(s(s(z)))))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[3589])).
% 2.44/2.67 tff(13573,plain,
% 2.44/2.67 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[3589])).
% 2.44/2.67 tff(13574,plain,
% 2.44/2.67 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(z))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[10])).
% 2.44/2.67 tff(13575,plain,
% 2.44/2.67 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(z)))), s(z))),
% 2.44/2.67 inference(transitivity,[status(thm)],[13574, 13573])).
% 2.44/2.67 tff(13576,plain,
% 2.44/2.67 (r(s(s(s(s(z)))), s(z))),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[1627, 13575])).
% 2.44/2.67 tff(13577,plain,
% 2.44/2.67 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 2.44/2.67 inference(rewrite,[status(thm)],[])).
% 2.44/2.67 tff(13578,plain,
% 2.44/2.67 (((~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(z, s(s(s(s(z)))))))),
% 2.44/2.67 inference(rewrite,[status(thm)],[])).
% 2.44/2.67 tff(13579,plain,
% 2.44/2.67 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z))))))))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[13578])).
% 2.44/2.67 tff(13580,plain,
% 2.44/2.67 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 2.44/2.67 inference(transitivity,[status(thm)],[13579, 13577])).
% 2.44/2.67 tff(13581,plain,
% 2.44/2.67 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))))),
% 2.44/2.67 inference(quant_inst,[status(thm)],[])).
% 2.44/2.67 tff(13582,plain,
% 2.44/2.67 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z))))))),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[13581, 13580])).
% 2.44/2.67 tff(13583,plain,
% 2.44/2.67 (~r(z, s(s(s(s(z)))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[13582, 124, 2265, 13576])).
% 2.44/2.67 tff(13584,plain,
% 2.44/2.67 (r(z, s(s(s(s(z))))) <=> r(z, s(s(s(elem!1))))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[5225])).
% 2.44/2.67 tff(13585,plain,
% 2.44/2.67 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(s(z)))))),
% 2.44/2.67 inference(symmetry,[status(thm)],[13584])).
% 2.44/2.67 tff(13586,plain,
% 2.44/2.67 (r(z, s(s(s(s(z)))))),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[564, 13585])).
% 2.44/2.67 tff(13587,assumption,(~r(z, s(s(s(s(z)))))), introduced(assumption)).
% 2.44/2.67 tff(13588,plain,
% 2.44/2.67 ($false),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[13587, 13586])).
% 2.44/2.67 tff(13589,plain,(r(z, s(s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.67 tff(13590,plain,
% 2.44/2.67 (~r(z, s(s(s(elem!1))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[13589, 13583, 10])).
% 2.44/2.67 tff(13591,plain,
% 2.44/2.67 (b(z, s(s(s(elem!1))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[585, 13590])).
% 2.44/2.67 tff(13592,plain,
% 2.44/2.67 (b(z, s(s(s(s(z)))))),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[13591, 13572])).
% 2.44/2.67 tff(13593,plain,
% 2.44/2.67 (~r(s(s(s(s(z)))), z)),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[3030, 5065])).
% 2.44/2.67 tff(13594,plain,
% 2.44/2.67 (b(s(s(s(s(z)))), z)),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[695, 13593])).
% 2.44/2.67 tff(13595,plain,
% 2.44/2.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 2.44/2.67 inference(rewrite,[status(thm)],[])).
% 2.44/2.67 tff(13596,plain,
% 2.44/2.67 (((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 2.44/2.67 inference(rewrite,[status(thm)],[])).
% 2.44/2.67 tff(13597,plain,
% 2.44/2.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z))))))))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[13596])).
% 2.44/2.67 tff(13598,plain,
% 2.44/2.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 2.44/2.67 inference(transitivity,[status(thm)],[13597, 13595])).
% 2.44/2.67 tff(13599,plain,
% 2.44/2.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.44/2.67 inference(quant_inst,[status(thm)],[])).
% 2.44/2.67 tff(13600,plain,
% 2.44/2.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z))))))),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[13599, 13598])).
% 2.44/2.67 tff(13601,plain,
% 2.44/2.67 ($false),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[13600, 306, 13594, 2061, 3455, 13592])).
% 2.44/2.67 tff(13602,plain,((~r(s(s(s(elem!1))), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~(elem!1 = s(z))) | (~r(z, s(z))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.67 tff(13603,plain,
% 2.44/2.67 (~r(s(s(s(elem!1))), elem!1)),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[13602, 13406, 13571, 10, 13397, 10451])).
% 2.44/2.67 tff(13604,plain,
% 2.44/2.67 (b(s(s(s(elem!1))), elem!1)),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[1636, 13603, 5076])).
% 2.44/2.67 tff(13605,plain,
% 2.44/2.67 (b(s(s(s(s(z)))), s(z))),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[13604, 5220])).
% 2.44/2.67 tff(13606,plain,
% 2.44/2.67 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[13437, 306, 13295, 13565, 13605])).
% 2.44/2.67 tff(13607,plain,
% 2.44/2.67 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[10124, 13606])).
% 2.44/2.67 tff(13608,plain,
% 2.44/2.67 (r(s(s(s(s(elem!1)))), s(s(elem!1))) <=> r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[3590, 15])).
% 2.44/2.67 tff(13609,plain,
% 2.44/2.67 (~r(z, s(s(elem!1)))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[950, 564, 11699])).
% 2.44/2.67 tff(13610,plain,
% 2.44/2.67 (b(z, s(s(elem!1)))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[460, 13609])).
% 2.44/2.67 tff(13611,plain,
% 2.44/2.67 (b(z, s(s(s(z))))),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[13610, 11743])).
% 2.44/2.67 tff(13612,plain,
% 2.44/2.67 (r(elem!1, s(s(s(elem!1)))) <=> r(s(z), s(s(s(s(z)))))),
% 2.44/2.67 inference(transitivity,[status(thm)],[11724, 11726])).
% 2.44/2.67 tff(13613,plain,
% 2.44/2.67 ((~r(elem!1, s(s(s(elem!1))))) <=> (~r(s(z), s(s(s(s(z))))))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[13612])).
% 2.44/2.67 tff(13614,plain,
% 2.44/2.67 (~r(elem!1, s(s(s(elem!1))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[573, 564, 374])).
% 2.44/2.67 tff(13615,plain,
% 2.44/2.67 (~r(s(z), s(s(s(s(z)))))),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[13614, 13613])).
% 2.44/2.67 tff(13616,plain,
% 2.44/2.67 (b(s(z), s(s(s(s(z)))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[5135, 13615])).
% 2.44/2.67 tff(13617,plain,
% 2.44/2.67 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[3629, 13616, 10, 2284, 204, 3620, 13611])).
% 2.44/2.67 tff(13618,plain,
% 2.44/2.67 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[5264, 13617, 10])).
% 2.44/2.67 tff(13619,plain,
% 2.44/2.67 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[1302, 13618, 13352])).
% 2.44/2.67 tff(13620,plain,
% 2.44/2.67 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[13619, 13608])).
% 2.44/2.67 tff(13621,plain,
% 2.44/2.67 (b(s(s(s(z))), elem!1)),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[4206, 13312, 2284])).
% 2.44/2.67 tff(13622,plain,
% 2.44/2.67 (~b(s(s(z)), s(s(s(z))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[5582, 13611, 1470, 13621, 2061])).
% 2.44/2.67 tff(13623,plain,
% 2.44/2.67 (r(s(s(z)), s(s(s(z))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[2514, 13622])).
% 2.44/2.67 tff(13624,plain,
% 2.44/2.67 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.44/2.67 inference(rewrite,[status(thm)],[])).
% 2.44/2.67 tff(13625,plain,
% 2.44/2.67 (((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z))))) <=> ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.44/2.67 inference(rewrite,[status(thm)],[])).
% 2.44/2.67 tff(13626,plain,
% 2.44/2.67 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[13625])).
% 2.44/2.67 tff(13627,plain,
% 2.44/2.67 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.44/2.67 inference(transitivity,[status(thm)],[13626, 13624])).
% 2.44/2.67 tff(13628,plain,
% 2.44/2.67 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.44/2.67 inference(quant_inst,[status(thm)],[])).
% 2.44/2.67 tff(13629,plain,
% 2.44/2.67 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[13628, 13627])).
% 2.44/2.67 tff(13630,plain,
% 2.44/2.67 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[13629, 124, 13623, 13620])).
% 2.44/2.67 tff(13631,plain,
% 2.44/2.67 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[13418, 43, 6464, 13630])).
% 2.44/2.67 tff(13632,plain,
% 2.44/2.67 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.44/2.67 inference(rewrite,[status(thm)],[])).
% 2.44/2.67 tff(13633,plain,
% 2.44/2.67 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.44/2.67 inference(quant_inst,[status(thm)],[])).
% 2.44/2.67 tff(13634,plain,
% 2.44/2.67 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[13633, 13632])).
% 2.44/2.67 tff(13635,plain,
% 2.44/2.67 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[13634, 124, 1033, 13623])).
% 2.44/2.67 tff(13636,plain,
% 2.44/2.67 (b(s(s(z)), s(s(s(s(z)))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[4510, 13635])).
% 2.44/2.67 tff(13637,plain,
% 2.44/2.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.44/2.67 inference(rewrite,[status(thm)],[])).
% 2.44/2.67 tff(13638,plain,
% 2.44/2.67 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.44/2.67 inference(rewrite,[status(thm)],[])).
% 2.44/2.67 tff(13639,plain,
% 2.44/2.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[13638])).
% 2.44/2.67 tff(13640,plain,
% 2.44/2.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.44/2.67 inference(transitivity,[status(thm)],[13639, 13637])).
% 2.44/2.67 tff(13641,plain,
% 2.44/2.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.44/2.67 inference(quant_inst,[status(thm)],[])).
% 2.44/2.67 tff(13642,plain,
% 2.44/2.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[13641, 13640])).
% 2.44/2.67 tff(13643,plain,
% 2.44/2.67 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[13642, 306, 13636, 3455, 13631])).
% 2.44/2.67 tff(13644,plain,
% 2.44/2.67 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[3661, 124, 1033, 13620])).
% 2.44/2.67 tff(13645,plain,
% 2.44/2.67 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) | b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[3665, 43, 13644])).
% 2.44/2.67 tff(13646,plain,
% 2.44/2.67 ($false),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[13645, 13643, 13364])).
% 2.44/2.67 tff(13647,plain,((~r(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~(elem!1 = s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~r(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), z)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.67 tff(13648,plain,
% 2.44/2.67 (~r(z, s(s(s(elem!1))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[13647, 13571, 10, 13567, 13295, 13298, 13605, 1470, 13406, 10425])).
% 2.44/2.67 tff(13649,plain,
% 2.44/2.67 (b(z, s(s(s(elem!1))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[585, 13648])).
% 2.44/2.67 tff(13650,plain,
% 2.44/2.67 (b(z, s(s(s(s(z)))))),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[13649, 13572])).
% 2.44/2.67 tff(13651,assumption,(b(s(s(z)), s(s(s(s(z)))))), introduced(assumption)).
% 2.44/2.67 tff(13652,plain,
% 2.44/2.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 2.44/2.67 inference(rewrite,[status(thm)],[])).
% 2.44/2.67 tff(13653,plain,
% 2.44/2.67 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 2.44/2.67 inference(rewrite,[status(thm)],[])).
% 2.44/2.67 tff(13654,plain,
% 2.44/2.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z))))))))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[13653])).
% 2.44/2.67 tff(13655,plain,
% 2.44/2.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 2.44/2.67 inference(transitivity,[status(thm)],[13654, 13652])).
% 2.44/2.67 tff(13656,plain,
% 2.44/2.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))),
% 2.44/2.67 inference(quant_inst,[status(thm)],[])).
% 2.44/2.67 tff(13657,plain,
% 2.44/2.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z))))))),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[13656, 13655])).
% 2.44/2.67 tff(13658,plain,
% 2.44/2.67 ($false),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[13657, 306, 13651, 2061, 3455, 13365])).
% 2.44/2.67 tff(13659,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.67 tff(13660,plain,
% 2.44/2.67 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[13659, 13406, 13571, 13650])).
% 2.44/2.67 tff(13661,plain,
% 2.44/2.67 (r(s(s(z)), s(s(s(s(z)))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[4510, 13660])).
% 2.44/2.67 tff(13662,plain,
% 2.44/2.67 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.44/2.67 inference(rewrite,[status(thm)],[])).
% 2.44/2.67 tff(13663,plain,
% 2.44/2.67 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z))))) <=> ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.44/2.67 inference(rewrite,[status(thm)],[])).
% 2.44/2.67 tff(13664,plain,
% 2.44/2.67 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[13663])).
% 2.44/2.67 tff(13665,plain,
% 2.44/2.67 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.44/2.68 inference(transitivity,[status(thm)],[13664, 13662])).
% 2.44/2.68 tff(13666,plain,
% 2.44/2.68 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.44/2.68 inference(quant_inst,[status(thm)],[])).
% 2.44/2.68 tff(13667,plain,
% 2.44/2.68 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[13666, 13665])).
% 2.44/2.68 tff(13668,plain,
% 2.44/2.68 ($false),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[13667, 124, 13661, 13607, 13563])).
% 2.44/2.68 tff(13669,plain,((~(elem!1 = s(z))) | (~b(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), s(elem!1))) | b(elem!1, z) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.44/2.68 tff(13670,plain,
% 2.44/2.68 (~(elem!1 = s(z))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[13669, 13561, 13280, 2, 6])).
% 2.44/2.68 tff(13671,plain,
% 2.44/2.68 (r(elem!1, s(z))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[97, 13670])).
% 2.44/2.68 tff(13672,plain,
% 2.44/2.68 (~(s(z) = elem!1)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[89, 13670])).
% 2.44/2.68 tff(13673,plain,
% 2.44/2.68 (~r(s(z), s(s(s(z))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[9853, 9, 2, 5, 6])).
% 2.44/2.68 tff(13674,plain,
% 2.44/2.68 (b(s(z), s(s(s(z))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[3302, 13673])).
% 2.44/2.68 tff(13675,plain,
% 2.44/2.68 (b(s(z), elem!1)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[13536, 13674, 2, 6, 9, 5])).
% 2.44/2.68 tff(13676,plain,
% 2.44/2.68 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[7520, 13675, 13280, 10425, 13281, 13671])).
% 2.44/2.68 tff(13677,plain,
% 2.44/2.68 (~r(s(s(s(z))), elem!1)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[1481, 114, 13671])).
% 2.44/2.68 tff(13678,plain,
% 2.44/2.68 (b(s(s(s(z))), elem!1)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[1489, 13677, 13281])).
% 2.44/2.68 tff(13679,plain,
% 2.44/2.68 (~b(s(s(s(z))), z)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[2939, 13675, 13280, 13674, 13678])).
% 2.44/2.68 tff(13680,plain,
% 2.44/2.68 (r(s(s(s(z))), z)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[2197, 13679])).
% 2.44/2.68 tff(13681,plain,
% 2.44/2.68 (~r(s(z), z)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[211, 13680, 114])).
% 2.44/2.68 tff(13682,plain,
% 2.44/2.68 (b(s(z), z)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[221, 13681])).
% 2.44/2.68 tff(13683,plain,
% 2.44/2.68 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[7480, 13682, 10425, 13671])).
% 2.44/2.68 tff(13684,plain,
% 2.44/2.68 (s(s(s(s(s(s(z)))))) = elem!1),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[1144, 13683, 13676])).
% 2.44/2.68 tff(13685,plain,
% 2.44/2.68 (elem!1 = s(s(s(s(s(s(z))))))),
% 2.44/2.68 inference(symmetry,[status(thm)],[13684])).
% 2.44/2.68 tff(13686,plain,
% 2.44/2.68 (~(s(elem!1) = elem!1)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[9225, 13676, 10425, 114, 2, 13671])).
% 2.44/2.68 tff(13687,plain,
% 2.44/2.68 (~(s(s(elem!1)) = s(elem!1))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[195, 13686])).
% 2.44/2.68 tff(13688,plain,
% 2.44/2.68 (~(s(elem!1) = s(s(elem!1)))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[4689, 13687])).
% 2.44/2.68 tff(13689,plain,
% 2.44/2.68 (~(s(s(elem!1)) = elem!1)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[4284, 13684])).
% 2.44/2.68 tff(13690,plain,
% 2.44/2.68 (b(s(elem!1), elem!1)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[9534, 13682, 10425, 13675, 13671, 13303, 114, 2, 13281, 13280])).
% 2.44/2.68 tff(13691,plain,
% 2.44/2.68 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[5403, 13684])).
% 2.44/2.68 tff(13692,plain,
% 2.44/2.68 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[143, 13689])).
% 2.44/2.68 tff(13693,plain,
% 2.44/2.68 (b(s(s(elem!1)), elem!1)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[47, 13689, 6])).
% 2.44/2.68 tff(13694,plain,
% 2.44/2.68 (r(s(elem!1), elem!1)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[13306, 13689, 2, 6])).
% 2.44/2.68 tff(13695,plain,
% 2.44/2.68 (~r(s(elem!1), s(z))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[2960, 13694, 13671])).
% 2.44/2.68 tff(13696,plain,
% 2.44/2.68 (b(s(elem!1), s(z))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[2964, 13695, 13303])).
% 2.44/2.68 tff(13697,plain,
% 2.44/2.68 (r(elem!1, s(s(elem!1)))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[8912, 13696, 13690, 13675, 6, 13689])).
% 2.44/2.68 tff(13698,plain,
% 2.44/2.68 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[1325, 13697, 13694, 13693, 10425, 13692])).
% 2.44/2.68 tff(13699,plain,
% 2.44/2.68 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[610, 13698, 13691])).
% 2.44/2.68 tff(13700,plain,
% 2.44/2.68 (b(s(s(s(elem!1))), s(elem!1))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[6608, 13699, 13302, 13690, 13689])).
% 2.44/2.68 tff(13701,plain,
% 2.44/2.68 (~(s(s(s(elem!1))) = elem!1)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[6947, 13699, 13690, 13302, 13689])).
% 2.44/2.68 tff(13702,plain,
% 2.44/2.68 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[152, 13692])).
% 2.44/2.68 tff(13703,plain,
% 2.44/2.68 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[3437, 13702])).
% 2.44/2.68 tff(13704,plain,
% 2.44/2.68 (~(elem!1 = s(s(s(elem!1))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[1641, 13701])).
% 2.44/2.68 tff(13705,plain,
% 2.44/2.68 (~(elem!1 = s(elem!1))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[364, 13686])).
% 2.44/2.68 tff(13706,plain,
% 2.44/2.68 (~r(elem!1, s(elem!1))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[1238, 13697, 13561])).
% 2.44/2.68 tff(13707,plain,
% 2.44/2.68 (b(elem!1, s(elem!1))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[372, 13706, 13705])).
% 2.44/2.68 tff(13708,plain,
% 2.44/2.68 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[1284, 13692])).
% 2.44/2.68 tff(13709,plain,
% 2.44/2.68 (inj_0(s(elem!1)) = inj_0(s(s(s(s(elem!1)))))),
% 2.44/2.68 inference(symmetry,[status(thm)],[6108])).
% 2.44/2.68 tff(13710,plain,
% 2.44/2.68 (elem!1 = s(s(s(elem!1)))),
% 2.44/2.68 inference(transitivity,[status(thm)],[1651, 13709, 1280])).
% 2.44/2.68 tff(13711,plain,
% 2.44/2.68 ($false),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[1653, 13710])).
% 2.44/2.68 tff(13712,plain,((~(s(s(s(s(elem!1)))) = s(elem!1))) | (elem!1 = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.68 tff(13713,plain,
% 2.44/2.68 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[13712, 13704])).
% 2.44/2.68 tff(13714,plain,
% 2.44/2.68 (s(s(s(s(elem!1)))) = elem!1),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[8887, 13713, 13690, 13693, 13708, 13707, 13704, 13703, 10425, 13701, 13700, 10451, 13688])).
% 2.44/2.68 tff(13715,plain,
% 2.44/2.68 (s(s(s(s(elem!1)))) = s(s(s(s(s(s(z))))))),
% 2.44/2.68 inference(transitivity,[status(thm)],[13714, 13685])).
% 2.44/2.68 tff(13716,plain,
% 2.44/2.68 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(s(s(z)))))))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[13715])).
% 2.44/2.68 tff(13717,plain,
% 2.44/2.68 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(s(s(elem!1)))))),
% 2.44/2.68 inference(symmetry,[status(thm)],[13716])).
% 2.44/2.68 tff(13718,plain,
% 2.44/2.68 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 2.44/2.68 inference(transitivity,[status(thm)],[2823, 13717, 1280])).
% 2.44/2.68 tff(13719,plain,
% 2.44/2.68 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(elem!1))))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[13718])).
% 2.44/2.68 tff(13720,plain,
% 2.44/2.68 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.44/2.68 inference(transitivity,[status(thm)],[497, 13719, 139])).
% 2.44/2.68 tff(13721,plain,
% 2.44/2.68 (inj_0(s(s(s(s(z))))) = inj_0(s(s(elem!1)))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[13720])).
% 2.44/2.68 tff(13722,plain,
% 2.44/2.68 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(z)))))),
% 2.44/2.68 inference(symmetry,[status(thm)],[13721])).
% 2.44/2.68 tff(13723,plain,
% 2.44/2.68 (s(elem!1) = s(s(s(z)))),
% 2.44/2.68 inference(transitivity,[status(thm)],[67, 13722, 320])).
% 2.44/2.68 tff(13724,plain,
% 2.44/2.68 (~(s(elem!1) = s(s(s(z))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[7863, 13694, 13677])).
% 2.44/2.68 tff(13725,plain,
% 2.44/2.68 ($false),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[13724, 13723])).
% 2.44/2.68 tff(13726,plain,(b(s(s(s(z))), s(z)) | r(s(s(elem!1)), elem!1) | b(elem!1, z) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.68 tff(13727,plain,
% 2.44/2.68 (b(s(s(s(z))), s(z))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[13726, 6, 2, 5])).
% 2.44/2.68 tff(13728,plain,
% 2.44/2.68 (~b(s(z), z)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[13505, 13727, 13671, 13280, 2, 6, 13672])).
% 2.44/2.68 tff(13729,plain,
% 2.44/2.68 (r(s(z), z)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[221, 13728])).
% 2.44/2.68 tff(13730,plain,
% 2.44/2.68 (~r(s(z), elem!1)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[12117, 13729, 10425])).
% 2.44/2.68 tff(13731,plain,
% 2.44/2.68 (b(s(z), elem!1)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[13156, 13730, 13672])).
% 2.44/2.68 tff(13732,plain,
% 2.44/2.68 (~r(s(s(s(z))), elem!1)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[7492, 13731, 13280, 10425, 13671])).
% 2.44/2.68 tff(13733,plain,
% 2.44/2.68 (b(s(s(s(z))), elem!1)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[1489, 13732, 13281])).
% 2.44/2.68 tff(13734,plain,
% 2.44/2.68 ($false),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[9088, 306, 13727, 13731, 13733, 13280])).
% 2.44/2.68 tff(13735,plain,(r(s(s(elem!1)), elem!1) | b(elem!1, z) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.68 tff(13736,plain,
% 2.44/2.68 (r(s(s(elem!1)), elem!1)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[13735, 2, 5])).
% 2.44/2.68 tff(13737,plain,
% 2.44/2.68 (r(s(s(elem!1)), z)),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[13736, 10485])).
% 2.44/2.68 tff(13738,plain,
% 2.44/2.68 (r(s(s(z)), elem!1)),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[13737, 13294])).
% 2.44/2.68 tff(13739,plain,
% 2.44/2.68 (~r(s(s(z)), s(z))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[2484, 13738, 13291])).
% 2.44/2.68 tff(13740,plain,
% 2.44/2.68 (b(s(s(z)), s(z))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[2476, 13739])).
% 2.44/2.68 tff(13741,plain,
% 2.44/2.68 (r(s(s(z)), z)),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[13737, 10484])).
% 2.44/2.68 tff(13742,plain,
% 2.44/2.68 (b(z, s(s(s(z))))),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[13280, 5011])).
% 2.44/2.68 tff(13743,plain,
% 2.44/2.68 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), z)),
% 2.44/2.68 inference(monotonicity,[status(thm)],[1620])).
% 2.44/2.68 tff(13744,plain,
% 2.44/2.68 ((~r(s(s(s(z))), elem!1)) <=> (~r(s(s(s(z))), z))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[13743])).
% 2.44/2.68 tff(13745,plain,
% 2.44/2.68 (~r(s(s(s(z))), elem!1)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[1481, 114, 359])).
% 2.44/2.68 tff(13746,plain,
% 2.44/2.68 (~r(s(s(s(z))), z)),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[13745, 13744])).
% 2.44/2.68 tff(13747,plain,
% 2.44/2.68 (b(z, elem!1) <=> b(z, z)),
% 2.44/2.68 inference(monotonicity,[status(thm)],[1620])).
% 2.44/2.68 tff(13748,plain,
% 2.44/2.68 (b(z, z) <=> b(z, elem!1)),
% 2.44/2.68 inference(symmetry,[status(thm)],[13747])).
% 2.44/2.68 tff(13749,plain,
% 2.44/2.68 ((~b(z, z)) <=> (~b(z, elem!1))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[13748])).
% 2.44/2.68 tff(13750,plain,
% 2.44/2.68 ((~![X: $i] : (~b(X, X))) | (~b(z, z))),
% 2.44/2.68 inference(quant_inst,[status(thm)],[])).
% 2.44/2.68 tff(13751,plain,
% 2.44/2.68 (~b(z, z)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[13750, 1466])).
% 2.44/2.68 tff(13752,plain,
% 2.44/2.68 (~b(z, elem!1)),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[13751, 13749])).
% 2.44/2.68 tff(13753,plain,
% 2.44/2.68 (~r(s(z), s(s(s(z))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[9791, 13745, 2, 13752, 9])).
% 2.44/2.68 tff(13754,plain,
% 2.44/2.68 (b(s(z), s(s(s(z))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[3302, 13753])).
% 2.44/2.68 tff(13755,plain,
% 2.44/2.68 (~r(s(z), z)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[2182, 114, 2, 4365, 359])).
% 2.44/2.68 tff(13756,plain,
% 2.44/2.68 (b(s(z), z)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[221, 13755])).
% 2.44/2.68 tff(13757,plain,
% 2.44/2.68 (~b(s(s(s(z))), z)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[4569, 13756, 13754, 859])).
% 2.44/2.68 tff(13758,plain,
% 2.44/2.68 (r(s(s(s(z))), z)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[2197, 13757])).
% 2.44/2.68 tff(13759,plain,
% 2.44/2.68 ($false),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[13758, 13746])).
% 2.44/2.68 tff(13760,plain,(b(s(s(s(z))), s(z)) | (~(elem!1 = z)) | (~b(z, s(s(s(z))))) | b(elem!1, z) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.68 tff(13761,plain,
% 2.44/2.68 (b(s(s(s(z))), s(z))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[13760, 3063, 13742, 2, 13291])).
% 2.44/2.68 tff(13762,plain,
% 2.44/2.68 (b(s(s(s(elem!1))), s(elem!1))),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[2284, 10333])).
% 2.44/2.68 tff(13763,plain,
% 2.44/2.68 (b(elem!1, s(s(s(elem!1))))),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[859, 10326])).
% 2.44/2.68 tff(13764,plain,
% 2.44/2.68 (b(s(elem!1), elem!1)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[10472, 247, 3332])).
% 2.44/2.68 tff(13765,plain,
% 2.44/2.68 (~b(s(s(s(elem!1))), elem!1)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[6138, 13764, 13763, 13762])).
% 2.44/2.68 tff(13766,plain,
% 2.44/2.68 (r(s(s(s(elem!1))), elem!1)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[1636, 13765, 4365])).
% 2.44/2.68 tff(13767,plain,
% 2.44/2.68 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[7010, 13766, 1730])).
% 2.44/2.68 tff(13768,plain,
% 2.44/2.68 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[891, 13767, 4354])).
% 2.44/2.68 tff(13769,plain,
% 2.44/2.68 (b(s(s(z)), s(s(s(z))))),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[13768, 4355])).
% 2.44/2.68 tff(13770,plain,
% 2.44/2.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 2.44/2.68 inference(rewrite,[status(thm)],[])).
% 2.44/2.68 tff(13771,plain,
% 2.44/2.68 (((~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 2.44/2.68 inference(rewrite,[status(thm)],[])).
% 2.44/2.68 tff(13772,plain,
% 2.44/2.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z)))))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[13771])).
% 2.44/2.68 tff(13773,plain,
% 2.44/2.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 2.44/2.68 inference(transitivity,[status(thm)],[13772, 13770])).
% 2.44/2.68 tff(13774,plain,
% 2.44/2.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.44/2.68 inference(quant_inst,[status(thm)],[])).
% 2.44/2.68 tff(13775,plain,
% 2.44/2.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z)))),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[13774, 13773])).
% 2.44/2.68 tff(13776,plain,
% 2.44/2.68 ($false),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[13775, 306, 2284, 859, 247, 13769, 3451])).
% 2.44/2.68 tff(13777,plain,((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~(elem!1 = z)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.68 tff(13778,plain,
% 2.44/2.68 (~b(s(z), z)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[13777, 13761, 13742, 13740, 3063, 13736])).
% 2.44/2.68 tff(13779,plain,
% 2.44/2.68 (r(s(z), z)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[221, 13778])).
% 2.44/2.68 tff(13780,plain,
% 2.44/2.68 (~r(s(z), s(s(z)))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[8168, 124, 13779, 13741])).
% 2.44/2.68 tff(13781,plain,
% 2.44/2.68 (b(s(z), s(s(z)))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[4434, 13780])).
% 2.44/2.68 tff(13782,plain,
% 2.44/2.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.44/2.68 inference(rewrite,[status(thm)],[])).
% 2.44/2.68 tff(13783,plain,
% 2.44/2.68 (((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.44/2.68 inference(rewrite,[status(thm)],[])).
% 2.44/2.68 tff(13784,plain,
% 2.44/2.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z))))))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[13783])).
% 2.44/2.68 tff(13785,plain,
% 2.44/2.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.44/2.68 inference(transitivity,[status(thm)],[13784, 13782])).
% 2.44/2.68 tff(13786,plain,
% 2.44/2.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.44/2.68 inference(quant_inst,[status(thm)],[])).
% 2.44/2.68 tff(13787,plain,
% 2.44/2.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z))))),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[13786, 13785])).
% 2.44/2.68 tff(13788,plain,
% 2.44/2.68 (~b(s(s(s(z))), s(s(z)))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[13787, 306, 13761, 13781, 13740])).
% 2.44/2.68 tff(13789,plain,
% 2.44/2.68 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[13788, 13285])).
% 2.44/2.68 tff(13790,plain,
% 2.44/2.68 (~(s(elem!1) = elem!1)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[2698, 3064])).
% 2.44/2.68 tff(13791,plain,
% 2.44/2.68 (~(s(s(elem!1)) = s(elem!1))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[195, 13790])).
% 2.44/2.68 tff(13792,plain,
% 2.44/2.68 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(z))), s(z))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[13282, 3069])).
% 2.44/2.68 tff(13793,plain,
% 2.44/2.68 (b(s(s(s(z))), s(z)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 2.44/2.68 inference(symmetry,[status(thm)],[13792])).
% 2.44/2.68 tff(13794,plain,
% 2.44/2.68 (b(s(s(s(elem!1))), s(elem!1))),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[13761, 13793])).
% 2.44/2.68 tff(13795,plain,
% 2.44/2.68 (~(elem!1 = s(elem!1))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[364, 13790])).
% 2.44/2.68 tff(13796,plain,
% 2.44/2.68 (b(elem!1, s(elem!1)) <=> b(z, s(elem!1))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[3063])).
% 2.44/2.68 tff(13797,plain,
% 2.44/2.68 (b(z, s(elem!1)) <=> b(elem!1, s(elem!1))),
% 2.44/2.68 inference(symmetry,[status(thm)],[13796])).
% 2.44/2.68 tff(13798,plain,
% 2.44/2.68 (b(z, s(elem!1)) <=> b(z, s(z))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[3069])).
% 2.44/2.68 tff(13799,plain,
% 2.44/2.68 (b(z, s(z)) <=> b(z, s(elem!1))),
% 2.44/2.68 inference(symmetry,[status(thm)],[13798])).
% 2.44/2.68 tff(13800,plain,
% 2.44/2.68 (b(z, s(z)) <=> b(elem!1, s(elem!1))),
% 2.44/2.68 inference(transitivity,[status(thm)],[13799, 13797])).
% 2.44/2.68 tff(13801,plain,
% 2.44/2.68 ((~b(z, s(z))) <=> (~b(elem!1, s(elem!1)))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[13800])).
% 2.44/2.68 tff(13802,plain,
% 2.44/2.68 (b(elem!1, s(z)) <=> b(z, s(z))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[3063])).
% 2.44/2.68 tff(13803,plain,
% 2.44/2.68 ((~b(elem!1, s(z))) <=> (~b(z, s(z)))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[13802])).
% 2.44/2.68 tff(13804,plain,
% 2.44/2.68 (~b(z, s(z))),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[5, 13803])).
% 2.44/2.68 tff(13805,plain,
% 2.44/2.68 (~b(elem!1, s(elem!1))),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[13804, 13801])).
% 2.44/2.68 tff(13806,plain,
% 2.44/2.68 (r(elem!1, s(elem!1))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[372, 13805, 13795])).
% 2.44/2.68 tff(13807,plain,
% 2.44/2.68 (~r(s(s(elem!1)), s(elem!1))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[5630, 13806, 13736])).
% 2.44/2.68 tff(13808,plain,
% 2.44/2.68 (b(s(s(elem!1)), s(elem!1))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[994, 13807, 13791])).
% 2.44/2.68 tff(13809,plain,
% 2.44/2.68 (b(elem!1, s(s(s(elem!1)))) <=> b(z, s(s(s(elem!1))))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[3063])).
% 2.44/2.68 tff(13810,plain,
% 2.44/2.68 (b(z, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 2.44/2.68 inference(symmetry,[status(thm)],[13809])).
% 2.44/2.68 tff(13811,plain,
% 2.44/2.68 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(s(z))))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[13282])).
% 2.44/2.68 tff(13812,plain,
% 2.44/2.68 (b(z, s(s(s(z)))) <=> b(z, s(s(s(elem!1))))),
% 2.44/2.68 inference(symmetry,[status(thm)],[13811])).
% 2.44/2.68 tff(13813,plain,
% 2.44/2.68 (b(z, s(s(s(z)))) <=> b(elem!1, s(s(s(elem!1))))),
% 2.44/2.68 inference(transitivity,[status(thm)],[13812, 13810])).
% 2.44/2.68 tff(13814,plain,
% 2.44/2.68 (b(elem!1, s(s(s(elem!1))))),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[13742, 13813])).
% 2.44/2.68 tff(13815,plain,
% 2.44/2.68 (b(s(elem!1), z) <=> b(s(elem!1), elem!1)),
% 2.44/2.68 inference(symmetry,[status(thm)],[3079])).
% 2.44/2.68 tff(13816,plain,
% 2.44/2.68 (b(s(z), z) <=> b(s(elem!1), z)),
% 2.44/2.68 inference(symmetry,[status(thm)],[3076])).
% 2.44/2.68 tff(13817,plain,
% 2.44/2.68 (b(s(z), z) <=> b(s(elem!1), elem!1)),
% 2.44/2.68 inference(transitivity,[status(thm)],[13816, 13815])).
% 2.44/2.68 tff(13818,plain,
% 2.44/2.68 ((~b(s(z), z)) <=> (~b(s(elem!1), elem!1))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[13817])).
% 2.44/2.68 tff(13819,plain,
% 2.44/2.68 (~b(s(elem!1), elem!1)),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[13778, 13818])).
% 2.44/2.68 tff(13820,plain,
% 2.44/2.68 (r(s(elem!1), elem!1)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[813, 13819, 13790])).
% 2.44/2.68 tff(13821,plain,
% 2.44/2.68 (~b(s(s(elem!1)), elem!1)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[3280, 13820, 3064, 13814, 13808, 13794, 3066, 13791])).
% 2.44/2.68 tff(13822,plain,
% 2.44/2.68 (b(s(elem!1), s(s(elem!1))) <=> b(s(z), s(s(elem!1)))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[3069])).
% 2.44/2.68 tff(13823,plain,
% 2.44/2.68 (b(s(z), s(s(elem!1))) <=> b(s(elem!1), s(s(elem!1)))),
% 2.44/2.68 inference(symmetry,[status(thm)],[13822])).
% 2.44/2.68 tff(13824,plain,
% 2.44/2.68 (s(s(z)) = s(s(elem!1))),
% 2.44/2.68 inference(symmetry,[status(thm)],[5311])).
% 2.44/2.68 tff(13825,plain,
% 2.44/2.68 (b(s(z), s(s(z))) <=> b(s(z), s(s(elem!1)))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[13824])).
% 2.44/2.68 tff(13826,plain,
% 2.44/2.68 (b(s(z), s(s(z))) <=> b(s(elem!1), s(s(elem!1)))),
% 2.44/2.68 inference(transitivity,[status(thm)],[13825, 13823])).
% 2.44/2.68 tff(13827,plain,
% 2.44/2.68 (b(s(elem!1), s(s(elem!1)))),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[13781, 13826])).
% 2.44/2.68 tff(13828,plain,
% 2.44/2.68 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[1511, 3064])).
% 2.44/2.68 tff(13829,plain,
% 2.44/2.68 (~(elem!1 = s(s(s(elem!1))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[1518, 13828])).
% 2.44/2.68 tff(13830,plain,
% 2.44/2.68 (~(s(s(s(elem!1))) = elem!1)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[2187, 13829])).
% 2.44/2.68 tff(13831,plain,
% 2.44/2.68 (~r(s(s(s(elem!1))), elem!1)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[12869, 13789, 3066, 13821])).
% 2.44/2.68 tff(13832,plain,
% 2.44/2.68 (b(s(s(s(elem!1))), elem!1)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[1636, 13831, 13830])).
% 2.44/2.68 tff(13833,plain,
% 2.44/2.68 (~b(elem!1, s(s(elem!1)))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[1803, 13832, 13736, 3064, 13814, 13827, 13820, 13808])).
% 2.44/2.68 tff(13834,plain,
% 2.44/2.68 (~b(z, s(s(elem!1)))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[2757, 13833, 3064])).
% 2.44/2.68 tff(13835,plain,
% 2.44/2.68 (s(s(elem!1)) = elem!1),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[143, 136])).
% 2.44/2.68 tff(13836,plain,
% 2.44/2.68 (~b(z, elem!1)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[8180, 13835, 8174])).
% 2.44/2.68 tff(13837,plain,
% 2.44/2.68 (~(s(elem!1) = s(z))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[2724, 136])).
% 2.44/2.68 tff(13838,plain,
% 2.44/2.68 (~(z = elem!1)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[2251, 13837])).
% 2.44/2.68 tff(13839,plain,
% 2.44/2.68 ($false),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[835, 13838, 13836, 7])).
% 2.44/2.68 tff(13840,plain,((~(s(s(s(elem!1))) = s(elem!1))) | r(z, elem!1) | b(z, s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.68 tff(13841,plain,
% 2.44/2.68 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[13840, 8174, 7])).
% 2.44/2.68 tff(13842,plain,
% 2.44/2.68 (~(elem!1 = s(s(elem!1)))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[1168, 13841])).
% 2.44/2.68 tff(13843,plain,
% 2.44/2.68 (~(s(s(elem!1)) = elem!1)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[1174, 13842])).
% 2.44/2.68 tff(13844,plain,
% 2.44/2.68 (~(s(elem!1) = elem!1)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[180, 13843])).
% 2.44/2.68 tff(13845,plain,
% 2.44/2.68 (r(s(s(elem!1)), elem!1)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[47, 13843, 6481])).
% 2.44/2.68 tff(13846,plain,
% 2.44/2.68 (~r(s(s(s(elem!1))), elem!1)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[12869, 13841, 6481, 8175])).
% 2.44/2.68 tff(13847,plain,
% 2.44/2.68 (r(s(s(elem!1)), s(elem!1))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[8402, 13846, 8175, 807, 2754, 6481, 8174, 3062, 7])).
% 2.44/2.68 tff(13848,plain,
% 2.44/2.68 (~r(s(elem!1), elem!1)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[7985, 13847, 13845])).
% 2.44/2.68 tff(13849,plain,
% 2.44/2.68 ($false),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[813, 13848, 13844, 807])).
% 2.44/2.68 tff(13850,plain,(b(z, s(s(elem!1))) | b(s(elem!1), elem!1) | b(s(s(elem!1)), elem!1) | b(s(s(s(elem!1))), s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, z) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.44/2.68 tff(13851,plain,
% 2.44/2.68 ($false),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[13850, 13834, 13833, 7, 13819, 13821, 13789, 3062])).
% 2.44/2.68 tff(13852,plain,(r(elem!1, z) | r(z, elem!1) | b(elem!1, z) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.68 tff(13853,plain,
% 2.44/2.68 (r(elem!1, z)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[13852, 7, 2, 5])).
% 2.44/2.68 tff(13854,plain,
% 2.44/2.68 (~r(s(s(elem!1)), z)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[7786, 13853, 13736])).
% 2.44/2.68 tff(13855,plain,
% 2.44/2.68 (b(s(s(elem!1)), z)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[476, 13854])).
% 2.44/2.68 tff(13856,plain,
% 2.44/2.68 (~(z = elem!1)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[9879, 13853])).
% 2.44/2.68 tff(13857,plain,
% 2.44/2.68 (b(z, elem!1)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[835, 13856, 7])).
% 2.44/2.68 tff(13858,plain,
% 2.44/2.68 (r(elem!1, s(z))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[97, 10058])).
% 2.44/2.68 tff(13859,plain,
% 2.44/2.68 (~r(s(s(elem!1)), s(z))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[9725, 13858, 13736])).
% 2.44/2.68 tff(13860,plain,
% 2.44/2.68 (b(s(s(elem!1)), s(z))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[3989, 13859])).
% 2.44/2.68 tff(13861,plain,
% 2.44/2.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)))),
% 2.44/2.68 inference(rewrite,[status(thm)],[])).
% 2.44/2.68 tff(13862,plain,
% 2.44/2.68 (((~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)))),
% 2.44/2.68 inference(rewrite,[status(thm)],[])).
% 2.44/2.68 tff(13863,plain,
% 2.44/2.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z))))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[13862])).
% 2.44/2.68 tff(13864,plain,
% 2.44/2.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)))),
% 2.44/2.69 inference(transitivity,[status(thm)],[13863, 13861])).
% 2.44/2.69 tff(13865,plain,
% 2.44/2.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))),
% 2.44/2.69 inference(quant_inst,[status(thm)],[])).
% 2.44/2.69 tff(13866,plain,
% 2.44/2.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z))),
% 2.44/2.69 inference(modus_ponens,[status(thm)],[13865, 13864])).
% 2.44/2.69 tff(13867,plain,
% 2.44/2.69 ($false),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[13866, 306, 838, 3968, 13860, 247, 13280])).
% 2.44/2.69 tff(13868,plain,((~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | b(elem!1, s(z)) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 2.44/2.69 tff(13869,plain,
% 2.44/2.69 (~b(s(z), z)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[13868, 13857, 13855, 5, 2])).
% 2.44/2.69 tff(13870,plain,
% 2.44/2.69 (r(s(z), z)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[221, 13869])).
% 2.44/2.69 tff(13871,plain,
% 2.44/2.69 (~(s(elem!1) = elem!1)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[2654, 13870, 13853, 5])).
% 2.44/2.69 tff(13872,plain,
% 2.44/2.69 (~(elem!1 = s(elem!1))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[364, 13871])).
% 2.44/2.69 tff(13873,plain,
% 2.44/2.69 (~r(elem!1, s(z))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[2180, 124, 13853, 13870])).
% 2.44/2.69 tff(13874,plain,
% 2.44/2.69 (elem!1 = s(z)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[97, 13873])).
% 2.44/2.69 tff(13875,plain,
% 2.44/2.69 ((s(s(elem!1)) = elem!1) <=> (s(s(elem!1)) = s(z))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[13874])).
% 2.44/2.69 tff(13876,plain,
% 2.44/2.69 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 2.44/2.69 inference(symmetry,[status(thm)],[13875])).
% 2.44/2.69 tff(13877,plain,
% 2.44/2.69 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = elem!1))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[13876])).
% 2.44/2.69 tff(13878,plain,
% 2.44/2.69 (~(s(s(elem!1)) = elem!1)),
% 2.44/2.69 inference(modus_ponens,[status(thm)],[80, 13877])).
% 2.44/2.69 tff(13879,plain,
% 2.44/2.69 (~(s(s(s(s(elem!1)))) = elem!1)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[6321, 13874])).
% 2.44/2.69 tff(13880,plain,
% 2.44/2.69 (s(elem!1) = s(s(z))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[13874])).
% 2.44/2.69 tff(13881,plain,
% 2.44/2.69 (s(s(elem!1)) = s(s(s(z)))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[13880])).
% 2.44/2.69 tff(13882,plain,
% 2.44/2.69 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[13881])).
% 2.44/2.69 tff(13883,plain,
% 2.44/2.69 (r(s(s(s(elem!1))), z) <=> r(s(s(s(s(z)))), z)),
% 2.44/2.69 inference(monotonicity,[status(thm)],[13882])).
% 2.44/2.69 tff(13884,plain,
% 2.44/2.69 (r(s(s(s(s(z)))), z) <=> r(s(s(s(elem!1))), z)),
% 2.44/2.69 inference(symmetry,[status(thm)],[13883])).
% 2.44/2.69 tff(13885,plain,
% 2.44/2.69 (r(s(s(elem!1)), s(z)) <=> r(s(s(s(z))), s(z))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[13881])).
% 2.44/2.69 tff(13886,plain,
% 2.44/2.69 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), s(z))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[13874])).
% 2.44/2.69 tff(13887,plain,
% 2.44/2.69 (r(s(s(elem!1)), s(z))),
% 2.44/2.69 inference(modus_ponens,[status(thm)],[13736, 13886])).
% 2.44/2.69 tff(13888,plain,
% 2.44/2.69 (r(s(s(s(z))), s(z))),
% 2.44/2.69 inference(modus_ponens,[status(thm)],[13887, 13885])).
% 2.44/2.69 tff(13889,plain,
% 2.44/2.69 (s(z) = elem!1),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[3096, 13874])).
% 2.44/2.69 tff(13890,plain,
% 2.44/2.69 (b(s(z), s(s(s(z))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[9887, 13889, 13280])).
% 2.44/2.69 tff(13891,plain,
% 2.44/2.69 (b(z, s(z))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[2281, 13857, 5, 13853])).
% 2.44/2.69 tff(13892,plain,
% 2.44/2.69 (b(s(s(elem!1)), z) <=> b(s(s(s(z))), z)),
% 2.44/2.69 inference(monotonicity,[status(thm)],[13881])).
% 2.44/2.69 tff(13893,plain,
% 2.44/2.69 (b(s(s(s(z))), z)),
% 2.44/2.69 inference(modus_ponens,[status(thm)],[13855, 13892])).
% 2.44/2.69 tff(13894,plain,
% 2.44/2.69 (~b(s(s(s(s(z)))), z)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[12019, 13893, 13891, 13890, 13888])).
% 2.44/2.69 tff(13895,plain,
% 2.44/2.69 (r(s(s(s(s(z)))), z)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[695, 13894])).
% 2.44/2.69 tff(13896,plain,
% 2.44/2.69 (r(s(s(s(elem!1))), z)),
% 2.44/2.69 inference(modus_ponens,[status(thm)],[13895, 13884])).
% 2.44/2.69 tff(13897,plain,
% 2.44/2.69 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(z)))), s(z))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[13882, 13874])).
% 2.44/2.69 tff(13898,plain,
% 2.44/2.69 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(elem!1))), elem!1)),
% 2.44/2.69 inference(symmetry,[status(thm)],[13897])).
% 2.44/2.69 tff(13899,plain,
% 2.44/2.69 (~r(s(s(s(s(z)))), s(z))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[10160, 13895, 13870])).
% 2.44/2.69 tff(13900,plain,
% 2.44/2.69 (b(s(s(s(s(z)))), s(z))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[4490, 13899])).
% 2.44/2.69 tff(13901,plain,
% 2.44/2.69 (b(s(s(s(elem!1))), elem!1)),
% 2.44/2.69 inference(modus_ponens,[status(thm)],[13900, 13898])).
% 2.44/2.69 tff(13902,plain,
% 2.44/2.69 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(s(z))) = s(s(s(s(z)))))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[13881, 13882])).
% 2.44/2.69 tff(13903,plain,
% 2.44/2.69 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 2.44/2.69 inference(transitivity,[status(thm)],[13902, 339])).
% 2.44/2.69 tff(13904,plain,
% 2.44/2.69 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 2.44/2.69 inference(symmetry,[status(thm)],[13903])).
% 2.44/2.69 tff(13905,plain,
% 2.44/2.69 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[13904])).
% 2.44/2.69 tff(13906,plain,
% 2.44/2.69 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.44/2.69 inference(modus_ponens,[status(thm)],[4470, 13905])).
% 2.44/2.69 tff(13907,plain,
% 2.44/2.69 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[3437, 13906])).
% 2.44/2.69 tff(13908,plain,
% 2.44/2.69 ((elem!1 = s(s(s(elem!1)))) <=> (s(z) = s(s(s(elem!1))))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[13874])).
% 2.44/2.69 tff(13909,plain,
% 2.44/2.69 ((s(z) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 2.44/2.69 inference(symmetry,[status(thm)],[13908])).
% 2.44/2.69 tff(13910,plain,
% 2.44/2.69 ((~(s(z) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[13909])).
% 2.44/2.69 tff(13911,plain,
% 2.44/2.69 (~(elem!1 = s(s(s(elem!1))))),
% 2.44/2.69 inference(modus_ponens,[status(thm)],[645, 13910])).
% 2.44/2.69 tff(13912,plain,
% 2.44/2.69 (~r(elem!1, s(s(s(elem!1))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[851, 13896, 13853])).
% 2.44/2.69 tff(13913,plain,
% 2.44/2.69 (b(elem!1, s(s(s(elem!1))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[3284, 13912, 13911])).
% 2.44/2.69 tff(13914,plain,
% 2.44/2.69 (~b(s(s(s(s(elem!1)))), elem!1)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[10780, 13913, 13857, 13907, 13901, 13896])).
% 2.44/2.69 tff(13915,plain,
% 2.44/2.69 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[1736, 13914, 13879])).
% 2.44/2.69 tff(13916,plain,
% 2.44/2.69 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[13882])).
% 2.44/2.69 tff(13917,plain,
% 2.44/2.69 ((s(s(s(s(elem!1)))) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(s(z)))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[13916, 13880])).
% 2.44/2.69 tff(13918,plain,
% 2.44/2.69 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 2.44/2.69 inference(symmetry,[status(thm)],[13917])).
% 2.44/2.69 tff(13919,plain,
% 2.44/2.69 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(s(s(elem!1)))) = s(elem!1)))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[13918])).
% 2.44/2.69 tff(13920,plain,
% 2.44/2.69 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 2.44/2.69 inference(modus_ponens,[status(thm)],[6464, 13919])).
% 2.44/2.69 tff(13921,plain,
% 2.44/2.69 (~(s(s(elem!1)) = s(elem!1))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[195, 13871])).
% 2.44/2.69 tff(13922,plain,
% 2.44/2.69 (b(elem!1, s(s(elem!1))) <=> b(s(z), s(s(elem!1)))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[13874])).
% 2.44/2.69 tff(13923,plain,
% 2.44/2.69 (b(s(z), s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 2.44/2.69 inference(symmetry,[status(thm)],[13922])).
% 2.44/2.69 tff(13924,plain,
% 2.44/2.69 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(s(z))))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[13881])).
% 2.44/2.69 tff(13925,plain,
% 2.44/2.69 (b(s(z), s(s(s(z)))) <=> b(s(z), s(s(elem!1)))),
% 2.44/2.69 inference(symmetry,[status(thm)],[13924])).
% 2.44/2.69 tff(13926,plain,
% 2.44/2.69 (b(s(z), s(s(s(z)))) <=> b(elem!1, s(s(elem!1)))),
% 2.44/2.69 inference(transitivity,[status(thm)],[13925, 13923])).
% 2.44/2.69 tff(13927,plain,
% 2.44/2.69 (b(elem!1, s(s(elem!1)))),
% 2.44/2.69 inference(modus_ponens,[status(thm)],[13890, 13926])).
% 2.44/2.69 tff(13928,plain,
% 2.44/2.69 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(z)))) = s(s(z)))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[13882, 13880])).
% 2.44/2.69 tff(13929,plain,
% 2.44/2.69 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(z)) = s(s(s(s(z)))))),
% 2.44/2.69 inference(transitivity,[status(thm)],[13928, 1707])).
% 2.44/2.69 tff(13930,plain,
% 2.44/2.69 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 2.44/2.69 inference(symmetry,[status(thm)],[13929])).
% 2.44/2.69 tff(13931,plain,
% 2.44/2.69 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[13930])).
% 2.44/2.69 tff(13932,plain,
% 2.44/2.69 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.44/2.69 inference(modus_ponens,[status(thm)],[1612, 13931])).
% 2.44/2.69 tff(13933,plain,
% 2.44/2.69 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[1284, 13932])).
% 2.44/2.69 tff(13934,plain,
% 2.44/2.69 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[1756, 13914, 13736, 13933, 13927])).
% 2.44/2.69 tff(13935,plain,
% 2.44/2.69 (~r(s(elem!1), elem!1)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[10800, 13934, 13736, 13921, 13920, 13915])).
% 2.44/2.69 tff(13936,plain,
% 2.44/2.69 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[7090, 13935, 13856, 13878])).
% 2.44/2.69 tff(13937,plain,
% 2.44/2.69 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(s(s(z)))))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[13882])).
% 2.44/2.69 tff(13938,plain,
% 2.44/2.69 (b(z, s(s(s(s(z))))) <=> b(z, s(s(s(elem!1))))),
% 2.44/2.69 inference(symmetry,[status(thm)],[13937])).
% 2.44/2.69 tff(13939,plain,
% 2.44/2.69 ((~b(z, s(s(s(s(z)))))) <=> (~b(z, s(s(s(elem!1)))))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[13938])).
% 2.44/2.69 tff(13940,plain,
% 2.44/2.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))),
% 2.44/2.69 inference(rewrite,[status(thm)],[])).
% 2.44/2.69 tff(13941,plain,
% 2.44/2.69 (((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))),
% 2.44/2.69 inference(rewrite,[status(thm)],[])).
% 2.44/2.69 tff(13942,plain,
% 2.44/2.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z))))))))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[13941])).
% 2.44/2.69 tff(13943,plain,
% 2.44/2.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))),
% 2.44/2.69 inference(transitivity,[status(thm)],[13942, 13940])).
% 2.44/2.69 tff(13944,plain,
% 2.44/2.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))),
% 2.44/2.69 inference(quant_inst,[status(thm)],[])).
% 2.44/2.69 tff(13945,plain,
% 2.44/2.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z))))))),
% 2.44/2.69 inference(modus_ponens,[status(thm)],[13944, 13943])).
% 2.44/2.69 tff(13946,plain,
% 2.44/2.69 (~b(z, s(s(s(s(z)))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[13945, 306, 13890, 13893, 13891, 13900])).
% 2.44/2.69 tff(13947,plain,
% 2.44/2.69 (~b(z, s(s(s(elem!1))))),
% 2.44/2.69 inference(modus_ponens,[status(thm)],[13946, 13939])).
% 2.44/2.69 tff(13948,plain,
% 2.44/2.69 (r(z, s(s(s(elem!1))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[585, 13947])).
% 2.44/2.69 tff(13949,plain,
% 2.44/2.69 (~r(z, s(s(elem!1)))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[950, 13948, 13936])).
% 2.44/2.69 tff(13950,plain,
% 2.44/2.69 (b(z, s(s(elem!1)))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[460, 13949])).
% 2.44/2.69 tff(13951,plain,
% 2.44/2.69 (b(s(elem!1), elem!1)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[813, 13935, 13871])).
% 2.44/2.69 tff(13952,plain,
% 2.44/2.69 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[6138, 13951, 13901, 13913])).
% 2.44/2.69 tff(13953,plain,
% 2.44/2.69 (r(s(s(s(elem!1))), s(elem!1))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[664, 13952, 13932])).
% 2.44/2.69 tff(13954,plain,
% 2.44/2.69 (~r(s(s(elem!1)), s(elem!1))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[659, 13953, 13936])).
% 2.44/2.69 tff(13955,plain,
% 2.44/2.69 (b(s(s(elem!1)), s(elem!1))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[994, 13954, 13921])).
% 2.44/2.69 tff(13956,plain,
% 2.44/2.69 (~r(z, s(elem!1))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[5741, 13948, 13953])).
% 2.44/2.69 tff(13957,plain,
% 2.44/2.69 (b(z, s(elem!1))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[275, 13956])).
% 2.44/2.69 tff(13958,plain,
% 2.44/2.69 (~b(elem!1, s(elem!1))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[6476, 13957, 13951, 13955, 13950])).
% 2.44/2.69 tff(13959,plain,
% 2.44/2.69 (r(elem!1, s(elem!1))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[372, 13958, 13872])).
% 2.44/2.69 tff(13960,plain,
% 2.44/2.69 (~b(s(elem!1), z)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[1218, 13957, 13955, 13950])).
% 2.44/2.69 tff(13961,plain,
% 2.44/2.69 (r(s(elem!1), z)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[2380, 13960])).
% 2.44/2.69 tff(13962,plain,
% 2.44/2.69 ($false),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[287, 13961, 13959, 13853])).
% 2.44/2.69 tff(13963,plain,(r(z, elem!1) | b(elem!1, s(z)) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 2.44/2.69 tff(13964,plain,
% 2.44/2.69 (r(z, elem!1)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[13963, 2, 5])).
% 2.44/2.69 tff(13965,plain,
% 2.44/2.69 (~(elem!1 = z)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[10449, 13964])).
% 2.44/2.69 tff(13966,plain,
% 2.44/2.69 (r(elem!1, z)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[174, 13965, 2])).
% 2.44/2.69 tff(13967,plain,
% 2.44/2.69 (~(s(elem!1) = elem!1)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[2654, 204, 13966, 5])).
% 2.44/2.69 tff(13968,plain,
% 2.44/2.69 (~(elem!1 = s(elem!1))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[364, 13967])).
% 2.44/2.69 tff(13969,plain,
% 2.44/2.69 (~r(z, s(s(elem!1)))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[5837, 13964, 13736])).
% 2.44/2.69 tff(13970,plain,
% 2.44/2.69 (b(z, s(s(elem!1)))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[460, 13969])).
% 2.44/2.69 tff(13971,plain,
% 2.44/2.69 (~r(s(s(elem!1)), z)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[7786, 13966, 13736])).
% 2.44/2.69 tff(13972,plain,
% 2.44/2.69 (b(s(s(elem!1)), z)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[476, 13971])).
% 2.44/2.69 tff(13973,plain,
% 2.44/2.69 (~(s(s(elem!1)) = s(elem!1))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[195, 13967])).
% 2.44/2.69 tff(13974,plain,
% 2.44/2.69 (~r(s(elem!1), elem!1)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[10562, 13973, 13736, 13964, 13972, 13970])).
% 2.44/2.69 tff(13975,plain,
% 2.44/2.69 (b(s(elem!1), elem!1)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[813, 13974, 13967])).
% 2.44/2.69 tff(13976,plain,
% 2.44/2.69 (~r(z, s(s(elem!1)))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[5837, 374, 1730])).
% 2.44/2.69 tff(13977,plain,
% 2.44/2.69 (b(z, s(s(elem!1)))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[460, 13976])).
% 2.44/2.69 tff(13978,plain,
% 2.44/2.69 (~r(s(elem!1), elem!1)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[10562, 403, 1730, 374, 7788, 13977])).
% 2.44/2.69 tff(13979,plain,
% 2.44/2.69 (~(elem!1 = z)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[10449, 374])).
% 2.44/2.69 tff(13980,plain,
% 2.44/2.69 (~(z = elem!1)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[1618, 13979])).
% 2.44/2.69 tff(13981,plain,
% 2.44/2.69 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[7090, 11840, 13980, 13978])).
% 2.44/2.69 tff(13982,plain,
% 2.44/2.69 (~r(s(s(s(elem!1))), elem!1)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[7780, 13981, 1730])).
% 2.44/2.69 tff(13983,plain,
% 2.44/2.69 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[7812, 13982, 1730, 246, 816, 366, 5076, 13362])).
% 2.44/2.69 tff(13984,plain,
% 2.44/2.69 (r(s(s(s(elem!1))), s(elem!1))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[664, 13983, 11704])).
% 2.44/2.69 tff(13985,plain,
% 2.44/2.69 (~r(s(s(elem!1)), s(elem!1))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[659, 13984, 13981])).
% 2.44/2.69 tff(13986,plain,
% 2.44/2.69 (b(s(s(elem!1)), s(elem!1))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[994, 13985, 403])).
% 2.44/2.69 tff(13987,plain,
% 2.44/2.69 (r(elem!1, s(elem!1)) <=> r(s(z), s(elem!1))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[10])).
% 2.44/2.69 tff(13988,plain,
% 2.44/2.69 (r(s(z), s(elem!1)) <=> r(elem!1, s(elem!1))),
% 2.44/2.69 inference(symmetry,[status(thm)],[13987])).
% 2.44/2.69 tff(13989,plain,
% 2.44/2.69 (r(s(z), s(elem!1)) <=> r(s(z), s(s(z)))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[14])).
% 2.44/2.69 tff(13990,plain,
% 2.44/2.69 (r(s(z), s(s(z))) <=> r(s(z), s(elem!1))),
% 2.44/2.69 inference(symmetry,[status(thm)],[13989])).
% 2.44/2.69 tff(13991,plain,
% 2.44/2.69 (r(s(z), s(s(z))) <=> r(elem!1, s(elem!1))),
% 2.44/2.69 inference(transitivity,[status(thm)],[13990, 13988])).
% 2.44/2.69 tff(13992,plain,
% 2.44/2.69 (b(s(s(s(z))), s(s(z)))),
% 2.44/2.69 inference(modus_ponens,[status(thm)],[13986, 11690])).
% 2.44/2.69 tff(13993,plain,
% 2.44/2.69 (b(s(elem!1), s(z)) <=> b(s(s(z)), s(z))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[14])).
% 2.44/2.69 tff(13994,plain,
% 2.44/2.69 (~(s(elem!1) = s(z))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[2689, 13980])).
% 2.44/2.69 tff(13995,plain,
% 2.44/2.69 (b(s(elem!1), s(z))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[7105, 13312, 13978, 13994])).
% 2.44/2.69 tff(13996,plain,
% 2.44/2.69 (b(s(s(z)), s(z))),
% 2.44/2.69 inference(modus_ponens,[status(thm)],[13995, 13993])).
% 2.44/2.69 tff(13997,plain,
% 2.44/2.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.44/2.69 inference(rewrite,[status(thm)],[])).
% 2.44/2.69 tff(13998,plain,
% 2.44/2.69 (((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), 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(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.44/2.69 inference(rewrite,[status(thm)],[])).
% 2.44/2.69 tff(13999,plain,
% 2.44/2.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z))))))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[13998])).
% 2.44/2.69 tff(14000,plain,
% 2.44/2.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.44/2.69 inference(transitivity,[status(thm)],[13999, 13997])).
% 2.44/2.69 tff(14001,plain,
% 2.44/2.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))),
% 2.44/2.69 inference(quant_inst,[status(thm)],[])).
% 2.44/2.69 tff(14002,plain,
% 2.44/2.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z))))),
% 2.44/2.69 inference(modus_ponens,[status(thm)],[14001, 14000])).
% 2.44/2.69 tff(14003,plain,
% 2.44/2.69 ($false),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[14002, 306, 8, 5097, 3451, 9247])).
% 2.44/2.69 tff(14004,plain,((~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.69 tff(14005,plain,
% 2.44/2.69 (~b(s(z), s(s(z)))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[14004, 13565, 13996, 13992])).
% 2.44/2.69 tff(14006,plain,
% 2.44/2.69 (r(s(z), s(s(z)))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[4434, 14005])).
% 2.44/2.69 tff(14007,plain,
% 2.44/2.69 (r(elem!1, s(elem!1))),
% 2.44/2.69 inference(modus_ponens,[status(thm)],[14006, 13991])).
% 2.44/2.69 tff(14008,plain,
% 2.44/2.69 (~r(z, s(elem!1))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[5668, 14007, 374])).
% 2.44/2.69 tff(14009,plain,
% 2.44/2.69 (b(z, s(elem!1))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[275, 14008])).
% 2.44/2.69 tff(14010,plain,
% 2.44/2.69 (~r(s(elem!1), z)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[287, 14007, 246])).
% 2.44/2.69 tff(14011,plain,
% 2.44/2.69 (b(s(elem!1), z)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[2380, 14010])).
% 2.44/2.69 tff(14012,plain,
% 2.44/2.69 ($false),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[1218, 14011, 14009, 13986, 13977])).
% 2.44/2.69 tff(14013,plain,((~(elem!1 = s(z))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (s(s(elem!1)) = s(elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (elem!1 = s(elem!1)) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.69 tff(14014,plain,
% 2.44/2.69 (~(elem!1 = s(z))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[14013, 13973, 13964, 13966, 13736, 13975, 13968, 13280])).
% 2.44/2.69 tff(14015,plain,
% 2.44/2.69 (r(elem!1, s(z))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[97, 14014])).
% 2.44/2.69 tff(14016,plain,
% 2.44/2.69 (~r(s(z), elem!1)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[8838, 13966, 13736, 13964])).
% 2.44/2.69 tff(14017,plain,
% 2.44/2.69 (~(s(z) = elem!1)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[89, 14014])).
% 2.44/2.69 tff(14018,plain,
% 2.44/2.69 (b(s(z), elem!1)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[13156, 14017, 14016])).
% 2.44/2.69 tff(14019,plain,
% 2.44/2.69 (~r(s(s(s(z))), elem!1)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[7492, 14018, 13280, 13964, 14015])).
% 2.44/2.69 tff(14020,plain,
% 2.44/2.69 (b(s(s(s(z))), elem!1)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[1489, 14019, 13281])).
% 2.44/2.69 tff(14021,plain,
% 2.44/2.69 (~b(s(s(s(z))), s(z))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[7510, 306, 14018, 14020, 13280])).
% 2.44/2.69 tff(14022,plain,
% 2.44/2.69 (r(s(s(s(z))), s(z))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[113, 14021])).
% 2.44/2.69 tff(14023,plain,
% 2.44/2.69 (~r(s(s(s(z))), z)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[211, 14022, 204])).
% 2.44/2.69 tff(14024,plain,
% 2.44/2.69 (~(z = elem!1)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[1618, 13965])).
% 2.44/2.69 tff(14025,plain,
% 2.44/2.69 (~b(s(s(s(z))), z)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[9326, 14022, 2, 13964, 13974, 14024, 14018, 13280, 14015, 14020, 14014, 14016, 13281, 5])).
% 2.44/2.69 tff(14026,plain,
% 2.44/2.69 ($false),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[2197, 14025, 14023])).
% 2.44/2.69 tff(14027,plain,((~r(s(z), z)) | b(elem!1, z) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.69 tff(14028,plain,
% 2.44/2.69 (~r(s(z), z)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[14027, 2, 5])).
% 2.44/2.69 tff(14029,plain,
% 2.44/2.69 (b(s(z), z)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[221, 14028])).
% 2.44/2.69 tff(14030,plain,
% 2.44/2.69 (~(elem!1 = s(z))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[4298, 14029, 2])).
% 2.44/2.69 tff(14031,plain,
% 2.44/2.69 (r(elem!1, s(z))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[97, 14030])).
% 2.44/2.69 tff(14032,plain,
% 2.44/2.69 (~(s(z) = elem!1)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[89, 14030])).
% 2.44/2.69 tff(14033,plain,
% 2.44/2.69 (b(s(z), elem!1)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[13156, 14032, 14016])).
% 2.44/2.69 tff(14034,plain,
% 2.44/2.69 (~r(s(s(s(z))), elem!1)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[7492, 14033, 13280, 13964, 14031])).
% 2.44/2.69 tff(14035,plain,
% 2.44/2.69 (b(s(s(s(z))), elem!1)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[1489, 14034, 13281])).
% 2.44/2.69 tff(14036,plain,
% 2.44/2.69 (((~b(s(s(s(z))), elem!1)) | (~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), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.44/2.69 inference(rewrite,[status(thm)],[])).
% 2.44/2.69 tff(14037,plain,
% 2.44/2.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[14036])).
% 2.44/2.69 tff(14038,plain,
% 2.44/2.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.44/2.69 inference(transitivity,[status(thm)],[14037, 1491])).
% 2.44/2.69 tff(14039,plain,
% 2.44/2.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~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))))))),
% 2.44/2.69 inference(quant_inst,[status(thm)],[])).
% 2.44/2.69 tff(14040,plain,
% 2.44/2.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 2.44/2.69 inference(modus_ponens,[status(thm)],[14039, 14038])).
% 2.44/2.69 tff(14041,plain,
% 2.44/2.69 (~b(s(z), s(s(s(z))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[14040, 306, 14033, 14035, 13280])).
% 2.44/2.69 tff(14042,plain,
% 2.44/2.69 (~b(z, elem!1)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[13868, 14029, 13972, 5, 2])).
% 2.44/2.69 tff(14043,plain,
% 2.44/2.69 (~b(s(s(s(z))), s(z))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[7510, 306, 14033, 14035, 13280])).
% 2.44/2.69 tff(14044,plain,
% 2.44/2.69 (~r(s(z), s(s(s(z))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[9784, 14043, 2, 14024, 14042, 14034])).
% 2.44/2.69 tff(14045,plain,
% 2.44/2.69 ($false),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[3302, 14044, 14041])).
% 2.44/2.69 tff(14046,plain,(b(elem!1, z) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.69 tff(14047,plain,
% 2.44/2.69 (b(elem!1, z)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[14046, 5])).
% 2.44/2.69 tff(14048,plain,
% 2.44/2.69 (~(z = elem!1)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[11005, 14047])).
% 2.44/2.69 tff(14049,plain,
% 2.44/2.69 (r(z, elem!1)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[835, 5318, 14048])).
% 2.44/2.69 tff(14050,plain,
% 2.44/2.69 (~(elem!1 = s(s(s(z))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[4555, 13281])).
% 2.44/2.69 tff(14051,plain,
% 2.44/2.69 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[7090, 808, 12587, 11840])).
% 2.44/2.69 tff(14052,plain,
% 2.44/2.69 (b(z, s(s(s(s(z))))) <=> b(z, s(s(s(elem!1))))),
% 2.44/2.69 inference(symmetry,[status(thm)],[13572])).
% 2.44/2.69 tff(14053,plain,
% 2.44/2.69 ((~b(z, s(s(s(s(z)))))) <=> (~b(z, s(s(s(elem!1)))))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[14052])).
% 2.44/2.69 tff(14054,plain,
% 2.44/2.69 (~r(s(s(z)), s(z))),
% 2.44/2.69 inference(modus_ponens,[status(thm)],[808, 11740])).
% 2.44/2.69 tff(14055,plain,
% 2.44/2.69 (b(s(s(z)), s(z))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[2474, 43, 2470, 14054])).
% 2.44/2.69 tff(14056,plain,
% 2.44/2.69 (b(elem!1, s(s(elem!1))) <=> b(s(z), s(s(elem!1)))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[10])).
% 2.44/2.69 tff(14057,plain,
% 2.44/2.69 (b(s(z), s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 2.44/2.69 inference(symmetry,[status(thm)],[14056])).
% 2.44/2.69 tff(14058,plain,
% 2.44/2.69 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(s(z))))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[15])).
% 2.44/2.69 tff(14059,plain,
% 2.44/2.69 (b(s(z), s(s(s(z)))) <=> b(s(z), s(s(elem!1)))),
% 2.44/2.69 inference(symmetry,[status(thm)],[14058])).
% 2.44/2.70 tff(14060,plain,
% 2.44/2.70 (b(s(z), s(s(s(z)))) <=> b(elem!1, s(s(elem!1)))),
% 2.44/2.70 inference(transitivity,[status(thm)],[14059, 14057])).
% 2.44/2.70 tff(14061,plain,
% 2.44/2.70 (b(elem!1, s(s(elem!1)))),
% 2.44/2.70 inference(modus_ponens,[status(thm)],[8, 14060])).
% 2.44/2.70 tff(14062,plain,
% 2.44/2.70 ((~(s(elem!1) = s(z))) <=> (~(s(elem!1) = elem!1))),
% 2.44/2.70 inference(monotonicity,[status(thm)],[11710])).
% 2.44/2.70 tff(14063,plain,
% 2.44/2.70 (~(s(elem!1) = elem!1)),
% 2.44/2.70 inference(modus_ponens,[status(thm)],[12588, 14062])).
% 2.44/2.70 tff(14064,plain,
% 2.44/2.70 (b(s(elem!1), elem!1)),
% 2.44/2.70 inference(unit_resolution,[status(thm)],[813, 808, 14063])).
% 2.44/2.70 tff(14065,plain,
% 2.44/2.70 (~b(s(s(elem!1)), s(elem!1))),
% 2.44/2.70 inference(unit_resolution,[status(thm)],[1024, 14064, 14061, 30])).
% 2.44/2.70 tff(14066,plain,
% 2.44/2.70 (r(s(s(elem!1)), s(elem!1))),
% 2.44/2.70 inference(unit_resolution,[status(thm)],[994, 14065, 11696])).
% 2.44/2.70 tff(14067,plain,
% 2.44/2.70 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.44/2.70 inference(unit_resolution,[status(thm)],[659, 14066, 14051])).
% 2.44/2.70 tff(14068,plain,
% 2.44/2.70 (b(s(s(s(elem!1))), s(elem!1))),
% 2.44/2.70 inference(unit_resolution,[status(thm)],[664, 14067, 11704])).
% 2.44/2.70 tff(14069,plain,
% 2.44/2.70 (b(s(s(s(s(z)))), s(s(z)))),
% 2.44/2.70 inference(modus_ponens,[status(thm)],[14068, 13564])).
% 2.44/2.70 tff(14070,plain,
% 2.44/2.70 (b(z, s(elem!1)) <=> b(z, s(s(z)))),
% 2.44/2.70 inference(monotonicity,[status(thm)],[14])).
% 2.44/2.70 tff(14071,plain,
% 2.44/2.70 ((s(elem!1) = s(z)) <=> (elem!1 = s(elem!1))),
% 2.44/2.70 inference(transitivity,[status(thm)],[11710, 1163])).
% 2.44/2.70 tff(14072,plain,
% 2.44/2.70 ((~(s(elem!1) = s(z))) <=> (~(elem!1 = s(elem!1)))),
% 2.44/2.70 inference(monotonicity,[status(thm)],[14071])).
% 2.44/2.70 tff(14073,plain,
% 2.44/2.70 (~(elem!1 = s(elem!1))),
% 2.44/2.70 inference(modus_ponens,[status(thm)],[12588, 14072])).
% 2.44/2.70 tff(14074,plain,
% 2.44/2.70 (~b(elem!1, s(elem!1))),
% 2.44/2.70 inference(unit_resolution,[status(thm)],[6655, 14066, 4012, 14061, 14064])).
% 2.44/2.70 tff(14075,plain,
% 2.44/2.70 (r(elem!1, s(elem!1))),
% 2.44/2.70 inference(unit_resolution,[status(thm)],[372, 14074, 14073])).
% 2.44/2.70 tff(14076,plain,
% 2.44/2.70 (~r(z, s(elem!1))),
% 2.44/2.70 inference(unit_resolution,[status(thm)],[5668, 14075, 374])).
% 2.44/2.70 tff(14077,plain,
% 2.44/2.70 (b(z, s(elem!1))),
% 2.44/2.70 inference(unit_resolution,[status(thm)],[275, 14076])).
% 2.44/2.70 tff(14078,plain,
% 2.44/2.70 (b(z, s(s(z)))),
% 2.44/2.70 inference(modus_ponens,[status(thm)],[14077, 14070])).
% 2.44/2.70 tff(14079,plain,
% 2.44/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 2.44/2.70 inference(rewrite,[status(thm)],[])).
% 2.44/2.70 tff(14080,plain,
% 2.44/2.70 (((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 2.44/2.70 inference(rewrite,[status(thm)],[])).
% 2.44/2.70 tff(14081,plain,
% 2.44/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(s(s(z))))))))),
% 2.44/2.70 inference(monotonicity,[status(thm)],[14080])).
% 2.44/2.70 tff(14082,plain,
% 2.44/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 2.54/2.70 inference(transitivity,[status(thm)],[14081, 14079])).
% 2.54/2.70 tff(14083,plain,
% 2.54/2.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 2.54/2.70 inference(quant_inst,[status(thm)],[])).
% 2.54/2.70 tff(14084,plain,
% 2.54/2.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(s(s(z))))))),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[14083, 14082])).
% 2.54/2.70 tff(14085,plain,
% 2.54/2.70 (~b(z, s(s(s(s(z)))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[14084, 306, 8, 14078, 14069, 14055])).
% 2.54/2.70 tff(14086,plain,
% 2.54/2.70 (~b(z, s(s(s(elem!1))))),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[14085, 14053])).
% 2.54/2.70 tff(14087,plain,
% 2.54/2.70 (r(z, s(s(s(elem!1))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[585, 14086])).
% 2.54/2.70 tff(14088,plain,
% 2.54/2.70 (~r(z, s(s(elem!1)))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[950, 14087, 14051])).
% 2.54/2.70 tff(14089,plain,
% 2.54/2.70 (b(z, s(s(elem!1)))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[460, 14088])).
% 2.54/2.70 tff(14090,plain,
% 2.54/2.70 (b(z, s(s(s(z))))),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[14089, 11743])).
% 2.54/2.70 tff(14091,plain,
% 2.54/2.70 (b(s(z), z)),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[4012, 4294])).
% 2.54/2.70 tff(14092,plain,
% 2.54/2.70 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[14051, 11697])).
% 2.54/2.70 tff(14093,plain,
% 2.54/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 2.54/2.70 inference(rewrite,[status(thm)],[])).
% 2.54/2.70 tff(14094,plain,
% 2.54/2.70 (((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 2.54/2.70 inference(rewrite,[status(thm)],[])).
% 2.54/2.70 tff(14095,plain,
% 2.54/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z)))))),
% 2.54/2.70 inference(monotonicity,[status(thm)],[14094])).
% 2.54/2.70 tff(14096,plain,
% 2.54/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 2.54/2.70 inference(transitivity,[status(thm)],[14095, 14093])).
% 2.54/2.70 tff(14097,plain,
% 2.54/2.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))),
% 2.54/2.70 inference(quant_inst,[status(thm)],[])).
% 2.54/2.70 tff(14098,plain,
% 2.54/2.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z)))),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[14097, 14096])).
% 2.54/2.70 tff(14099,plain,
% 2.54/2.70 (~b(s(s(s(s(z)))), z)),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[14098, 306, 8, 14078, 14069, 14055])).
% 2.54/2.70 tff(14100,plain,
% 2.54/2.70 (r(s(s(s(s(z)))), z)),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[695, 14099])).
% 2.54/2.70 tff(14101,plain,
% 2.54/2.70 (~r(s(s(s(z))), z)),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[4737, 14100, 14092])).
% 2.54/2.70 tff(14102,plain,
% 2.54/2.70 (b(s(s(s(z))), z)),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[2197, 14101])).
% 2.54/2.70 tff(14103,plain,
% 2.54/2.70 (~b(z, s(s(s(z))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[4569, 14102, 14091, 8])).
% 2.54/2.70 tff(14104,plain,
% 2.54/2.70 ($false),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[14103, 14090])).
% 2.54/2.70 tff(14105,plain,(r(s(elem!1), elem!1) | (~(elem!1 = s(z))) | (~b(s(z), s(s(s(z))))) | (~r(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.70 tff(14106,plain,
% 2.54/2.70 (r(s(elem!1), elem!1)),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[14105, 10, 13565, 374, 4012, 13296])).
% 2.54/2.70 tff(14107,plain,
% 2.54/2.70 (r(s(elem!1), s(z))),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[14106, 11738])).
% 2.54/2.70 tff(14108,plain,
% 2.54/2.70 ((s(elem!1) = s(s(s(z)))) <=> (s(s(s(z))) = s(elem!1))),
% 2.54/2.70 inference(symmetry,[status(thm)],[7552])).
% 2.54/2.70 tff(14109,plain,
% 2.54/2.70 ((s(elem!1) = s(s(s(z)))) <=> (s(s(z)) = s(s(s(z))))),
% 2.54/2.70 inference(monotonicity,[status(thm)],[14])).
% 2.54/2.70 tff(14110,plain,
% 2.54/2.70 ((s(s(z)) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 2.54/2.70 inference(symmetry,[status(thm)],[14109])).
% 2.54/2.70 tff(14111,plain,
% 2.54/2.70 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = s(elem!1))),
% 2.54/2.70 inference(transitivity,[status(thm)],[14110, 14108])).
% 2.54/2.70 tff(14112,plain,
% 2.54/2.70 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(elem!1)))),
% 2.54/2.70 inference(monotonicity,[status(thm)],[14111])).
% 2.54/2.70 tff(14113,plain,
% 2.54/2.70 (~(s(s(s(z))) = s(elem!1))),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[2508, 14112])).
% 2.54/2.70 tff(14114,plain,
% 2.54/2.70 (~r(s(elem!1), z)),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[416, 14106, 374])).
% 2.54/2.70 tff(14115,plain,
% 2.54/2.70 (b(s(elem!1), z)),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[2380, 14114])).
% 2.54/2.70 tff(14116,plain,
% 2.54/2.70 (s(s(z)) = s(elem!1)),
% 2.54/2.70 inference(symmetry,[status(thm)],[14])).
% 2.54/2.70 tff(14117,plain,
% 2.54/2.70 (r(z, s(s(z))) <=> r(z, s(elem!1))),
% 2.54/2.70 inference(monotonicity,[status(thm)],[14116])).
% 2.54/2.70 tff(14118,plain,
% 2.54/2.70 ((~r(z, s(s(z)))) <=> (~r(z, s(elem!1)))),
% 2.54/2.70 inference(monotonicity,[status(thm)],[14117])).
% 2.54/2.70 tff(14119,plain,
% 2.54/2.70 (r(s(s(z)), s(z))),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[14106, 11739])).
% 2.54/2.70 tff(14120,plain,
% 2.54/2.70 (r(z, s(z))),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[374, 13396])).
% 2.54/2.70 tff(14121,plain,
% 2.54/2.70 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))))),
% 2.54/2.70 inference(rewrite,[status(thm)],[])).
% 2.54/2.70 tff(14122,plain,
% 2.54/2.70 (((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z))))) <=> ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))))),
% 2.54/2.70 inference(rewrite,[status(thm)],[])).
% 2.54/2.70 tff(14123,plain,
% 2.54/2.70 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z))))))),
% 2.54/2.70 inference(monotonicity,[status(thm)],[14122])).
% 2.54/2.70 tff(14124,plain,
% 2.54/2.70 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))))),
% 2.54/2.70 inference(transitivity,[status(thm)],[14123, 14121])).
% 2.54/2.70 tff(14125,plain,
% 2.54/2.70 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))),
% 2.54/2.70 inference(quant_inst,[status(thm)],[])).
% 2.54/2.70 tff(14126,plain,
% 2.54/2.70 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z))))),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[14125, 14124])).
% 2.54/2.70 tff(14127,plain,
% 2.54/2.70 (~r(z, s(s(z)))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[14126, 124, 14120, 14119])).
% 2.54/2.70 tff(14128,plain,
% 2.54/2.70 (~r(z, s(elem!1))),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[14127, 14118])).
% 2.54/2.70 tff(14129,plain,
% 2.54/2.70 (b(z, s(elem!1))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[275, 14128])).
% 2.54/2.70 tff(14130,plain,
% 2.54/2.70 (~b(s(s(s(z))), z)),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[6790, 14129, 14091, 14115, 14113, 14107])).
% 2.54/2.70 tff(14131,plain,
% 2.54/2.70 (r(s(s(s(z))), z)),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[2197, 14130])).
% 2.54/2.70 tff(14132,plain,
% 2.54/2.70 ((~b(s(s(s(elem!1))), z)) <=> (~b(s(s(s(s(z)))), z))),
% 2.54/2.70 inference(monotonicity,[status(thm)],[13420])).
% 2.54/2.70 tff(14133,plain,
% 2.54/2.70 (~r(s(s(z)), z)),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[14114, 13323])).
% 2.54/2.70 tff(14134,plain,
% 2.54/2.70 (b(s(s(z)), z)),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[2529, 43, 106, 14133])).
% 2.54/2.70 tff(14135,plain,
% 2.54/2.70 (b(z, s(s(z)))),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[14129, 14070])).
% 2.54/2.70 tff(14136,plain,
% 2.54/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))),
% 2.54/2.70 inference(rewrite,[status(thm)],[])).
% 2.54/2.70 tff(14137,plain,
% 2.54/2.70 (((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))),
% 2.54/2.70 inference(rewrite,[status(thm)],[])).
% 2.54/2.70 tff(14138,plain,
% 2.54/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z))))))),
% 2.54/2.70 inference(monotonicity,[status(thm)],[14137])).
% 2.54/2.70 tff(14139,plain,
% 2.54/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))),
% 2.54/2.70 inference(transitivity,[status(thm)],[14138, 14136])).
% 2.54/2.70 tff(14140,plain,
% 2.54/2.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))),
% 2.54/2.70 inference(quant_inst,[status(thm)],[])).
% 2.54/2.70 tff(14141,plain,
% 2.54/2.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z))))),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[14140, 14139])).
% 2.54/2.70 tff(14142,plain,
% 2.54/2.70 (~b(s(z), s(s(z)))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[14141, 306, 14135, 14134, 14091])).
% 2.54/2.70 tff(14143,plain,
% 2.54/2.70 (r(s(z), s(s(z)))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[4434, 14142])).
% 2.54/2.70 tff(14144,plain,
% 2.54/2.70 (r(elem!1, s(elem!1))),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[14143, 13991])).
% 2.54/2.70 tff(14145,plain,
% 2.54/2.70 (~r(elem!1, s(s(s(elem!1))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[6042, 14144, 374, 11704, 14115, 14129])).
% 2.54/2.70 tff(14146,plain,
% 2.54/2.70 (b(elem!1, s(s(s(elem!1))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[3284, 14145, 5069])).
% 2.54/2.70 tff(14147,plain,
% 2.54/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))))),
% 2.54/2.70 inference(rewrite,[status(thm)],[])).
% 2.54/2.70 tff(14148,plain,
% 2.54/2.70 (((~b(s(elem!1), z)) | (~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, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))))),
% 2.54/2.70 inference(rewrite,[status(thm)],[])).
% 2.54/2.70 tff(14149,plain,
% 2.54/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1)))))),
% 2.54/2.70 inference(monotonicity,[status(thm)],[14148])).
% 2.54/2.70 tff(14150,plain,
% 2.54/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))))),
% 2.54/2.70 inference(transitivity,[status(thm)],[14149, 14147])).
% 2.54/2.70 tff(14151,plain,
% 2.54/2.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))))),
% 2.54/2.70 inference(quant_inst,[status(thm)],[])).
% 2.54/2.70 tff(14152,plain,
% 2.54/2.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1)))),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[14151, 14150])).
% 2.54/2.70 tff(14153,plain,
% 2.54/2.70 ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1)))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[14152, 306])).
% 2.54/2.70 tff(14154,plain,
% 2.54/2.70 (~b(s(s(s(elem!1))), z)),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[14153, 14146, 4012, 14115, 14129])).
% 2.54/2.70 tff(14155,plain,
% 2.54/2.70 (~b(s(s(s(s(z)))), z)),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[14154, 14132])).
% 2.54/2.70 tff(14156,plain,
% 2.54/2.70 (r(s(s(s(s(z)))), z)),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[695, 14155])).
% 2.54/2.70 tff(14157,plain,
% 2.54/2.70 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[4737, 14156, 14131])).
% 2.54/2.70 tff(14158,plain,
% 2.54/2.70 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[4471, 14157])).
% 2.54/2.70 tff(14159,plain,
% 2.54/2.70 (~r(s(z), s(s(s(s(z)))))),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[14145, 13613])).
% 2.54/2.70 tff(14160,plain,
% 2.54/2.70 (b(s(z), s(s(s(s(z)))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[5135, 14159])).
% 2.54/2.70 tff(14161,plain,
% 2.54/2.70 (((~b(s(z), s(s(s(s(z)))))) | (~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(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.54/2.70 inference(rewrite,[status(thm)],[])).
% 2.54/2.70 tff(14162,plain,
% 2.54/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.54/2.71 inference(monotonicity,[status(thm)],[14161])).
% 2.54/2.71 tff(14163,plain,
% 2.54/2.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.54/2.71 inference(transitivity,[status(thm)],[14162, 12344])).
% 2.54/2.71 tff(14164,plain,
% 2.54/2.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(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)))))))),
% 2.54/2.71 inference(quant_inst,[status(thm)],[])).
% 2.54/2.71 tff(14165,plain,
% 2.54/2.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.54/2.71 inference(modus_ponens,[status(thm)],[14164, 14163])).
% 2.54/2.71 tff(14166,plain,
% 2.54/2.71 ($false),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[14165, 306, 13295, 13565, 14160, 14158])).
% 2.54/2.71 tff(14167,plain,((~(elem!1 = s(z))) | (~b(elem!1, z)) | (~r(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.54/2.71 tff(14168,plain,
% 2.54/2.71 (~(elem!1 = s(z))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[14167, 6, 374, 13280, 14047])).
% 2.54/2.71 tff(14169,plain,
% 2.54/2.71 (r(elem!1, s(z))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[97, 14168])).
% 2.54/2.71 tff(14170,plain,
% 2.54/2.71 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(14171,plain,
% 2.54/2.71 (((~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(z)))))) <=> ((~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(14172,plain,
% 2.54/2.71 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z)))))))),
% 2.54/2.71 inference(monotonicity,[status(thm)],[14171])).
% 2.54/2.71 tff(14173,plain,
% 2.54/2.71 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))))),
% 2.54/2.71 inference(transitivity,[status(thm)],[14172, 14170])).
% 2.54/2.71 tff(14174,plain,
% 2.54/2.71 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))))),
% 2.54/2.71 inference(quant_inst,[status(thm)],[])).
% 2.54/2.71 tff(14175,plain,
% 2.54/2.71 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z)))))),
% 2.54/2.71 inference(modus_ponens,[status(thm)],[14174, 14173])).
% 2.54/2.71 tff(14176,plain,
% 2.54/2.71 (~r(z, s(s(s(z))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[14175, 124, 374, 2859])).
% 2.54/2.71 tff(14177,plain,
% 2.54/2.71 ((z = s(s(s(z)))) | b(z, s(s(s(z))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[2415, 43, 14176])).
% 2.54/2.71 tff(14178,plain,
% 2.54/2.71 (b(z, s(s(s(z))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[14177, 3385])).
% 2.54/2.71 tff(14179,plain,
% 2.54/2.71 (~r(s(s(s(z))), z)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[6831, 374, 2859])).
% 2.54/2.71 tff(14180,plain,
% 2.54/2.71 (b(s(s(s(z))), z)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[2197, 14179])).
% 2.54/2.71 tff(14181,plain,
% 2.54/2.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(14182,plain,
% 2.54/2.71 (((~b(s(s(s(z))), s(z))) | (~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(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(14183,plain,
% 2.54/2.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z)))))))),
% 2.54/2.71 inference(monotonicity,[status(thm)],[14182])).
% 2.54/2.71 tff(14184,plain,
% 2.54/2.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 2.54/2.71 inference(transitivity,[status(thm)],[14183, 14181])).
% 2.54/2.71 tff(14185,plain,
% 2.54/2.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))))),
% 2.54/2.71 inference(quant_inst,[status(thm)],[])).
% 2.54/2.71 tff(14186,plain,
% 2.54/2.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z)))))),
% 2.54/2.71 inference(modus_ponens,[status(thm)],[14185, 14184])).
% 2.54/2.71 tff(14187,plain,
% 2.54/2.71 (~b(elem!1, s(s(s(z))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[14186, 306, 4012, 12200, 14180, 14178])).
% 2.54/2.71 tff(14188,plain,
% 2.54/2.71 (r(elem!1, s(s(s(z))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[131, 43, 14187, 2301])).
% 2.54/2.71 tff(14189,plain,
% 2.54/2.71 (~r(s(z), s(s(s(z))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[3293, 14188, 359])).
% 2.54/2.71 tff(14190,plain,
% 2.54/2.71 (b(s(z), s(s(s(z))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[3302, 14189])).
% 2.54/2.71 tff(14191,plain,
% 2.54/2.71 ($false),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[10458, 306, 12200, 14190, 14178, 11091])).
% 2.54/2.71 tff(14192,plain,((~r(z, elem!1)) | (~r(elem!1, s(z))) | (elem!1 = s(s(s(z)))) | (~b(elem!1, z)) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.71 tff(14193,plain,
% 2.54/2.71 (~r(s(s(s(z))), elem!1)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[14192, 14169, 14047, 14050, 374])).
% 2.54/2.71 tff(14194,plain,
% 2.54/2.71 (b(s(s(s(z))), elem!1)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[1489, 14193, 13281])).
% 2.54/2.71 tff(14195,plain,
% 2.54/2.71 (~(s(z) = elem!1)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[89, 14168])).
% 2.54/2.71 tff(14196,plain,
% 2.54/2.71 (~(s(elem!1) = s(z))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[2689, 14048])).
% 2.54/2.71 tff(14197,plain,
% 2.54/2.71 (~(elem!1 = s(s(s(z))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[4555, 4198])).
% 2.54/2.71 tff(14198,plain,
% 2.54/2.71 (~r(s(s(s(z))), elem!1)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[14192, 359, 4012, 14197, 374])).
% 2.54/2.71 tff(14199,plain,
% 2.54/2.71 (b(s(s(s(z))), elem!1)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[1489, 14198, 4198])).
% 2.54/2.71 tff(14200,plain,
% 2.54/2.71 (~(elem!1 = s(z))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[14167, 6, 374, 1470, 4012])).
% 2.54/2.71 tff(14201,plain,
% 2.54/2.71 (~(s(z) = elem!1)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[89, 14200])).
% 2.54/2.71 tff(14202,assumption,(~b(s(s(s(s(z)))), elem!1)), introduced(assumption)).
% 2.54/2.71 tff(14203,plain,
% 2.54/2.71 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[2974, 14200])).
% 2.54/2.71 tff(14204,plain,
% 2.54/2.71 (~(s(elem!1) = elem!1)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[2436, 233])).
% 2.54/2.71 tff(14205,plain,
% 2.54/2.71 (b(s(elem!1), elem!1)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[813, 14204, 808])).
% 2.54/2.71 tff(14206,plain,
% 2.54/2.71 (b(s(s(elem!1)), elem!1)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[47, 1175, 6])).
% 2.54/2.71 tff(14207,plain,
% 2.54/2.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(z))))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(14208,plain,
% 2.54/2.71 (((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(z))))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(14209,plain,
% 2.54/2.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(z)))))),
% 2.54/2.71 inference(monotonicity,[status(thm)],[14208])).
% 2.54/2.71 tff(14210,plain,
% 2.54/2.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(z))))),
% 2.54/2.71 inference(transitivity,[status(thm)],[14209, 14207])).
% 2.54/2.71 tff(14211,plain,
% 2.54/2.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 2.54/2.71 inference(quant_inst,[status(thm)],[])).
% 2.54/2.71 tff(14212,plain,
% 2.54/2.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(z)))),
% 2.54/2.71 inference(modus_ponens,[status(thm)],[14211, 14210])).
% 2.54/2.71 tff(14213,plain,
% 2.54/2.71 (~b(s(elem!1), s(s(elem!1)))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[14212, 306, 4012, 14206, 14205, 485])).
% 2.54/2.71 tff(14214,plain,
% 2.54/2.71 (r(s(elem!1), s(s(elem!1)))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[1684, 43, 14213, 11324])).
% 2.54/2.71 tff(14215,plain,
% 2.54/2.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(z))))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(14216,plain,
% 2.54/2.71 (((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1))))) <=> ((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(z))))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(14217,plain,
% 2.54/2.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(z)))))),
% 2.54/2.71 inference(monotonicity,[status(thm)],[14216])).
% 2.54/2.71 tff(14218,plain,
% 2.54/2.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(z))))),
% 2.54/2.71 inference(transitivity,[status(thm)],[14217, 14215])).
% 2.54/2.71 tff(14219,plain,
% 2.54/2.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.54/2.71 inference(quant_inst,[status(thm)],[])).
% 2.54/2.71 tff(14220,plain,
% 2.54/2.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(z)))),
% 2.54/2.71 inference(modus_ponens,[status(thm)],[14219, 14218])).
% 2.54/2.71 tff(14221,plain,
% 2.54/2.71 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[14220, 306, 4012, 14206, 1967, 485])).
% 2.54/2.71 tff(14222,plain,
% 2.54/2.71 (r(s(s(s(z))), s(s(elem!1)))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[2986, 43, 14221, 2976])).
% 2.54/2.71 tff(14223,plain,
% 2.54/2.71 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(14224,plain,
% 2.54/2.71 (((~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(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(14225,plain,
% 2.54/2.71 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1))))))),
% 2.54/2.71 inference(monotonicity,[status(thm)],[14224])).
% 2.54/2.71 tff(14226,plain,
% 2.54/2.71 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.54/2.71 inference(transitivity,[status(thm)],[14225, 14223])).
% 2.54/2.71 tff(14227,plain,
% 2.54/2.71 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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))))))),
% 2.54/2.71 inference(quant_inst,[status(thm)],[])).
% 2.54/2.71 tff(14228,plain,
% 2.54/2.71 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1))))),
% 2.54/2.71 inference(modus_ponens,[status(thm)],[14227, 14226])).
% 2.54/2.71 tff(14229,plain,
% 2.54/2.71 (~r(s(elem!1), s(s(s(z))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[14228, 124, 14222, 14214])).
% 2.54/2.71 tff(14230,plain,
% 2.54/2.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(z))))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(14231,plain,
% 2.54/2.71 (((~b(z, s(z))) | (~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(elem!1, z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(z))))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(14232,plain,
% 2.54/2.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(z)))))),
% 2.54/2.71 inference(monotonicity,[status(thm)],[14231])).
% 2.54/2.71 tff(14233,plain,
% 2.54/2.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(z))))),
% 2.54/2.71 inference(transitivity,[status(thm)],[14232, 14230])).
% 2.54/2.71 tff(14234,plain,
% 2.54/2.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))))),
% 2.54/2.71 inference(quant_inst,[status(thm)],[])).
% 2.54/2.71 tff(14235,plain,
% 2.54/2.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(z)))),
% 2.54/2.71 inference(modus_ponens,[status(thm)],[14234, 14233])).
% 2.54/2.71 tff(14236,plain,
% 2.54/2.71 (~b(s(elem!1), s(s(s(z))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[14235, 306, 4012, 14205, 1967, 485])).
% 2.54/2.71 tff(14237,plain,
% 2.54/2.71 ((s(elem!1) = s(s(s(z)))) | r(s(elem!1), s(s(s(z))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[2367, 43, 14236])).
% 2.54/2.71 tff(14238,plain,
% 2.54/2.71 (s(elem!1) = s(s(s(z)))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[14237, 14229])).
% 2.54/2.71 tff(14239,plain,
% 2.54/2.71 (s(s(elem!1)) = s(s(s(s(z))))),
% 2.54/2.71 inference(monotonicity,[status(thm)],[14238])).
% 2.54/2.71 tff(14240,plain,
% 2.54/2.71 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 2.54/2.71 inference(monotonicity,[status(thm)],[14239])).
% 2.54/2.71 tff(14241,plain,
% 2.54/2.71 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 2.54/2.71 inference(symmetry,[status(thm)],[14240])).
% 2.54/2.71 tff(14242,plain,
% 2.54/2.71 ((~b(s(s(s(s(z)))), elem!1)) <=> (~b(s(s(elem!1)), elem!1))),
% 2.54/2.71 inference(monotonicity,[status(thm)],[14241])).
% 2.54/2.71 tff(14243,plain,
% 2.54/2.71 (~b(s(s(elem!1)), elem!1)),
% 2.54/2.71 inference(modus_ponens,[status(thm)],[14202, 14242])).
% 2.54/2.71 tff(14244,plain,
% 2.54/2.71 ($false),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[14206, 14243])).
% 2.54/2.71 tff(14245,plain,((s(s(s(elem!1))) = s(elem!1)) | b(s(s(s(s(z)))), elem!1) | (s(s(s(z))) = s(s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(z))) | r(s(elem!1), elem!1) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.54/2.71 tff(14246,plain,
% 2.54/2.71 (s(s(s(elem!1))) = s(elem!1)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[14245, 14202, 14203, 4012, 14199, 9519, 808, 6])).
% 2.54/2.71 tff(14247,plain,
% 2.54/2.71 (s(s(elem!1)) = elem!1),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[143, 14246])).
% 2.54/2.71 tff(14248,plain,
% 2.54/2.71 (~(s(s(s(s(z)))) = elem!1)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[9813, 14247])).
% 2.54/2.71 tff(14249,plain,
% 2.54/2.71 (r(s(s(s(s(z)))), elem!1)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[9832, 14248, 14202])).
% 2.54/2.71 tff(14250,plain,
% 2.54/2.71 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[4284, 14247])).
% 2.54/2.71 tff(14251,assumption,(r(s(s(s(s(z)))), elem!1)), introduced(assumption)).
% 2.54/2.71 tff(14252,plain,
% 2.54/2.71 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(14253,plain,
% 2.54/2.71 (((~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(14254,plain,
% 2.54/2.71 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1))))),
% 2.54/2.71 inference(monotonicity,[status(thm)],[14253])).
% 2.54/2.71 tff(14255,plain,
% 2.54/2.71 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.54/2.71 inference(transitivity,[status(thm)],[14254, 14252])).
% 2.54/2.71 tff(14256,plain,
% 2.54/2.71 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(z)))))))),
% 2.54/2.71 inference(quant_inst,[status(thm)],[])).
% 2.54/2.71 tff(14257,plain,
% 2.54/2.71 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1))),
% 2.54/2.71 inference(modus_ponens,[status(thm)],[14256, 14255])).
% 2.54/2.71 tff(14258,plain,
% 2.54/2.71 (~r(z, s(s(s(s(z)))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[14257, 124, 374, 14251])).
% 2.54/2.71 tff(14259,plain,
% 2.54/2.71 ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z)))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[12341, 43, 14258])).
% 2.54/2.71 tff(14260,plain,
% 2.54/2.71 (b(z, s(s(s(s(z)))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[14259, 12313])).
% 2.54/2.71 tff(14261,plain,
% 2.54/2.71 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.54/2.72 inference(rewrite,[status(thm)],[])).
% 2.54/2.72 tff(14262,plain,
% 2.54/2.72 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.54/2.72 inference(quant_inst,[status(thm)],[])).
% 2.54/2.72 tff(14263,plain,
% 2.54/2.72 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 2.54/2.72 inference(modus_ponens,[status(thm)],[14262, 14261])).
% 2.54/2.72 tff(14264,plain,
% 2.54/2.72 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[14263, 124, 2858, 14251])).
% 2.54/2.72 tff(14265,plain,
% 2.54/2.72 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[10662, 14264])).
% 2.54/2.72 tff(14266,plain,
% 2.54/2.72 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z)))),
% 2.54/2.72 inference(rewrite,[status(thm)],[])).
% 2.54/2.72 tff(14267,plain,
% 2.54/2.72 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z)))),
% 2.54/2.72 inference(quant_inst,[status(thm)],[])).
% 2.54/2.72 tff(14268,plain,
% 2.54/2.72 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z))),
% 2.54/2.72 inference(modus_ponens,[status(thm)],[14267, 14266])).
% 2.54/2.72 tff(14269,plain,
% 2.54/2.72 (~r(s(s(s(s(z)))), z)),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[14268, 124, 374, 14251])).
% 2.54/2.72 tff(14270,plain,
% 2.54/2.72 (b(s(s(s(s(z)))), z)),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[695, 14269])).
% 2.54/2.72 tff(14271,plain,
% 2.54/2.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 2.54/2.72 inference(rewrite,[status(thm)],[])).
% 2.54/2.72 tff(14272,plain,
% 2.54/2.72 (((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 2.54/2.72 inference(rewrite,[status(thm)],[])).
% 2.54/2.72 tff(14273,plain,
% 2.54/2.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))))),
% 2.54/2.72 inference(monotonicity,[status(thm)],[14272])).
% 2.54/2.72 tff(14274,plain,
% 2.54/2.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 2.54/2.72 inference(transitivity,[status(thm)],[14273, 14271])).
% 2.54/2.72 tff(14275,plain,
% 2.54/2.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 2.54/2.72 inference(quant_inst,[status(thm)],[])).
% 2.54/2.72 tff(14276,plain,
% 2.54/2.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))),
% 2.54/2.72 inference(modus_ponens,[status(thm)],[14275, 14274])).
% 2.54/2.72 tff(14277,plain,
% 2.54/2.72 ($false),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[14276, 306, 14270, 5454, 485, 14265, 14260])).
% 2.54/2.72 tff(14278,plain,((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~b(z, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.72 tff(14279,plain,
% 2.54/2.72 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[14278, 14249, 9519, 374])).
% 2.54/2.72 tff(14280,plain,
% 2.54/2.72 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[1144, 14279, 14250])).
% 2.54/2.72 tff(14281,plain,
% 2.54/2.72 (~b(s(z), elem!1)),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[7520, 14280, 1470, 374, 4198, 359])).
% 2.54/2.72 tff(14282,plain,
% 2.54/2.72 (r(s(z), elem!1)),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[13156, 14281, 14201])).
% 2.54/2.72 tff(14283,plain,
% 2.54/2.72 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.54/2.72 inference(rewrite,[status(thm)],[])).
% 2.54/2.72 tff(14284,plain,
% 2.54/2.72 (((~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.54/2.72 inference(rewrite,[status(thm)],[])).
% 2.54/2.72 tff(14285,plain,
% 2.54/2.72 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1))))),
% 2.54/2.72 inference(monotonicity,[status(thm)],[14284])).
% 2.54/2.72 tff(14286,plain,
% 2.54/2.72 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.54/2.72 inference(transitivity,[status(thm)],[14285, 14283])).
% 2.54/2.72 tff(14287,plain,
% 2.54/2.72 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z)))))))),
% 2.54/2.72 inference(quant_inst,[status(thm)],[])).
% 2.54/2.72 tff(14288,plain,
% 2.54/2.72 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1))),
% 2.54/2.72 inference(modus_ponens,[status(thm)],[14287, 14286])).
% 2.54/2.72 tff(14289,plain,
% 2.54/2.72 (~r(s(z), s(s(s(s(z)))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[14288, 124, 14282, 14249])).
% 2.54/2.72 tff(14290,plain,
% 2.54/2.72 (~r(s(z), z)),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[12117, 14282, 374])).
% 2.54/2.72 tff(14291,plain,
% 2.54/2.72 (b(s(z), z)),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[221, 14290])).
% 2.54/2.72 tff(14292,plain,
% 2.54/2.72 (~r(s(s(s(s(z)))), z)),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[14268, 124, 374, 14249])).
% 2.54/2.72 tff(14293,plain,
% 2.54/2.72 (b(s(s(s(s(z)))), z)),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[695, 14292])).
% 2.54/2.72 tff(14294,plain,
% 2.54/2.72 (~b(s(z), s(s(s(s(z)))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[719, 306, 14293, 14291, 9519])).
% 2.54/2.72 tff(14295,plain,
% 2.54/2.72 ($false),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[5135, 14294, 14289])).
% 2.54/2.72 tff(14296,plain,(b(s(s(s(s(z)))), elem!1) | (~r(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~r(elem!1, s(z))) | (~b(elem!1, z)) | r(s(elem!1), elem!1) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.54/2.72 tff(14297,plain,
% 2.54/2.72 (b(s(s(s(s(z)))), elem!1)),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[14296, 808, 1470, 359, 4012, 374, 6])).
% 2.54/2.72 tff(14298,plain,
% 2.54/2.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 2.54/2.72 inference(rewrite,[status(thm)],[])).
% 2.54/2.72 tff(14299,plain,
% 2.54/2.72 (((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))) <=> ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 2.54/2.72 inference(rewrite,[status(thm)],[])).
% 2.54/2.72 tff(14300,plain,
% 2.54/2.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), elem!1))))),
% 2.54/2.72 inference(monotonicity,[status(thm)],[14299])).
% 2.54/2.72 tff(14301,plain,
% 2.54/2.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 2.54/2.72 inference(transitivity,[status(thm)],[14300, 14298])).
% 2.54/2.72 tff(14302,plain,
% 2.54/2.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.54/2.72 inference(quant_inst,[status(thm)],[])).
% 2.54/2.72 tff(14303,plain,
% 2.54/2.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), elem!1))),
% 2.54/2.72 inference(modus_ponens,[status(thm)],[14302, 14301])).
% 2.54/2.72 tff(14304,plain,
% 2.54/2.72 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[14303, 306, 4012, 2812, 12426, 485])).
% 2.54/2.72 tff(14305,plain,
% 2.54/2.72 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[10662, 14304])).
% 2.54/2.72 tff(14306,plain,
% 2.54/2.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 2.54/2.72 inference(rewrite,[status(thm)],[])).
% 2.54/2.72 tff(14307,plain,
% 2.54/2.72 (((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))) <=> ((~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 2.54/2.72 inference(rewrite,[status(thm)],[])).
% 2.54/2.72 tff(14308,plain,
% 2.54/2.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), elem!1))))),
% 2.54/2.72 inference(monotonicity,[status(thm)],[14307])).
% 2.54/2.72 tff(14309,plain,
% 2.54/2.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 2.54/2.72 inference(transitivity,[status(thm)],[14308, 14306])).
% 2.54/2.72 tff(14310,plain,
% 2.54/2.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 2.54/2.72 inference(quant_inst,[status(thm)],[])).
% 2.54/2.72 tff(14311,plain,
% 2.54/2.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), elem!1))),
% 2.54/2.72 inference(modus_ponens,[status(thm)],[14310, 14309])).
% 2.54/2.72 tff(14312,plain,
% 2.54/2.72 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[14311, 306, 4012, 1967, 2812, 485])).
% 2.54/2.72 tff(14313,plain,
% 2.54/2.72 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[4603, 43, 14312, 4577])).
% 2.54/2.72 tff(14314,plain,
% 2.54/2.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.54/2.72 inference(rewrite,[status(thm)],[])).
% 2.54/2.72 tff(14315,plain,
% 2.54/2.72 (((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(elem!1, z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.54/2.72 inference(rewrite,[status(thm)],[])).
% 2.54/2.72 tff(14316,plain,
% 2.54/2.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), elem!1))))),
% 2.54/2.72 inference(monotonicity,[status(thm)],[14315])).
% 2.54/2.72 tff(14317,plain,
% 2.54/2.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.54/2.72 inference(transitivity,[status(thm)],[14316, 14314])).
% 2.54/2.72 tff(14318,plain,
% 2.54/2.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.54/2.72 inference(quant_inst,[status(thm)],[])).
% 2.54/2.72 tff(14319,plain,
% 2.54/2.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), elem!1))),
% 2.54/2.72 inference(modus_ponens,[status(thm)],[14318, 14317])).
% 2.54/2.72 tff(14320,plain,
% 2.54/2.72 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[14319, 306, 4012, 1967, 12426, 485])).
% 2.54/2.72 tff(14321,plain,
% 2.54/2.72 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[10124, 14320])).
% 2.54/2.72 tff(14322,plain,
% 2.54/2.72 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.54/2.72 inference(rewrite,[status(thm)],[])).
% 2.54/2.72 tff(14323,plain,
% 2.54/2.72 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))) <=> ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.54/2.72 inference(rewrite,[status(thm)],[])).
% 2.54/2.72 tff(14324,plain,
% 2.54/2.72 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 2.54/2.72 inference(monotonicity,[status(thm)],[14323])).
% 2.54/2.72 tff(14325,plain,
% 2.54/2.72 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.54/2.72 inference(transitivity,[status(thm)],[14324, 14322])).
% 2.54/2.72 tff(14326,plain,
% 2.54/2.72 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 2.54/2.72 inference(quant_inst,[status(thm)],[])).
% 2.54/2.72 tff(14327,plain,
% 2.54/2.72 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 2.54/2.72 inference(modus_ponens,[status(thm)],[14326, 14325])).
% 2.54/2.72 tff(14328,plain,
% 2.54/2.72 ($false),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[14327, 124, 14321, 14313, 14305])).
% 2.54/2.72 tff(14329,plain,((~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.72 tff(14330,plain,
% 2.54/2.72 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[14329, 14297, 4012, 9519, 14199])).
% 2.54/2.73 tff(14331,plain,
% 2.54/2.73 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[707, 124, 206, 10126])).
% 2.54/2.73 tff(14332,plain,
% 2.54/2.73 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[4471, 14331])).
% 2.54/2.73 tff(14333,plain,
% 2.54/2.73 (b(s(s(s(s(z)))), elem!1)),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[9832, 12143, 9815])).
% 2.54/2.73 tff(14334,plain,
% 2.54/2.73 (~r(s(s(s(z))), elem!1)),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[1481, 206, 359])).
% 2.54/2.73 tff(14335,plain,
% 2.54/2.73 (b(s(s(s(z))), elem!1)),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[1489, 14334, 4198])).
% 2.54/2.73 tff(14336,plain,
% 2.54/2.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.54/2.73 inference(rewrite,[status(thm)],[])).
% 2.54/2.73 tff(14337,plain,
% 2.54/2.73 (((~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.54/2.73 inference(rewrite,[status(thm)],[])).
% 2.54/2.73 tff(14338,plain,
% 2.54/2.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1))))),
% 2.54/2.73 inference(monotonicity,[status(thm)],[14337])).
% 2.54/2.73 tff(14339,plain,
% 2.54/2.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.54/2.73 inference(transitivity,[status(thm)],[14338, 14336])).
% 2.54/2.73 tff(14340,plain,
% 2.54/2.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~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)))),
% 2.54/2.73 inference(quant_inst,[status(thm)],[])).
% 2.54/2.73 tff(14341,plain,
% 2.54/2.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1))),
% 2.54/2.73 inference(modus_ponens,[status(thm)],[14340, 14339])).
% 2.54/2.73 tff(14342,plain,
% 2.54/2.73 ($false),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[14341, 306, 4012, 14335, 1470, 14333, 14332])).
% 2.54/2.73 tff(14343,plain,((~r(s(s(s(s(z)))), s(z))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))) | (s(s(s(s(z)))) = elem!1) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.73 tff(14344,plain,
% 2.54/2.73 (~r(s(s(s(s(z)))), s(z))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[14343, 14248, 1470, 4012, 359, 206])).
% 2.54/2.73 tff(14345,plain,
% 2.54/2.73 (b(s(s(s(s(z)))), s(z))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[4490, 14344])).
% 2.54/2.73 tff(14346,plain,
% 2.54/2.73 ($false),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[702, 306, 14293, 14291, 9519, 14345])).
% 2.54/2.73 tff(14347,plain,(b(s(s(s(s(z)))), elem!1) | (~r(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~r(elem!1, s(z))) | (~b(elem!1, z)) | (~r(s(s(s(z))), s(z))) | r(s(elem!1), elem!1) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.54/2.73 tff(14348,plain,
% 2.54/2.73 (b(s(s(s(s(z)))), elem!1)),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[14347, 206, 1470, 359, 4012, 374, 808, 6])).
% 2.54/2.73 tff(14349,plain,
% 2.54/2.73 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[14319, 306, 4012, 14199, 14348, 9519])).
% 2.54/2.73 tff(14350,plain,
% 2.54/2.73 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[10124, 14349])).
% 2.54/2.73 tff(14351,plain,
% 2.54/2.73 (~r(elem!1, s(s(s(z))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[11591, 206, 359])).
% 2.54/2.73 tff(14352,plain,
% 2.54/2.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 2.54/2.73 inference(rewrite,[status(thm)],[])).
% 2.54/2.73 tff(14353,plain,
% 2.54/2.73 (((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1)))) <=> ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 2.54/2.73 inference(rewrite,[status(thm)],[])).
% 2.54/2.73 tff(14354,plain,
% 2.54/2.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 2.54/2.73 inference(monotonicity,[status(thm)],[14353])).
% 2.54/2.73 tff(14355,plain,
% 2.54/2.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 2.54/2.73 inference(transitivity,[status(thm)],[14354, 14352])).
% 2.54/2.73 tff(14356,plain,
% 2.54/2.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 2.54/2.73 inference(quant_inst,[status(thm)],[])).
% 2.54/2.73 tff(14357,plain,
% 2.54/2.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 2.54/2.73 inference(modus_ponens,[status(thm)],[14356, 14355])).
% 2.54/2.73 tff(14358,plain,
% 2.54/2.73 (~b(s(s(s(s(z)))), s(elem!1))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[14357, 306, 4012, 14205, 12426, 9519])).
% 2.54/2.73 tff(14359,assumption,(s(s(s(s(z)))) = s(elem!1)), introduced(assumption)).
% 2.54/2.73 tff(14360,plain,
% 2.54/2.73 (inj_0(s(s(s(s(z))))) = inj_0(s(elem!1))),
% 2.54/2.73 inference(monotonicity,[status(thm)],[14359])).
% 2.54/2.73 tff(14361,plain,
% 2.54/2.73 (s(s(s(z))) = elem!1),
% 2.54/2.73 inference(transitivity,[status(thm)],[321, 14360, 135])).
% 2.54/2.73 tff(14362,plain,
% 2.54/2.73 ($false),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[1483, 14361])).
% 2.54/2.73 tff(14363,plain,((~(s(s(s(s(z)))) = s(elem!1))) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.54/2.73 tff(14364,plain,
% 2.54/2.73 (~(s(s(s(s(z)))) = s(elem!1))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[14363, 4198])).
% 2.54/2.73 tff(14365,plain,
% 2.54/2.73 (((~![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)))),
% 2.54/2.73 inference(rewrite,[status(thm)],[])).
% 2.54/2.73 tff(14366,plain,
% 2.54/2.73 ((~![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)))),
% 2.54/2.73 inference(quant_inst,[status(thm)],[])).
% 2.54/2.73 tff(14367,plain,
% 2.54/2.73 ((~![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))),
% 2.54/2.73 inference(modus_ponens,[status(thm)],[14366, 14365])).
% 2.54/2.73 tff(14368,plain,
% 2.54/2.73 (r(s(s(s(s(z)))), s(elem!1))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[14367, 43, 14364, 14358])).
% 2.54/2.73 tff(14369,plain,
% 2.54/2.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(z))))),
% 2.54/2.73 inference(rewrite,[status(thm)],[])).
% 2.54/2.73 tff(14370,plain,
% 2.54/2.73 (((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(z))))),
% 2.54/2.73 inference(rewrite,[status(thm)],[])).
% 2.54/2.73 tff(14371,plain,
% 2.54/2.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(z)))))),
% 2.54/2.73 inference(monotonicity,[status(thm)],[14370])).
% 2.54/2.73 tff(14372,plain,
% 2.54/2.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(z))))),
% 2.54/2.73 inference(transitivity,[status(thm)],[14371, 14369])).
% 2.54/2.73 tff(14373,plain,
% 2.54/2.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.54/2.73 inference(quant_inst,[status(thm)],[])).
% 2.54/2.73 tff(14374,plain,
% 2.54/2.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(z)))),
% 2.54/2.73 inference(modus_ponens,[status(thm)],[14373, 14372])).
% 2.54/2.73 tff(14375,plain,
% 2.54/2.73 (~b(s(s(elem!1)), s(elem!1))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[14374, 306, 4012, 14206, 14205, 9519])).
% 2.54/2.73 tff(14376,plain,
% 2.54/2.73 (r(s(s(elem!1)), s(elem!1))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[994, 14375, 1182])).
% 2.54/2.73 tff(14377,plain,
% 2.54/2.73 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.54/2.73 inference(rewrite,[status(thm)],[])).
% 2.54/2.73 tff(14378,plain,
% 2.54/2.73 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.54/2.73 inference(quant_inst,[status(thm)],[])).
% 2.54/2.73 tff(14379,plain,
% 2.54/2.73 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 2.54/2.73 inference(modus_ponens,[status(thm)],[14378, 14377])).
% 2.54/2.73 tff(14380,plain,
% 2.54/2.73 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[14379, 124, 14376, 14368])).
% 2.54/2.73 tff(14381,plain,
% 2.54/2.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.54/2.73 inference(rewrite,[status(thm)],[])).
% 2.54/2.73 tff(14382,plain,
% 2.54/2.73 (((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.54/2.73 inference(rewrite,[status(thm)],[])).
% 2.54/2.73 tff(14383,plain,
% 2.54/2.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1))))))),
% 2.54/2.73 inference(monotonicity,[status(thm)],[14382])).
% 2.54/2.73 tff(14384,plain,
% 2.54/2.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.54/2.73 inference(transitivity,[status(thm)],[14383, 14381])).
% 2.54/2.73 tff(14385,plain,
% 2.54/2.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.54/2.73 inference(quant_inst,[status(thm)],[])).
% 2.54/2.73 tff(14386,plain,
% 2.54/2.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 2.54/2.73 inference(modus_ponens,[status(thm)],[14385, 14384])).
% 2.54/2.73 tff(14387,plain,
% 2.54/2.73 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[14386, 306, 4012, 14206, 12426, 9519])).
% 2.54/2.73 tff(14388,plain,
% 2.54/2.73 (((~![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))))),
% 2.54/2.73 inference(rewrite,[status(thm)],[])).
% 2.54/2.73 tff(14389,plain,
% 2.54/2.73 ((~![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))))),
% 2.54/2.73 inference(quant_inst,[status(thm)],[])).
% 2.54/2.73 tff(14390,plain,
% 2.54/2.73 ((~![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)))),
% 2.54/2.73 inference(modus_ponens,[status(thm)],[14389, 14388])).
% 2.54/2.73 tff(14391,plain,
% 2.54/2.73 ((s(s(s(s(z)))) = s(s(elem!1))) | r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[14390, 43, 14387])).
% 2.54/2.73 tff(14392,plain,
% 2.54/2.73 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[14391, 14380])).
% 2.54/2.73 tff(14393,plain,
% 2.54/2.73 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 2.54/2.73 inference(monotonicity,[status(thm)],[14392])).
% 2.54/2.73 tff(14394,plain,
% 2.54/2.73 (s(s(s(s(s(s(z)))))) = s(s(s(s(elem!1))))),
% 2.54/2.73 inference(monotonicity,[status(thm)],[14393])).
% 2.54/2.73 tff(14395,plain,
% 2.54/2.73 (r(s(s(s(s(s(s(z)))))), elem!1) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 2.54/2.73 inference(monotonicity,[status(thm)],[14394])).
% 2.54/2.73 tff(14396,plain,
% 2.54/2.73 (r(s(s(s(s(elem!1)))), elem!1) <=> r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.54/2.73 inference(symmetry,[status(thm)],[14395])).
% 2.54/2.73 tff(14397,plain,
% 2.54/2.73 (~b(s(elem!1), s(s(elem!1)))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[14212, 306, 4012, 14206, 14205, 9519])).
% 2.54/2.73 tff(14398,plain,
% 2.54/2.73 (r(s(elem!1), s(s(elem!1)))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[1684, 43, 14397, 11324])).
% 2.54/2.73 tff(14399,plain,
% 2.54/2.73 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[14220, 306, 4012, 14206, 14199, 9519])).
% 2.54/2.73 tff(14400,plain,
% 2.54/2.73 (r(s(s(s(z))), s(s(elem!1)))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[2986, 43, 14399, 14203])).
% 2.54/2.73 tff(14401,plain,
% 2.54/2.73 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.54/2.73 inference(rewrite,[status(thm)],[])).
% 2.54/2.73 tff(14402,plain,
% 2.54/2.73 (((~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(s(z))), s(s(elem!1)))))),
% 2.54/2.73 inference(rewrite,[status(thm)],[])).
% 2.54/2.73 tff(14403,plain,
% 2.54/2.73 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(elem!1))))))),
% 2.54/2.73 inference(monotonicity,[status(thm)],[14402])).
% 2.54/2.73 tff(14404,plain,
% 2.54/2.73 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.54/2.73 inference(transitivity,[status(thm)],[14403, 14401])).
% 2.54/2.73 tff(14405,plain,
% 2.54/2.73 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1))))),
% 2.54/2.73 inference(quant_inst,[status(thm)],[])).
% 2.54/2.73 tff(14406,plain,
% 2.54/2.73 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(elem!1))))),
% 2.54/2.73 inference(modus_ponens,[status(thm)],[14405, 14404])).
% 2.54/2.73 tff(14407,plain,
% 2.54/2.73 (~r(s(s(s(z))), s(elem!1))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[14406, 124, 14400, 14398])).
% 2.54/2.73 tff(14408,plain,
% 2.54/2.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(z, s(z))) | (~b(s(s(s(z))), s(elem!1))))),
% 2.54/2.74 inference(rewrite,[status(thm)],[])).
% 2.54/2.74 tff(14409,plain,
% 2.54/2.74 (((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1)))) <=> ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(elem!1))))),
% 2.54/2.74 inference(rewrite,[status(thm)],[])).
% 2.54/2.74 tff(14410,plain,
% 2.54/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(z, s(z))) | (~b(s(s(s(z))), s(elem!1)))))),
% 2.54/2.74 inference(monotonicity,[status(thm)],[14409])).
% 2.54/2.74 tff(14411,plain,
% 2.54/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(z, s(z))) | (~b(s(s(s(z))), s(elem!1))))),
% 2.54/2.74 inference(transitivity,[status(thm)],[14410, 14408])).
% 2.54/2.74 tff(14412,plain,
% 2.54/2.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~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))))),
% 2.54/2.74 inference(quant_inst,[status(thm)],[])).
% 2.54/2.74 tff(14413,plain,
% 2.54/2.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(elem!1)))),
% 2.54/2.74 inference(modus_ponens,[status(thm)],[14412, 14411])).
% 2.54/2.74 tff(14414,plain,
% 2.54/2.74 (~b(s(s(s(z))), s(elem!1))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[14413, 306, 4012, 14205, 14199, 9519])).
% 2.54/2.74 tff(14415,plain,
% 2.54/2.74 ((s(s(s(z))) = s(elem!1)) | r(s(s(s(z))), s(elem!1))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[4132, 43, 14414])).
% 2.54/2.74 tff(14416,plain,
% 2.54/2.74 (s(s(s(z))) = s(elem!1)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[14415, 14407])).
% 2.54/2.74 tff(14417,plain,
% 2.54/2.74 (~(s(s(s(elem!1))) = elem!1)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[4128, 14416])).
% 2.54/2.74 tff(14418,plain,
% 2.54/2.74 (~(elem!1 = s(s(s(elem!1))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[1641, 14417])).
% 2.54/2.74 tff(14419,plain,
% 2.54/2.74 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[13712, 14418])).
% 2.54/2.74 tff(14420,plain,
% 2.54/2.74 (~r(s(elem!1), s(s(s(z))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[14228, 124, 14400, 14398])).
% 2.54/2.74 tff(14421,plain,
% 2.54/2.74 (~b(s(elem!1), s(s(s(z))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[14235, 306, 4012, 14205, 14199, 9519])).
% 2.54/2.74 tff(14422,plain,
% 2.54/2.74 ((s(elem!1) = s(s(s(z)))) | r(s(elem!1), s(s(s(z))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[2367, 43, 14421])).
% 2.54/2.74 tff(14423,plain,
% 2.54/2.74 (s(elem!1) = s(s(s(z)))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[14422, 14420])).
% 2.54/2.74 tff(14424,plain,
% 2.54/2.74 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(s(z))))),
% 2.54/2.74 inference(monotonicity,[status(thm)],[14423])).
% 2.54/2.74 tff(14425,plain,
% 2.54/2.74 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(elem!1))),
% 2.54/2.74 inference(symmetry,[status(thm)],[14424])).
% 2.54/2.74 tff(14426,plain,
% 2.54/2.74 (b(elem!1, s(elem!1))),
% 2.54/2.74 inference(modus_ponens,[status(thm)],[1470, 14425])).
% 2.54/2.74 tff(14427,plain,
% 2.54/2.74 (~b(s(s(s(s(elem!1)))), elem!1)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[4458, 14426, 14206, 14205, 14398, 1285, 14419])).
% 2.54/2.74 tff(14428,plain,
% 2.54/2.74 ((s(s(s(s(s(s(z)))))) = elem!1) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 2.54/2.74 inference(monotonicity,[status(thm)],[14394])).
% 2.54/2.74 tff(14429,plain,
% 2.54/2.74 ((s(s(s(s(s(s(z)))))) = elem!1) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 2.54/2.74 inference(transitivity,[status(thm)],[14428, 1542])).
% 2.54/2.74 tff(14430,plain,
% 2.54/2.74 ((s(s(s(s(s(s(z)))))) = elem!1) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 2.54/2.74 inference(transitivity,[status(thm)],[14429, 1543])).
% 2.54/2.74 tff(14431,plain,
% 2.54/2.74 ((~(s(s(s(s(s(s(z)))))) = elem!1)) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 2.54/2.74 inference(monotonicity,[status(thm)],[14430])).
% 2.54/2.74 tff(14432,plain,
% 2.54/2.74 (s(s(z)) = elem!1),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[5384, 14423])).
% 2.54/2.74 tff(14433,plain,
% 2.54/2.74 ((s(s(z)) = s(s(s(s(s(s(z))))))) <=> (elem!1 = s(s(s(s(s(s(z)))))))),
% 2.54/2.74 inference(monotonicity,[status(thm)],[14432])).
% 2.54/2.74 tff(14434,plain,
% 2.54/2.74 ((s(s(z)) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = elem!1)),
% 2.54/2.74 inference(transitivity,[status(thm)],[14433, 3891])).
% 2.54/2.74 tff(14435,plain,
% 2.54/2.74 ((~(s(s(z)) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(s(s(s(s(z)))))) = elem!1))),
% 2.54/2.74 inference(monotonicity,[status(thm)],[14434])).
% 2.54/2.74 tff(14436,plain,
% 2.54/2.74 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 2.54/2.74 inference(modus_ponens,[status(thm)],[2826, 14435])).
% 2.54/2.74 tff(14437,plain,
% 2.54/2.74 (~(s(s(s(s(elem!1)))) = elem!1)),
% 2.54/2.74 inference(modus_ponens,[status(thm)],[14436, 14431])).
% 2.54/2.74 tff(14438,plain,
% 2.54/2.74 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[1736, 14437, 14427])).
% 2.54/2.74 tff(14439,plain,
% 2.54/2.74 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.54/2.74 inference(modus_ponens,[status(thm)],[14438, 14396])).
% 2.54/2.74 tff(14440,plain,
% 2.54/2.74 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(z))))),
% 2.54/2.74 inference(monotonicity,[status(thm)],[14423])).
% 2.54/2.74 tff(14441,plain,
% 2.54/2.74 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(elem!1))),
% 2.54/2.74 inference(symmetry,[status(thm)],[14440])).
% 2.54/2.74 tff(14442,plain,
% 2.54/2.74 ((~r(elem!1, s(s(s(z))))) <=> (~r(elem!1, s(elem!1)))),
% 2.54/2.74 inference(monotonicity,[status(thm)],[14441])).
% 2.54/2.74 tff(14443,plain,
% 2.54/2.74 (~r(elem!1, s(elem!1))),
% 2.54/2.74 inference(modus_ponens,[status(thm)],[2302, 14442])).
% 2.54/2.74 tff(14444,plain,
% 2.54/2.74 (~b(s(z), elem!1)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[7449, 14443, 6, 808, 12588, 14204, 14375])).
% 2.54/2.74 tff(14445,plain,
% 2.54/2.74 (r(s(z), elem!1)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[13156, 14444, 14201])).
% 2.54/2.74 tff(14446,plain,
% 2.54/2.74 (~r(s(z), z)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[12117, 14445, 374])).
% 2.54/2.74 tff(14447,plain,
% 2.54/2.74 (b(s(z), z)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[221, 14446])).
% 2.54/2.74 tff(14448,plain,
% 2.54/2.74 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[7480, 14447, 374, 359])).
% 2.54/2.74 tff(14449,plain,
% 2.54/2.74 ($false),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[14448, 14439])).
% 2.54/2.74 tff(14450,plain,((s(s(s(elem!1))) = s(elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(z))) | r(s(s(elem!1)), elem!1) | r(s(elem!1), elem!1) | (~b(elem!1, s(s(s(z))))) | r(elem!1, s(s(s(z)))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.74 tff(14451,plain,
% 2.54/2.74 (s(s(s(elem!1))) = s(elem!1)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[14450, 14351, 359, 6, 808, 1470, 374, 4012, 14348])).
% 2.54/2.74 tff(14452,plain,
% 2.54/2.74 (s(s(elem!1)) = elem!1),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[143, 14451])).
% 2.54/2.74 tff(14453,plain,
% 2.54/2.74 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[4284, 14452])).
% 2.54/2.74 tff(14454,plain,
% 2.54/2.74 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[14329, 14348, 4012, 9519, 14199])).
% 2.54/2.74 tff(14455,plain,
% 2.54/2.74 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[1144, 14454, 14453])).
% 2.54/2.74 tff(14456,plain,
% 2.54/2.74 (~b(s(z), z)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[7480, 14455, 374, 359])).
% 2.54/2.74 tff(14457,plain,
% 2.54/2.74 (r(s(z), z)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[221, 14456])).
% 2.54/2.74 tff(14458,plain,
% 2.54/2.74 (~r(s(s(s(z))), z)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[211, 14457, 206])).
% 2.54/2.74 tff(14459,plain,
% 2.54/2.74 (b(s(s(s(z))), z)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[2197, 14458])).
% 2.54/2.74 tff(14460,plain,
% 2.54/2.74 (~r(s(z), elem!1)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[12117, 14457, 374])).
% 2.54/2.74 tff(14461,plain,
% 2.54/2.74 (b(s(z), elem!1)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[13156, 14460, 14201])).
% 2.54/2.74 tff(14462,plain,
% 2.54/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.54/2.74 inference(rewrite,[status(thm)],[])).
% 2.54/2.74 tff(14463,plain,
% 2.54/2.74 (((~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.54/2.74 inference(rewrite,[status(thm)],[])).
% 2.54/2.74 tff(14464,plain,
% 2.54/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))))),
% 2.54/2.74 inference(monotonicity,[status(thm)],[14463])).
% 2.54/2.74 tff(14465,plain,
% 2.54/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.54/2.74 inference(transitivity,[status(thm)],[14464, 14462])).
% 2.54/2.74 tff(14466,plain,
% 2.54/2.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 2.54/2.74 inference(quant_inst,[status(thm)],[])).
% 2.54/2.74 tff(14467,plain,
% 2.54/2.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))),
% 2.54/2.74 inference(modus_ponens,[status(thm)],[14466, 14465])).
% 2.54/2.74 tff(14468,plain,
% 2.54/2.74 ((~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[14467, 306])).
% 2.54/2.74 tff(14469,plain,
% 2.54/2.74 (~b(s(z), s(s(s(s(z)))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[14468, 14461, 1470, 14348, 14459])).
% 2.54/2.74 tff(14470,plain,
% 2.54/2.74 (r(s(z), s(s(s(s(z)))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[5135, 14469])).
% 2.54/2.74 tff(14471,plain,
% 2.54/2.74 (~b(s(z), s(s(s(z))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[2939, 14461, 1470, 14459, 14199])).
% 2.54/2.74 tff(14472,plain,
% 2.54/2.74 (r(s(z), s(s(s(z))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[3302, 14471])).
% 2.54/2.74 tff(14473,plain,
% 2.54/2.74 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 2.54/2.74 inference(rewrite,[status(thm)],[])).
% 2.54/2.74 tff(14474,plain,
% 2.54/2.74 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 2.54/2.74 inference(rewrite,[status(thm)],[])).
% 2.54/2.74 tff(14475,plain,
% 2.54/2.74 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))))),
% 2.54/2.74 inference(monotonicity,[status(thm)],[14474])).
% 2.54/2.74 tff(14476,plain,
% 2.54/2.74 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 2.54/2.74 inference(transitivity,[status(thm)],[14475, 14473])).
% 2.54/2.74 tff(14477,plain,
% 2.54/2.74 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))))),
% 2.54/2.74 inference(quant_inst,[status(thm)],[])).
% 2.54/2.74 tff(14478,plain,
% 2.54/2.74 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))),
% 2.54/2.74 inference(modus_ponens,[status(thm)],[14477, 14476])).
% 2.54/2.74 tff(14479,plain,
% 2.54/2.74 ($false),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[14478, 124, 14472, 14470, 14350])).
% 2.54/2.74 tff(14480,plain,((~r(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~r(z, elem!1)) | (~r(elem!1, s(z))) | (~b(elem!1, z)) | r(s(s(elem!1)), elem!1) | r(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.54/2.74 tff(14481,plain,
% 2.54/2.74 (~r(s(s(s(z))), s(z))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[14480, 808, 374, 359, 4012, 6, 1470])).
% 2.54/2.74 tff(14482,plain,
% 2.54/2.74 (b(s(s(s(z))), s(z))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[113, 14481])).
% 2.54/2.74 tff(14483,plain,
% 2.54/2.74 (~r(s(z), s(s(s(z))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[3293, 3313, 359])).
% 2.54/2.74 tff(14484,plain,
% 2.54/2.74 (b(s(z), s(s(s(z))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[3302, 14483])).
% 2.54/2.74 tff(14485,plain,
% 2.54/2.74 (~b(s(z), elem!1)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[2928, 14484, 1470, 2284])).
% 2.54/2.74 tff(14486,plain,
% 2.54/2.74 (~r(s(z), elem!1)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[12269, 14484, 374, 3313, 2284, 14485])).
% 2.54/2.74 tff(14487,plain,
% 2.54/2.74 ($false),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[13156, 14486, 14485, 3094])).
% 2.54/2.74 tff(14488,plain,((~r(elem!1, s(s(s(z))))) | (s(z) = elem!1) | (~r(z, elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.74 tff(14489,plain,
% 2.54/2.74 (~r(elem!1, s(s(s(z))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[14488, 14482, 374, 14201, 1470, 359])).
% 2.54/2.74 tff(14490,plain,
% 2.54/2.74 (s(s(s(elem!1))) = s(elem!1)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[14450, 14489, 359, 6, 808, 1470, 374, 4012, 14297])).
% 2.54/2.74 tff(14491,plain,
% 2.54/2.74 (s(s(elem!1)) = elem!1),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[143, 14490])).
% 2.54/2.74 tff(14492,plain,
% 2.54/2.74 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[4284, 14491])).
% 2.54/2.74 tff(14493,plain,
% 2.54/2.74 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[1144, 14492, 14330])).
% 2.54/2.74 tff(14494,plain,
% 2.54/2.74 (~b(s(z), z)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[7480, 14493, 374, 359])).
% 2.54/2.74 tff(14495,plain,
% 2.54/2.74 (r(s(z), z)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[221, 14494])).
% 2.54/2.74 tff(14496,plain,
% 2.54/2.74 (~r(s(z), elem!1)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[12117, 14495, 374])).
% 2.54/2.74 tff(14497,plain,
% 2.54/2.74 (b(s(z), elem!1)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[13156, 14496, 14201])).
% 2.54/2.74 tff(14498,plain,
% 2.54/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(z))))),
% 2.54/2.74 inference(rewrite,[status(thm)],[])).
% 2.54/2.74 tff(14499,plain,
% 2.54/2.74 (((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(elem!1, z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(z))))),
% 2.54/2.74 inference(rewrite,[status(thm)],[])).
% 2.54/2.74 tff(14500,plain,
% 2.54/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(z)))))),
% 2.54/2.74 inference(monotonicity,[status(thm)],[14499])).
% 2.54/2.74 tff(14501,plain,
% 2.54/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(z))))),
% 2.54/2.74 inference(transitivity,[status(thm)],[14500, 14498])).
% 2.54/2.74 tff(14502,plain,
% 2.54/2.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 2.54/2.74 inference(quant_inst,[status(thm)],[])).
% 2.54/2.74 tff(14503,plain,
% 2.54/2.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(z)))),
% 2.54/2.74 inference(modus_ponens,[status(thm)],[14502, 14501])).
% 2.54/2.74 tff(14504,plain,
% 2.54/2.74 ($false),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[14503, 306, 4012, 14482, 14497, 14199, 9519])).
% 2.54/2.74 tff(14505,plain,(r(s(elem!1), elem!1) | (~b(elem!1, z)) | (~r(z, elem!1)) | (~r(elem!1, s(z))) | r(s(s(elem!1)), elem!1) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.74 tff(14506,plain,
% 2.54/2.74 (r(s(elem!1), elem!1)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[14505, 14169, 374, 14047, 6, 13280])).
% 2.54/2.74 tff(14507,plain,
% 2.54/2.74 (~r(s(z), z)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[12117, 4, 374])).
% 2.54/2.74 tff(14508,plain,
% 2.54/2.74 (~b(s(z), z)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[9508, 4, 374, 802, 2249])).
% 2.54/2.74 tff(14509,plain,
% 2.54/2.74 ($false),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[221, 14508, 14507])).
% 2.54/2.74 tff(14510,plain,((~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.74 tff(14511,plain,
% 2.54/2.74 (~r(s(z), elem!1)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[14510, 14506, 374, 14196])).
% 2.54/2.74 tff(14512,plain,
% 2.54/2.74 (b(s(z), elem!1)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[13156, 14511, 14195])).
% 2.54/2.74 tff(14513,plain,
% 2.54/2.74 (~r(z, s(elem!1))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[7870, 124, 374, 14506])).
% 2.54/2.74 tff(14514,plain,
% 2.54/2.74 (b(z, s(elem!1))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[275, 14513])).
% 2.54/2.74 tff(14515,plain,
% 2.54/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)))),
% 2.54/2.74 inference(rewrite,[status(thm)],[])).
% 2.54/2.74 tff(14516,plain,
% 2.54/2.74 (((~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)))),
% 2.54/2.74 inference(rewrite,[status(thm)],[])).
% 2.54/2.74 tff(14517,plain,
% 2.54/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1))))),
% 2.54/2.74 inference(monotonicity,[status(thm)],[14516])).
% 2.54/2.74 tff(14518,plain,
% 2.54/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)))),
% 2.54/2.74 inference(transitivity,[status(thm)],[14517, 14515])).
% 2.54/2.74 tff(14519,plain,
% 2.54/2.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 2.54/2.74 inference(quant_inst,[status(thm)],[])).
% 2.54/2.74 tff(14520,plain,
% 2.54/2.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1))),
% 2.54/2.74 inference(modus_ponens,[status(thm)],[14519, 14518])).
% 2.54/2.74 tff(14521,plain,
% 2.54/2.74 (~b(s(s(s(z))), s(z))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[14520, 306, 14047, 14514, 14512, 14194])).
% 2.54/2.74 tff(14522,plain,
% 2.54/2.74 (r(s(s(s(z))), s(z))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[113, 14521])).
% 2.54/2.74 tff(14523,plain,
% 2.54/2.74 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[2974, 14168])).
% 2.54/2.74 tff(14524,plain,
% 2.54/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)))),
% 2.54/2.74 inference(rewrite,[status(thm)],[])).
% 2.54/2.74 tff(14525,plain,
% 2.54/2.74 (((~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)))),
% 2.54/2.74 inference(rewrite,[status(thm)],[])).
% 2.54/2.74 tff(14526,plain,
% 2.54/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1))))),
% 2.54/2.74 inference(monotonicity,[status(thm)],[14525])).
% 2.54/2.74 tff(14527,plain,
% 2.54/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)))),
% 2.54/2.75 inference(transitivity,[status(thm)],[14526, 14524])).
% 2.54/2.75 tff(14528,plain,
% 2.54/2.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))))),
% 2.54/2.75 inference(quant_inst,[status(thm)],[])).
% 2.54/2.75 tff(14529,plain,
% 2.54/2.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1))),
% 2.54/2.75 inference(modus_ponens,[status(thm)],[14528, 14527])).
% 2.54/2.75 tff(14530,plain,
% 2.54/2.75 (~b(s(z), s(s(elem!1)))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[14529, 306, 4012, 30, 817, 2831])).
% 2.54/2.75 tff(14531,plain,
% 2.54/2.75 (r(s(z), s(s(elem!1)))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[3997, 43, 14530, 79])).
% 2.54/2.75 tff(14532,assumption,(r(s(s(s(z))), s(s(elem!1)))), introduced(assumption)).
% 2.54/2.75 tff(14533,plain,
% 2.54/2.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)))),
% 2.54/2.75 inference(rewrite,[status(thm)],[])).
% 2.54/2.75 tff(14534,plain,
% 2.54/2.75 (((~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)))),
% 2.54/2.75 inference(rewrite,[status(thm)],[])).
% 2.54/2.75 tff(14535,plain,
% 2.54/2.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1))))),
% 2.54/2.75 inference(monotonicity,[status(thm)],[14534])).
% 2.54/2.75 tff(14536,plain,
% 2.54/2.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)))),
% 2.54/2.75 inference(transitivity,[status(thm)],[14535, 14533])).
% 2.54/2.75 tff(14537,plain,
% 2.54/2.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 2.54/2.75 inference(quant_inst,[status(thm)],[])).
% 2.54/2.75 tff(14538,plain,
% 2.54/2.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1))),
% 2.54/2.75 inference(modus_ponens,[status(thm)],[14537, 14536])).
% 2.54/2.75 tff(14539,plain,
% 2.54/2.75 (~b(s(z), s(s(s(z))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[14538, 306, 4012, 817, 2831, 1967])).
% 2.54/2.75 tff(14540,plain,
% 2.54/2.75 (r(s(z), s(s(s(z))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[3302, 14539])).
% 2.54/2.75 tff(14541,plain,
% 2.54/2.75 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))))),
% 2.54/2.75 inference(rewrite,[status(thm)],[])).
% 2.54/2.75 tff(14542,plain,
% 2.54/2.75 (((~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(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))))),
% 2.54/2.75 inference(rewrite,[status(thm)],[])).
% 2.54/2.75 tff(14543,plain,
% 2.54/2.75 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1))))))),
% 2.54/2.75 inference(monotonicity,[status(thm)],[14542])).
% 2.54/2.75 tff(14544,plain,
% 2.54/2.75 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))))),
% 2.54/2.75 inference(transitivity,[status(thm)],[14543, 14541])).
% 2.54/2.75 tff(14545,plain,
% 2.54/2.75 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))))),
% 2.54/2.75 inference(quant_inst,[status(thm)],[])).
% 2.54/2.75 tff(14546,plain,
% 2.54/2.75 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1))))),
% 2.54/2.75 inference(modus_ponens,[status(thm)],[14545, 14544])).
% 2.54/2.75 tff(14547,plain,
% 2.54/2.75 ($false),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[14546, 124, 14540, 14532, 14531])).
% 2.54/2.75 tff(14548,plain,((~b(s(z), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.75 tff(14549,plain,
% 2.54/2.75 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[14548, 30, 4012, 817, 1967, 2831])).
% 2.54/2.75 tff(14550,plain,
% 2.54/2.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(elem!1))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.54/2.75 inference(rewrite,[status(thm)],[])).
% 2.54/2.75 tff(14551,plain,
% 2.54/2.75 (((~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1))))) <=> ((~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.54/2.75 inference(rewrite,[status(thm)],[])).
% 2.54/2.75 tff(14552,plain,
% 2.54/2.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(elem!1, 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 2.54/2.75 inference(monotonicity,[status(thm)],[14551])).
% 2.54/2.75 tff(14553,plain,
% 2.54/2.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(elem!1, 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.54/2.75 inference(transitivity,[status(thm)],[14552, 14550])).
% 2.54/2.75 tff(14554,plain,
% 2.54/2.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.54/2.75 inference(quant_inst,[status(thm)],[])).
% 2.54/2.75 tff(14555,plain,
% 2.54/2.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1))))),
% 2.54/2.75 inference(modus_ponens,[status(thm)],[14554, 14553])).
% 2.54/2.75 tff(14556,plain,
% 2.54/2.75 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[14555, 306, 4012, 30, 817, 1967])).
% 2.54/2.75 tff(14557,plain,
% 2.54/2.75 ($false),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[2986, 43, 14556, 14549, 2976])).
% 2.54/2.75 tff(14558,plain,((~b(s(s(elem!1)), elem!1)) | (s(s(s(z))) = s(s(elem!1))) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.75 tff(14559,plain,
% 2.54/2.75 (~b(s(s(elem!1)), elem!1)),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[14558, 14523, 14047, 14514, 14194, 14512])).
% 2.54/2.75 tff(14560,plain,
% 2.54/2.75 (s(s(elem!1)) = elem!1),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[47, 14559, 6])).
% 2.54/2.75 tff(14561,plain,
% 2.54/2.75 (~(s(s(s(s(z)))) = elem!1)),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[9813, 14560])).
% 2.54/2.75 tff(14562,plain,
% 2.54/2.75 (~r(s(s(s(s(z)))), s(z))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[14343, 14561, 13280, 14047, 14169, 14522])).
% 2.54/2.75 tff(14563,plain,
% 2.54/2.75 (b(s(s(s(s(z)))), s(z))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[4490, 14562])).
% 2.54/2.75 tff(14564,plain,
% 2.54/2.75 (~r(z, s(z))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[385, 14169, 374])).
% 2.54/2.75 tff(14565,plain,
% 2.54/2.75 (b(z, s(z))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[2263, 14564])).
% 2.54/2.75 tff(14566,plain,
% 2.54/2.75 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[7520, 14512, 13280, 374, 13281, 14169])).
% 2.54/2.75 tff(14567,plain,
% 2.54/2.75 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[4284, 14560])).
% 2.54/2.75 tff(14568,plain,
% 2.54/2.75 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[1144, 14567, 14566])).
% 2.54/2.75 tff(14569,plain,
% 2.54/2.75 (~r(s(s(s(s(z)))), elem!1)),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[14278, 14568, 14565, 374])).
% 2.54/2.75 tff(14570,plain,
% 2.54/2.75 (b(s(s(s(s(z)))), elem!1)),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[9832, 14569, 14561])).
% 2.54/2.75 tff(14571,plain,
% 2.54/2.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.54/2.75 inference(rewrite,[status(thm)],[])).
% 2.54/2.75 tff(14572,plain,
% 2.54/2.75 (((~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.54/2.75 inference(rewrite,[status(thm)],[])).
% 2.54/2.75 tff(14573,plain,
% 2.54/2.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1))))),
% 2.54/2.75 inference(monotonicity,[status(thm)],[14572])).
% 2.54/2.75 tff(14574,plain,
% 2.54/2.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.54/2.75 inference(transitivity,[status(thm)],[14573, 14571])).
% 2.54/2.75 tff(14575,plain,
% 2.54/2.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 2.54/2.75 inference(quant_inst,[status(thm)],[])).
% 2.54/2.75 tff(14576,plain,
% 2.54/2.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1))),
% 2.54/2.75 inference(modus_ponens,[status(thm)],[14575, 14574])).
% 2.54/2.75 tff(14577,plain,
% 2.54/2.75 ($false),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[14576, 306, 14047, 14514, 14512, 14570, 14563])).
% 2.54/2.75 tff(14578,plain,(r(s(s(elem!1)), elem!1) | (~r(z, elem!1)) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.75 tff(14579,plain,
% 2.54/2.75 (r(s(s(elem!1)), elem!1)),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[14578, 14049, 5])).
% 2.54/2.75 tff(14580,plain,
% 2.54/2.75 (~r(s(s(elem!1)), z)),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[6539, 124, 14049, 14579])).
% 2.54/2.75 tff(14581,plain,
% 2.54/2.75 (b(s(s(elem!1)), z)),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[476, 14580])).
% 2.54/2.75 tff(14582,plain,
% 2.54/2.75 (~r(z, s(s(elem!1)))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[5837, 14579, 14049])).
% 2.54/2.75 tff(14583,plain,
% 2.54/2.75 (b(z, s(s(elem!1)))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[460, 14582])).
% 2.54/2.75 tff(14584,plain,
% 2.54/2.75 (~b(elem!1, s(s(elem!1)))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[6653, 306, 14047, 14583, 14581])).
% 2.54/2.75 tff(14585,plain,
% 2.54/2.75 (b(s(z), s(s(elem!1)))),
% 2.54/2.75 inference(modus_ponens,[status(thm)],[13565, 14059])).
% 2.54/2.75 tff(14586,plain,
% 2.54/2.75 ((~b(elem!1, s(s(elem!1)))) <=> (~b(s(z), s(s(elem!1))))),
% 2.54/2.75 inference(monotonicity,[status(thm)],[14056])).
% 2.54/2.75 tff(14587,plain,
% 2.54/2.75 (~b(s(z), s(s(elem!1)))),
% 2.54/2.75 inference(modus_ponens,[status(thm)],[2754, 14586])).
% 2.54/2.75 tff(14588,plain,
% 2.54/2.75 ($false),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[14587, 14585])).
% 2.54/2.75 tff(14589,plain,((~(elem!1 = s(z))) | b(elem!1, s(s(elem!1))) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.75 tff(14590,plain,
% 2.54/2.75 (~(elem!1 = s(z))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[14589, 14584, 13280])).
% 2.54/2.75 tff(14591,plain,
% 2.54/2.75 (~(s(z) = elem!1)),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[89, 14590])).
% 2.54/2.75 tff(14592,plain,
% 2.54/2.75 (b(z, elem!1) <=> b(z, s(s(elem!1)))),
% 2.54/2.75 inference(monotonicity,[status(thm)],[183])).
% 2.54/2.75 tff(14593,plain,
% 2.54/2.75 (b(z, s(s(elem!1))) <=> b(z, elem!1)),
% 2.54/2.75 inference(symmetry,[status(thm)],[14592])).
% 2.54/2.75 tff(14594,plain,
% 2.54/2.75 (b(z, elem!1)),
% 2.54/2.75 inference(modus_ponens,[status(thm)],[1198, 14593])).
% 2.54/2.75 tff(14595,plain,
% 2.54/2.75 ($false),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[5318, 14594])).
% 2.54/2.75 tff(14596,plain,((~(elem!1 = s(s(elem!1)))) | b(z, elem!1) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.75 tff(14597,plain,
% 2.54/2.75 (~(elem!1 = s(s(elem!1)))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[14596, 5318, 14583])).
% 2.54/2.75 tff(14598,plain,
% 2.54/2.75 (~(s(s(elem!1)) = elem!1)),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[1174, 14597])).
% 2.54/2.75 tff(14599,plain,
% 2.54/2.75 (r(elem!1, s(z))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[97, 14590])).
% 2.54/2.75 tff(14600,plain,
% 2.54/2.75 (~r(s(s(s(z))), elem!1)),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[14192, 14599, 14047, 14050, 14049])).
% 2.54/2.75 tff(14601,plain,
% 2.54/2.75 (b(s(s(s(z))), elem!1)),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[1489, 14600, 13281])).
% 2.54/2.75 tff(14602,plain,
% 2.54/2.75 (~(s(elem!1) = elem!1)),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[180, 14598])).
% 2.54/2.75 tff(14603,plain,
% 2.54/2.75 (~(s(s(elem!1)) = s(elem!1))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[195, 14602])).
% 2.54/2.75 tff(14604,plain,
% 2.54/2.75 (~r(s(elem!1), elem!1)),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[10562, 14603, 14579, 14049, 14581, 14583])).
% 2.54/2.75 tff(14605,plain,
% 2.54/2.75 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[7090, 91, 12587, 808])).
% 2.54/2.75 tff(14606,plain,
% 2.54/2.75 (r(elem!1, s(s(elem!1)))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[516, 187, 2754])).
% 2.54/2.75 tff(14607,plain,
% 2.54/2.75 (~r(elem!1, s(s(s(elem!1))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[1256, 124, 14606, 14605])).
% 2.54/2.75 tff(14608,plain,
% 2.54/2.75 (~r(s(s(s(elem!1))), elem!1)),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[7780, 14605, 1730])).
% 2.54/2.75 tff(14609,plain,
% 2.54/2.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(z))))),
% 2.54/2.75 inference(rewrite,[status(thm)],[])).
% 2.54/2.75 tff(14610,plain,
% 2.54/2.75 (((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z)))) <=> ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(z))))),
% 2.54/2.75 inference(rewrite,[status(thm)],[])).
% 2.54/2.75 tff(14611,plain,
% 2.54/2.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(z, s(s(elem!1)))) | (~b(s(elem!1), s(z)))))),
% 2.54/2.75 inference(monotonicity,[status(thm)],[14610])).
% 2.54/2.75 tff(14612,plain,
% 2.54/2.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(z, s(s(elem!1)))) | (~b(s(elem!1), s(z))))),
% 2.54/2.75 inference(transitivity,[status(thm)],[14611, 14609])).
% 2.54/2.75 tff(14613,plain,
% 2.54/2.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))),
% 2.54/2.75 inference(quant_inst,[status(thm)],[])).
% 2.54/2.75 tff(14614,plain,
% 2.54/2.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(z)))),
% 2.54/2.75 inference(modus_ponens,[status(thm)],[14613, 14612])).
% 2.54/2.75 tff(14615,plain,
% 2.54/2.75 (~b(s(elem!1), s(z))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[14614, 306, 4012, 1198, 5620, 2831])).
% 2.54/2.75 tff(14616,plain,
% 2.54/2.75 (r(s(elem!1), s(z))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[2964, 14615, 12588])).
% 2.54/2.75 tff(14617,plain,
% 2.54/2.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)))),
% 2.54/2.76 inference(rewrite,[status(thm)],[])).
% 2.54/2.76 tff(14618,plain,
% 2.54/2.76 (((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(elem!1, z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)))),
% 2.54/2.76 inference(rewrite,[status(thm)],[])).
% 2.54/2.76 tff(14619,plain,
% 2.54/2.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1))))),
% 2.54/2.76 inference(monotonicity,[status(thm)],[14618])).
% 2.54/2.76 tff(14620,plain,
% 2.54/2.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)))),
% 2.54/2.76 inference(transitivity,[status(thm)],[14619, 14617])).
% 2.54/2.76 tff(14621,plain,
% 2.54/2.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 2.54/2.76 inference(quant_inst,[status(thm)],[])).
% 2.54/2.76 tff(14622,plain,
% 2.54/2.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1))),
% 2.54/2.76 inference(modus_ponens,[status(thm)],[14621, 14620])).
% 2.54/2.76 tff(14623,plain,
% 2.54/2.76 (~b(s(s(s(z))), s(z))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[14622, 306, 4012, 1198, 2831, 1967])).
% 2.54/2.76 tff(14624,plain,
% 2.54/2.76 (r(s(s(s(z))), s(z))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[113, 14623])).
% 2.54/2.76 tff(14625,plain,
% 2.54/2.76 (~r(s(s(s(z))), s(elem!1))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[5600, 124, 14624, 14616])).
% 2.54/2.76 tff(14626,plain,
% 2.54/2.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))),
% 2.54/2.76 inference(rewrite,[status(thm)],[])).
% 2.54/2.76 tff(14627,plain,
% 2.54/2.76 (((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1)))) <=> ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))),
% 2.54/2.76 inference(rewrite,[status(thm)],[])).
% 2.54/2.76 tff(14628,plain,
% 2.54/2.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1)))))),
% 2.54/2.76 inference(monotonicity,[status(thm)],[14627])).
% 2.54/2.76 tff(14629,plain,
% 2.54/2.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))),
% 2.54/2.76 inference(transitivity,[status(thm)],[14628, 14626])).
% 2.54/2.76 tff(14630,plain,
% 2.54/2.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))),
% 2.54/2.76 inference(quant_inst,[status(thm)],[])).
% 2.54/2.76 tff(14631,plain,
% 2.54/2.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1)))),
% 2.54/2.76 inference(modus_ponens,[status(thm)],[14630, 14629])).
% 2.54/2.76 tff(14632,plain,
% 2.54/2.76 (~b(s(s(s(z))), s(elem!1))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[14631, 306, 4012, 1198, 5620, 1967])).
% 2.54/2.76 tff(14633,plain,
% 2.54/2.76 ((s(s(s(z))) = s(elem!1)) | r(s(s(s(z))), s(elem!1))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[4132, 43, 14632])).
% 2.54/2.76 tff(14634,plain,
% 2.54/2.76 (s(s(s(z))) = s(elem!1)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[14633, 14625])).
% 2.54/2.76 tff(14635,plain,
% 2.54/2.76 (~(s(s(s(elem!1))) = elem!1)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[4128, 14634])).
% 2.54/2.76 tff(14636,plain,
% 2.54/2.76 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[7793, 14635, 14608, 14607, 5620])).
% 2.54/2.76 tff(14637,plain,
% 2.54/2.76 (r(s(s(s(elem!1))), s(elem!1))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[664, 14636, 144])).
% 2.54/2.76 tff(14638,plain,
% 2.54/2.76 (~(elem!1 = s(z))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[14589, 2754, 1470])).
% 2.54/2.76 tff(14639,plain,
% 2.54/2.76 (~(s(z) = elem!1)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[89, 14638])).
% 2.54/2.76 tff(14640,plain,
% 2.54/2.76 (~r(s(s(elem!1)), s(elem!1))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[13111, 14635, 4012, 1730, 187, 14605, 144, 5621, 5620])).
% 2.54/2.76 tff(14641,plain,
% 2.54/2.76 (b(s(s(elem!1)), s(elem!1))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[994, 14640, 196])).
% 2.54/2.76 tff(14642,plain,
% 2.54/2.76 (~r(s(elem!1), s(s(s(z))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[5427, 124, 14624, 14616])).
% 2.54/2.76 tff(14643,plain,
% 2.54/2.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)))),
% 2.54/2.76 inference(rewrite,[status(thm)],[])).
% 2.54/2.76 tff(14644,plain,
% 2.54/2.76 (((~b(z, s(s(elem!1)))) | (~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(elem!1, z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)))),
% 2.54/2.76 inference(rewrite,[status(thm)],[])).
% 2.54/2.76 tff(14645,plain,
% 2.54/2.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1))))),
% 2.54/2.76 inference(monotonicity,[status(thm)],[14644])).
% 2.54/2.76 tff(14646,plain,
% 2.54/2.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)))),
% 2.54/2.76 inference(transitivity,[status(thm)],[14645, 14643])).
% 2.54/2.76 tff(14647,plain,
% 2.54/2.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))))),
% 2.54/2.76 inference(quant_inst,[status(thm)],[])).
% 2.54/2.76 tff(14648,plain,
% 2.54/2.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1))),
% 2.54/2.76 inference(modus_ponens,[status(thm)],[14647, 14646])).
% 2.54/2.76 tff(14649,plain,
% 2.54/2.76 (~b(s(elem!1), s(s(s(z))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[14648, 306, 4012, 1198, 5620, 1967])).
% 2.54/2.76 tff(14650,plain,
% 2.54/2.76 ((s(elem!1) = s(s(s(z)))) | r(s(elem!1), s(s(s(z))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[2367, 43, 14649])).
% 2.54/2.76 tff(14651,plain,
% 2.54/2.76 (s(elem!1) = s(s(s(z)))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[14650, 14642])).
% 2.54/2.76 tff(14652,plain,
% 2.54/2.76 (~b(s(s(s(z))), z)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[9310, 14651, 1730, 2831, 12587, 359, 1967, 1470, 196])).
% 2.54/2.76 tff(14653,plain,
% 2.54/2.76 (r(s(s(s(z))), z)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[2197, 14652])).
% 2.54/2.76 tff(14654,plain,
% 2.54/2.76 (~r(s(z), z)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[211, 14653, 14624])).
% 2.54/2.76 tff(14655,plain,
% 2.54/2.76 (b(s(z), z)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[221, 14654])).
% 2.54/2.76 tff(14656,plain,
% 2.54/2.76 ($false),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[11366, 14655, 14641, 1730, 12587, 14639, 14608, 5621, 4012, 14616, 14637, 14636, 5620])).
% 2.54/2.76 tff(14657,plain,((s(s(elem!1)) = elem!1) | (~r(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~r(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(elem!1)))) | r(s(elem!1), elem!1) | b(elem!1, s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.76 tff(14658,plain,
% 2.54/2.76 (~b(s(z), elem!1)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[14657, 14604, 14047, 14579, 14599, 14601, 13280, 14583, 14598, 14584])).
% 2.54/2.76 tff(14659,plain,
% 2.54/2.76 (r(s(z), elem!1)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[13156, 14658, 14591])).
% 2.54/2.76 tff(14660,plain,
% 2.54/2.76 (~r(s(z), z)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[12117, 14659, 14049])).
% 2.54/2.76 tff(14661,plain,
% 2.54/2.76 (b(s(z), z)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[221, 14660])).
% 2.54/2.76 tff(14662,plain,
% 2.54/2.76 (~r(s(z), s(s(elem!1)))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[13075, 14659, 14579])).
% 2.54/2.76 tff(14663,plain,
% 2.54/2.76 (b(s(z), s(s(elem!1)))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[3997, 43, 79, 14662])).
% 2.54/2.76 tff(14664,plain,
% 2.54/2.76 ($false),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[6747, 306, 14583, 14581, 14663, 14661])).
% 2.54/2.76 tff(14665,plain,(b(z, elem!1) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.76 tff(14666,plain,
% 2.54/2.76 (b(z, elem!1)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[14665, 5])).
% 2.54/2.76 tff(14667,plain,
% 2.54/2.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.54/2.76 inference(rewrite,[status(thm)],[])).
% 2.54/2.76 tff(14668,plain,
% 2.54/2.76 (((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.54/2.76 inference(rewrite,[status(thm)],[])).
% 2.54/2.76 tff(14669,plain,
% 2.54/2.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 2.54/2.76 inference(monotonicity,[status(thm)],[14668])).
% 2.54/2.76 tff(14670,plain,
% 2.54/2.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.54/2.76 inference(transitivity,[status(thm)],[14669, 14667])).
% 2.54/2.76 tff(14671,plain,
% 2.54/2.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))))),
% 2.54/2.76 inference(quant_inst,[status(thm)],[])).
% 2.54/2.76 tff(14672,plain,
% 2.54/2.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 2.54/2.76 inference(modus_ponens,[status(thm)],[14671, 14670])).
% 2.54/2.76 tff(14673,plain,
% 2.54/2.76 ($false),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[14672, 306, 838, 4012, 1531, 1470])).
% 2.54/2.76 tff(14674,plain,((~b(s(s(s(z))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.76 tff(14675,plain,
% 2.54/2.76 (~b(s(s(s(z))), z)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[14674, 14666, 14047, 13280])).
% 2.54/2.76 tff(14676,plain,
% 2.54/2.76 (r(s(s(s(z))), z)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[2197, 14675])).
% 2.54/2.76 tff(14677,plain,
% 2.54/2.76 (r(s(s(s(z))), elem!1)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[1489, 1, 13281])).
% 2.54/2.76 tff(14678,plain,
% 2.54/2.76 (~r(elem!1, z)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[2561, 14677, 14676])).
% 2.54/2.76 tff(14679,plain,
% 2.54/2.76 (~r(z, elem!1)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[6831, 14677, 14676])).
% 2.54/2.76 tff(14680,plain,
% 2.54/2.76 (b(z, elem!1)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[835, 7, 14048])).
% 2.54/2.76 tff(14681,plain,
% 2.54/2.76 (~b(s(s(elem!1)), z)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[3976, 14206, 7, 12587, 3062])).
% 2.54/2.76 tff(14682,plain,
% 2.54/2.76 (r(s(s(elem!1)), z)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[476, 14681])).
% 2.54/2.76 tff(14683,plain,
% 2.54/2.76 (b(z, elem!1)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[835, 7, 12587])).
% 2.54/2.76 tff(14684,plain,
% 2.54/2.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.54/2.76 inference(rewrite,[status(thm)],[])).
% 2.54/2.76 tff(14685,plain,
% 2.54/2.76 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.54/2.76 inference(rewrite,[status(thm)],[])).
% 2.54/2.76 tff(14686,plain,
% 2.54/2.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))))),
% 2.54/2.76 inference(monotonicity,[status(thm)],[14685])).
% 2.54/2.76 tff(14687,plain,
% 2.54/2.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.54/2.76 inference(transitivity,[status(thm)],[14686, 14684])).
% 2.54/2.76 tff(14688,plain,
% 2.54/2.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.54/2.76 inference(quant_inst,[status(thm)],[])).
% 2.54/2.76 tff(14689,plain,
% 2.54/2.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))),
% 2.54/2.76 inference(modus_ponens,[status(thm)],[14688, 14687])).
% 2.54/2.76 tff(14690,plain,
% 2.54/2.76 (~b(s(s(elem!1)), s(elem!1))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[14689, 306, 14683, 4012, 14206, 14205])).
% 2.54/2.76 tff(14691,plain,
% 2.54/2.76 (r(s(s(elem!1)), s(elem!1))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[994, 14690, 1182])).
% 2.54/2.76 tff(14692,plain,
% 2.54/2.76 (~b(s(elem!1), z)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[3111, 306, 14683, 4012, 14205])).
% 2.54/2.76 tff(14693,plain,
% 2.54/2.76 (r(s(elem!1), z)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[2380, 14692])).
% 2.54/2.76 tff(14694,plain,
% 2.54/2.76 ($false),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[471, 14693, 14691, 14682])).
% 2.54/2.76 tff(14695,plain,((s(s(s(elem!1))) = s(elem!1)) | (~b(elem!1, z)) | r(z, elem!1) | r(elem!1, z) | r(s(elem!1), elem!1) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.54/2.76 tff(14696,plain,
% 2.54/2.76 (s(s(s(elem!1))) = s(elem!1)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[14695, 808, 7, 3062, 14047, 6])).
% 2.54/2.76 tff(14697,plain,
% 2.54/2.76 (s(s(elem!1)) = elem!1),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[143, 14696])).
% 2.54/2.76 tff(14698,plain,
% 2.54/2.76 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[4284, 14697])).
% 2.54/2.76 tff(14699,plain,
% 2.54/2.76 (s(s(z)) = s(s(elem!1))),
% 2.54/2.76 inference(transitivity,[status(thm)],[2392, 1427])).
% 2.54/2.76 tff(14700,plain,
% 2.54/2.76 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 2.54/2.76 inference(monotonicity,[status(thm)],[14699])).
% 2.54/2.76 tff(14701,plain,
% 2.54/2.76 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 2.54/2.76 inference(symmetry,[status(thm)],[14700])).
% 2.54/2.76 tff(14702,plain,
% 2.54/2.76 (s(elem!1) = s(z)),
% 2.54/2.76 inference(transitivity,[status(thm)],[67, 14701, 546])).
% 2.54/2.76 tff(14703,plain,
% 2.54/2.76 ($false),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[2249, 14702])).
% 2.54/2.76 tff(14704,plain,((~(s(s(z)) = elem!1)) | (s(elem!1) = s(z)) | (~(s(s(elem!1)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.76 tff(14705,plain,
% 2.54/2.76 (~(s(s(z)) = elem!1)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[14704, 14697, 14196])).
% 2.54/2.76 tff(14706,plain,
% 2.54/2.76 (r(s(s(s(s(s(s(z)))))), elem!1) <=> r(s(s(s(s(s(s(z)))))), s(z))),
% 2.54/2.76 inference(monotonicity,[status(thm)],[10])).
% 2.54/2.76 tff(14707,plain,
% 2.54/2.76 (b(s(s(s(z))), elem!1)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[4206, 13295, 13312])).
% 2.54/2.76 tff(14708,plain,
% 2.54/2.76 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[12298, 14707, 4012, 838])).
% 2.54/2.76 tff(14709,plain,
% 2.54/2.76 ((s(s(s(s(s(s(z)))))) = elem!1) <=> (s(s(s(s(s(s(z)))))) = s(z))),
% 2.54/2.76 inference(monotonicity,[status(thm)],[10])).
% 2.54/2.76 tff(14710,plain,
% 2.54/2.76 ((s(s(s(s(s(s(z)))))) = s(z)) <=> (s(s(s(s(s(s(z)))))) = elem!1)),
% 2.54/2.76 inference(symmetry,[status(thm)],[14709])).
% 2.54/2.76 tff(14711,plain,
% 2.54/2.76 ((~(s(s(s(s(s(s(z)))))) = s(z))) <=> (~(s(s(s(s(s(s(z)))))) = elem!1))),
% 2.54/2.76 inference(monotonicity,[status(thm)],[14710])).
% 2.54/2.76 tff(14712,plain,
% 2.54/2.76 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 2.54/2.76 inference(modus_ponens,[status(thm)],[2844, 14711])).
% 2.54/2.76 tff(14713,plain,
% 2.54/2.76 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[1144, 14712, 14708])).
% 2.54/2.76 tff(14714,plain,
% 2.54/2.76 (r(s(s(s(s(s(s(z)))))), s(z))),
% 2.54/2.76 inference(modus_ponens,[status(thm)],[14713, 14706])).
% 2.54/2.76 tff(14715,plain,
% 2.54/2.76 (~r(s(z), z)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[3089, 13312, 3062])).
% 2.54/2.76 tff(14716,plain,
% 2.54/2.76 (b(s(z), z)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[221, 14715])).
% 2.54/2.76 tff(14717,plain,
% 2.54/2.76 (~b(s(s(s(z))), z)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[2228, 14707, 1470, 838])).
% 2.54/2.76 tff(14718,plain,
% 2.54/2.76 (r(s(s(s(z))), z)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[2197, 14717])).
% 2.54/2.76 tff(14719,plain,
% 2.54/2.76 (~b(z, s(s(s(z))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[2298, 306, 13295, 13565, 11849])).
% 2.54/2.76 tff(14720,plain,
% 2.54/2.76 (~b(z, s(s(elem!1)))),
% 2.54/2.76 inference(modus_ponens,[status(thm)],[14719, 11847])).
% 2.54/2.76 tff(14721,plain,
% 2.54/2.76 (r(z, s(s(elem!1)))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[460, 14720])).
% 2.54/2.76 tff(14722,plain,
% 2.54/2.76 (b(s(s(elem!1)), s(z))),
% 2.54/2.76 inference(modus_ponens,[status(thm)],[13295, 5071])).
% 2.54/2.76 tff(14723,plain,
% 2.54/2.76 ((s(s(elem!1)) = s(z)) <=> (elem!1 = s(s(elem!1)))),
% 2.54/2.76 inference(transitivity,[status(thm)],[11838, 1170])).
% 2.54/2.76 tff(14724,plain,
% 2.54/2.76 ((~(s(s(elem!1)) = s(z))) <=> (~(elem!1 = s(s(elem!1))))),
% 2.54/2.76 inference(monotonicity,[status(thm)],[14723])).
% 2.54/2.76 tff(14725,plain,
% 2.54/2.76 (~(elem!1 = s(s(elem!1)))),
% 2.54/2.76 inference(modus_ponens,[status(thm)],[80, 14724])).
% 2.54/2.76 tff(14726,plain,
% 2.54/2.76 (b(s(elem!1), s(z))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[7105, 808, 85, 3099])).
% 2.54/2.76 tff(14727,plain,
% 2.54/2.76 (~b(s(s(elem!1)), s(elem!1))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[4007, 14726, 24, 3999])).
% 2.54/2.76 tff(14728,plain,
% 2.54/2.76 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[7090, 808, 2170, 91])).
% 2.54/2.76 tff(14729,plain,
% 2.54/2.76 (b(s(elem!1), elem!1)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[813, 808, 193])).
% 2.54/2.76 tff(14730,plain,
% 2.54/2.76 (~r(s(s(elem!1)), s(elem!1))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[13009, 14729, 838, 366, 360, 30, 437, 14728, 150])).
% 2.54/2.76 tff(14731,plain,
% 2.54/2.76 ($false),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[994, 14730, 14727, 403])).
% 2.54/2.76 tff(14732,plain,(r(s(elem!1), elem!1) | (s(s(elem!1)) = s(elem!1)) | (~b(z, elem!1)) | (elem!1 = s(elem!1)) | (elem!1 = s(s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (s(elem!1) = elem!1) | (z = elem!1) | (s(s(elem!1)) = elem!1) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.76 tff(14733,plain,
% 2.54/2.76 (r(s(elem!1), elem!1)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[14732, 11696, 838, 14073, 14725, 13296, 14721, 11704, 14722, 14585, 14063, 12587, 11840, 13312])).
% 2.54/2.76 tff(14734,plain,
% 2.54/2.76 (~b(s(s(s(s(z)))), s(z))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[13528, 306, 8, 12315, 247, 485])).
% 2.54/2.76 tff(14735,plain,
% 2.54/2.76 (r(s(s(s(s(z)))), s(z))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[4490, 14734])).
% 2.54/2.76 tff(14736,plain,
% 2.54/2.76 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 2.54/2.76 inference(rewrite,[status(thm)],[])).
% 2.54/2.76 tff(14737,plain,
% 2.54/2.76 (((~r(s(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(s(z))))))))) <=> ((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 2.54/2.77 inference(rewrite,[status(thm)],[])).
% 2.54/2.77 tff(14738,plain,
% 2.54/2.77 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(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(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z)))))),
% 2.54/2.77 inference(monotonicity,[status(thm)],[14737])).
% 2.54/2.77 tff(14739,plain,
% 2.54/2.77 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(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(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 2.54/2.77 inference(transitivity,[status(thm)],[14738, 14736])).
% 2.54/2.77 tff(14740,plain,
% 2.54/2.77 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(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(s(z)))))))))),
% 2.54/2.77 inference(quant_inst,[status(thm)],[])).
% 2.54/2.77 tff(14741,plain,
% 2.54/2.77 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z)))),
% 2.54/2.77 inference(modus_ponens,[status(thm)],[14740, 14739])).
% 2.54/2.77 tff(14742,plain,
% 2.54/2.77 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[14741, 124, 14735, 4268])).
% 2.54/2.77 tff(14743,plain,
% 2.54/2.77 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[13486, 14742])).
% 2.54/2.77 tff(14744,plain,
% 2.54/2.77 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.54/2.77 inference(rewrite,[status(thm)],[])).
% 2.54/2.77 tff(14745,plain,
% 2.54/2.77 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.54/2.77 inference(quant_inst,[status(thm)],[])).
% 2.54/2.77 tff(14746,plain,
% 2.54/2.77 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 2.54/2.77 inference(modus_ponens,[status(thm)],[14745, 14744])).
% 2.54/2.77 tff(14747,plain,
% 2.54/2.77 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[14746, 124, 14735, 4268])).
% 2.54/2.77 tff(14748,plain,
% 2.54/2.77 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[10662, 14747])).
% 2.54/2.77 tff(14749,plain,
% 2.54/2.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)))),
% 2.54/2.77 inference(rewrite,[status(thm)],[])).
% 2.54/2.77 tff(14750,plain,
% 2.54/2.77 (((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)))),
% 2.54/2.77 inference(rewrite,[status(thm)],[])).
% 2.54/2.77 tff(14751,plain,
% 2.54/2.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z))))),
% 2.54/2.77 inference(monotonicity,[status(thm)],[14750])).
% 2.54/2.77 tff(14752,plain,
% 2.54/2.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)))),
% 2.54/2.77 inference(transitivity,[status(thm)],[14751, 14749])).
% 2.54/2.77 tff(14753,plain,
% 2.54/2.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 2.54/2.77 inference(quant_inst,[status(thm)],[])).
% 2.54/2.77 tff(14754,plain,
% 2.54/2.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z))),
% 2.54/2.77 inference(modus_ponens,[status(thm)],[14753, 14752])).
% 2.54/2.77 tff(14755,plain,
% 2.54/2.77 (~b(s(z), s(s(s(s(z)))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[14754, 306, 8, 12315, 247, 485])).
% 2.54/2.77 tff(14756,plain,
% 2.54/2.77 (r(s(z), s(s(s(s(z)))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[5135, 14755])).
% 2.54/2.77 tff(14757,plain,
% 2.54/2.77 (r(elem!1, s(s(s(elem!1))))),
% 2.54/2.77 inference(modus_ponens,[status(thm)],[14756, 11728])).
% 2.54/2.77 tff(14758,plain,
% 2.54/2.77 (~r(s(elem!1), s(s(s(elem!1))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[3447, 14757, 802])).
% 2.54/2.77 tff(14759,assumption,(r(s(s(z)), s(s(s(s(z)))))), introduced(assumption)).
% 2.54/2.77 tff(14760,plain,
% 2.54/2.77 (r(s(elem!1), s(s(s(elem!1))))),
% 2.54/2.77 inference(modus_ponens,[status(thm)],[14759, 13315])).
% 2.54/2.77 tff(14761,assumption,(~r(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 2.54/2.77 tff(14762,plain,
% 2.54/2.77 ($false),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[14761, 14760])).
% 2.54/2.77 tff(14763,plain,((~r(s(s(z)), s(s(s(s(z)))))) | r(s(elem!1), s(s(s(elem!1)))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.77 tff(14764,plain,
% 2.54/2.77 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[14763, 14758, 10])).
% 2.54/2.77 tff(14765,plain,
% 2.54/2.77 (b(s(s(z)), s(s(s(s(z)))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[4510, 14764])).
% 2.54/2.77 tff(14766,plain,
% 2.54/2.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.54/2.77 inference(rewrite,[status(thm)],[])).
% 2.54/2.77 tff(14767,plain,
% 2.54/2.77 (((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.54/2.77 inference(rewrite,[status(thm)],[])).
% 2.54/2.77 tff(14768,plain,
% 2.54/2.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))))),
% 2.54/2.77 inference(monotonicity,[status(thm)],[14767])).
% 2.54/2.77 tff(14769,plain,
% 2.54/2.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.54/2.77 inference(transitivity,[status(thm)],[14768, 14766])).
% 2.54/2.77 tff(14770,plain,
% 2.54/2.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.54/2.77 inference(quant_inst,[status(thm)],[])).
% 2.54/2.77 tff(14771,plain,
% 2.54/2.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))),
% 2.54/2.77 inference(modus_ponens,[status(thm)],[14770, 14769])).
% 2.54/2.77 tff(14772,plain,
% 2.54/2.77 (~b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[14771, 306, 14765, 14748, 14743])).
% 2.54/2.77 tff(14773,plain,
% 2.54/2.77 (r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[2829, 43, 2826, 14772])).
% 2.54/2.77 tff(14774,plain,
% 2.54/2.77 (~r(z, s(s(s(elem!1))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[950, 11699, 437])).
% 2.54/2.77 tff(14775,plain,
% 2.54/2.77 (b(z, s(s(s(elem!1))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[585, 14774])).
% 2.54/2.77 tff(14776,plain,
% 2.54/2.77 (b(z, s(s(s(s(z)))))),
% 2.54/2.77 inference(modus_ponens,[status(thm)],[14775, 13572])).
% 2.54/2.77 tff(14777,plain,
% 2.54/2.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 2.54/2.77 inference(rewrite,[status(thm)],[])).
% 2.54/2.77 tff(14778,plain,
% 2.54/2.77 (((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 2.54/2.77 inference(rewrite,[status(thm)],[])).
% 2.54/2.77 tff(14779,plain,
% 2.54/2.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))))),
% 2.54/2.77 inference(monotonicity,[status(thm)],[14778])).
% 2.54/2.77 tff(14780,plain,
% 2.54/2.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 2.54/2.77 inference(transitivity,[status(thm)],[14779, 14777])).
% 2.54/2.77 tff(14781,plain,
% 2.54/2.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))),
% 2.54/2.77 inference(quant_inst,[status(thm)],[])).
% 2.54/2.77 tff(14782,plain,
% 2.54/2.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))),
% 2.54/2.77 inference(modus_ponens,[status(thm)],[14781, 14780])).
% 2.54/2.77 tff(14783,plain,
% 2.54/2.77 (~b(s(s(z)), z)),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[14782, 306, 14765, 14748, 14743, 14776])).
% 2.54/2.77 tff(14784,plain,
% 2.54/2.77 (r(s(s(z)), z)),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[2531, 14783])).
% 2.54/2.77 tff(14785,plain,
% 2.54/2.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 2.54/2.77 inference(rewrite,[status(thm)],[])).
% 2.54/2.77 tff(14786,plain,
% 2.54/2.77 (((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z))) <=> ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 2.54/2.77 inference(rewrite,[status(thm)],[])).
% 2.54/2.77 tff(14787,plain,
% 2.54/2.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))))),
% 2.54/2.77 inference(monotonicity,[status(thm)],[14786])).
% 2.54/2.77 tff(14788,plain,
% 2.54/2.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 2.54/2.77 inference(transitivity,[status(thm)],[14787, 14785])).
% 2.54/2.77 tff(14789,plain,
% 2.54/2.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 2.54/2.77 inference(quant_inst,[status(thm)],[])).
% 2.54/2.77 tff(14790,plain,
% 2.54/2.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))),
% 2.54/2.77 inference(modus_ponens,[status(thm)],[14789, 14788])).
% 2.54/2.77 tff(14791,plain,
% 2.54/2.77 (~b(s(s(s(s(s(s(z)))))), z)),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[14790, 306, 14748, 14743, 14776])).
% 2.54/2.77 tff(14792,plain,
% 2.54/2.77 (r(s(s(s(s(s(s(z)))))), z)),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[4232, 14791])).
% 2.54/2.77 tff(14793,plain,
% 2.54/2.77 ($false),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[12242, 124, 14792, 14784, 14773])).
% 2.54/2.77 tff(14794,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~(elem!1 = s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(z, s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.77 tff(14795,plain,
% 2.54/2.77 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[14794, 10, 14733, 14714, 14721, 13565, 14716, 11849, 14718])).
% 2.54/2.77 tff(14796,plain,
% 2.54/2.77 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[4471, 14795])).
% 2.54/2.77 tff(14797,plain,
% 2.54/2.77 (~b(s(s(s(s(z)))), s(z))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[11880, 14796, 14716, 11849, 13295])).
% 2.54/2.77 tff(14798,plain,
% 2.54/2.77 (r(s(s(s(s(z)))), s(z))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[4490, 14797])).
% 2.54/2.77 tff(14799,plain,
% 2.54/2.77 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[14746, 124, 14798, 14714])).
% 2.54/2.77 tff(14800,plain,
% 2.54/2.77 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[10662, 14799])).
% 2.54/2.77 tff(14801,plain,
% 2.54/2.77 (r(s(s(z)), s(z))),
% 2.54/2.77 inference(modus_ponens,[status(thm)],[14733, 11739])).
% 2.54/2.77 tff(14802,plain,
% 2.54/2.77 (~r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[2853, 124, 14801, 14714])).
% 2.54/2.77 tff(14803,plain,
% 2.54/2.77 (b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[2829, 43, 2826, 14802])).
% 2.54/2.77 tff(14804,plain,
% 2.54/2.77 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[4514, 124, 14798, 14801])).
% 2.54/2.77 tff(14805,plain,
% 2.54/2.77 (b(s(s(z)), s(s(s(s(z)))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[4510, 14804])).
% 2.54/2.77 tff(14806,plain,
% 2.54/2.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.54/2.77 inference(rewrite,[status(thm)],[])).
% 2.54/2.77 tff(14807,plain,
% 2.54/2.77 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.54/2.77 inference(rewrite,[status(thm)],[])).
% 2.54/2.77 tff(14808,plain,
% 2.54/2.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))))),
% 2.54/2.78 inference(monotonicity,[status(thm)],[14807])).
% 2.54/2.78 tff(14809,plain,
% 2.54/2.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.54/2.78 inference(transitivity,[status(thm)],[14808, 14806])).
% 2.54/2.78 tff(14810,plain,
% 2.54/2.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.54/2.78 inference(quant_inst,[status(thm)],[])).
% 2.54/2.78 tff(14811,plain,
% 2.54/2.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))),
% 2.54/2.78 inference(modus_ponens,[status(thm)],[14810, 14809])).
% 2.54/2.78 tff(14812,plain,
% 2.54/2.78 ($false),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[14811, 306, 13295, 14805, 14796, 14803, 14800])).
% 2.54/2.78 tff(14813,plain,((~(elem!1 = s(z))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, z)) | r(elem!1, z) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.54/2.78 tff(14814,plain,
% 2.54/2.78 (~(elem!1 = s(z))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[14813, 3062, 13280, 14047, 14680, 6])).
% 2.54/2.78 tff(14815,plain,
% 2.54/2.78 (r(elem!1, s(z))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[97, 14814])).
% 2.54/2.78 tff(14816,plain,
% 2.54/2.78 (~(s(z) = elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[89, 14814])).
% 2.54/2.78 tff(14817,plain,
% 2.54/2.78 (b(s(z), elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[4167, 1175, 5, 6, 7, 3062, 204])).
% 2.54/2.78 tff(14818,plain,
% 2.54/2.78 (~r(s(elem!1), z)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[7030, 14817, 14047, 14680, 14196, 14205])).
% 2.54/2.78 tff(14819,plain,
% 2.54/2.78 (b(s(elem!1), z)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[2380, 14818])).
% 2.54/2.78 tff(14820,plain,
% 2.54/2.78 (((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1))) <=> ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)))),
% 2.54/2.78 inference(rewrite,[status(thm)],[])).
% 2.54/2.78 tff(14821,plain,
% 2.54/2.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1))))),
% 2.54/2.78 inference(monotonicity,[status(thm)],[14820])).
% 2.54/2.78 tff(14822,plain,
% 2.54/2.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)))),
% 2.54/2.78 inference(transitivity,[status(thm)],[14821, 3106])).
% 2.54/2.78 tff(14823,plain,
% 2.54/2.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)))),
% 2.54/2.78 inference(quant_inst,[status(thm)],[])).
% 2.54/2.78 tff(14824,plain,
% 2.54/2.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1))),
% 2.54/2.78 inference(modus_ponens,[status(thm)],[14823, 14822])).
% 2.54/2.78 tff(14825,plain,
% 2.54/2.78 ($false),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[14824, 306, 14680, 14047, 14819, 14205])).
% 2.54/2.78 tff(14826,plain,((s(s(s(elem!1))) = s(elem!1)) | r(s(elem!1), elem!1) | b(elem!1, s(z)) | r(s(s(elem!1)), elem!1) | r(z, elem!1) | r(elem!1, z) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.78 tff(14827,plain,
% 2.54/2.78 (s(s(s(elem!1))) = s(elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[14826, 204, 5, 6, 7, 3062, 808])).
% 2.54/2.78 tff(14828,plain,
% 2.54/2.78 (s(s(elem!1)) = elem!1),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[143, 14827])).
% 2.54/2.78 tff(14829,plain,
% 2.54/2.78 (elem!1 = s(s(elem!1))),
% 2.54/2.78 inference(symmetry,[status(thm)],[14828])).
% 2.54/2.78 tff(14830,plain,
% 2.54/2.78 ($false),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[2228, 14335, 7717, 1470, 838])).
% 2.54/2.78 tff(14831,plain,((~r(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~r(elem!1, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.78 tff(14832,plain,
% 2.54/2.78 (~r(s(s(s(z))), s(z))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[14831, 204, 14680, 14815, 13280])).
% 2.54/2.78 tff(14833,plain,
% 2.54/2.78 (b(s(s(s(z))), s(z))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[113, 14832])).
% 2.54/2.78 tff(14834,plain,
% 2.54/2.78 (~(s(s(s(s(z)))) = elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[9813, 14828])).
% 2.54/2.78 tff(14835,plain,
% 2.54/2.78 (~r(s(s(s(s(z)))), s(z))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[12145, 14834, 14680, 14815, 14047, 204])).
% 2.54/2.78 tff(14836,plain,
% 2.54/2.78 (b(s(s(s(s(z)))), s(z))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[4490, 14835])).
% 2.54/2.78 tff(14837,plain,
% 2.54/2.78 (~(s(s(s(s(z)))) = elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[9813, 13835])).
% 2.54/2.78 tff(14838,plain,
% 2.54/2.78 ((s(s(elem!1)) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 2.54/2.78 inference(monotonicity,[status(thm)],[13835])).
% 2.54/2.78 tff(14839,plain,
% 2.54/2.78 ((s(s(elem!1)) = s(s(s(z)))) <=> (s(s(s(z))) = elem!1)),
% 2.54/2.78 inference(transitivity,[status(thm)],[14838, 1414])).
% 2.54/2.78 tff(14840,plain,
% 2.54/2.78 ((s(s(s(z))) = elem!1) <=> (s(s(elem!1)) = s(s(s(z))))),
% 2.54/2.78 inference(symmetry,[status(thm)],[14839])).
% 2.54/2.78 tff(14841,plain,
% 2.54/2.78 ((~(s(s(s(z))) = elem!1)) <=> (~(s(s(elem!1)) = s(s(s(z)))))),
% 2.54/2.78 inference(monotonicity,[status(thm)],[14840])).
% 2.54/2.78 tff(14842,plain,
% 2.54/2.78 (~(s(s(elem!1)) = s(s(s(z))))),
% 2.54/2.78 inference(modus_ponens,[status(thm)],[13281, 14841])).
% 2.54/2.78 tff(14843,plain,
% 2.54/2.78 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[4284, 13835])).
% 2.54/2.78 tff(14844,plain,
% 2.54/2.78 (b(s(s(s(elem!1))), elem!1) <=> b(s(elem!1), elem!1)),
% 2.54/2.78 inference(monotonicity,[status(thm)],[136])).
% 2.54/2.78 tff(14845,plain,
% 2.54/2.78 (b(s(elem!1), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 2.54/2.78 inference(symmetry,[status(thm)],[14844])).
% 2.54/2.78 tff(14846,plain,
% 2.54/2.78 (b(s(s(s(elem!1))), elem!1)),
% 2.54/2.78 inference(modus_ponens,[status(thm)],[816, 14845])).
% 2.54/2.78 tff(14847,plain,
% 2.54/2.78 (~b(s(z), elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[13176, 14846, 4012, 838])).
% 2.54/2.78 tff(14848,plain,
% 2.54/2.78 (r(s(z), elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[13156, 14847, 3094])).
% 2.54/2.78 tff(14849,plain,
% 2.54/2.78 (~r(s(s(s(z))), elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[3790, 14848, 1034])).
% 2.54/2.78 tff(14850,plain,
% 2.54/2.78 (b(s(s(s(z))), elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[1489, 14849, 4198])).
% 2.54/2.78 tff(14851,plain,
% 2.54/2.78 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[12298, 14850, 4012, 838])).
% 2.54/2.78 tff(14852,plain,
% 2.54/2.78 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[1144, 14851, 14843])).
% 2.54/2.78 tff(14853,plain,
% 2.54/2.78 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[9918, 124, 14848, 14852])).
% 2.54/2.78 tff(14854,plain,
% 2.54/2.78 (b(s(z), s(s(s(s(s(s(z)))))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[5358, 43, 5355, 14853])).
% 2.54/2.78 tff(14855,plain,
% 2.54/2.78 (~b(s(s(s(z))), z)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[2228, 14850, 1470, 838])).
% 2.54/2.78 tff(14856,plain,
% 2.54/2.78 (r(s(s(s(z))), z)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[2197, 14855])).
% 2.54/2.78 tff(14857,plain,
% 2.54/2.78 (~b(s(elem!1), z)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[3111, 306, 838, 4012, 816])).
% 2.54/2.78 tff(14858,plain,
% 2.54/2.78 (r(s(elem!1), z)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[2380, 14857])).
% 2.54/2.78 tff(14859,plain,
% 2.54/2.78 (~r(s(elem!1), s(s(s(z))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[2387, 124, 14858, 14856])).
% 2.54/2.78 tff(14860,plain,
% 2.54/2.78 (~(s(elem!1) = s(s(s(z))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[2356, 13835])).
% 2.54/2.78 tff(14861,plain,
% 2.54/2.78 (b(s(elem!1), s(s(s(z))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[2367, 43, 14860, 14859])).
% 2.54/2.78 tff(14862,plain,
% 2.54/2.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 2.54/2.78 inference(rewrite,[status(thm)],[])).
% 2.54/2.78 tff(14863,plain,
% 2.54/2.78 (((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 2.54/2.78 inference(rewrite,[status(thm)],[])).
% 2.54/2.78 tff(14864,plain,
% 2.54/2.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(z))))))))))),
% 2.54/2.78 inference(monotonicity,[status(thm)],[14863])).
% 2.54/2.78 tff(14865,plain,
% 2.54/2.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 2.54/2.78 inference(transitivity,[status(thm)],[14864, 14862])).
% 2.54/2.78 tff(14866,plain,
% 2.54/2.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1)))),
% 2.54/2.78 inference(quant_inst,[status(thm)],[])).
% 2.54/2.78 tff(14867,plain,
% 2.54/2.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(z))))))))),
% 2.54/2.78 inference(modus_ponens,[status(thm)],[14866, 14865])).
% 2.54/2.78 tff(14868,plain,
% 2.54/2.78 ($false),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[14867, 306, 816, 2284, 14861, 1470, 14854])).
% 2.54/2.78 tff(14869,plain,((~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~r(s(z), s(s(s(z))))) | (s(z) = elem!1) | (~(s(s(s(elem!1))) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.78 tff(14870,plain,
% 2.54/2.78 (~b(s(elem!1), elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[14869, 1034, 13280, 838, 14047, 2284, 8965, 136])).
% 2.54/2.78 tff(14871,plain,
% 2.54/2.78 (s(elem!1) = elem!1),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[813, 14870, 808])).
% 2.54/2.78 tff(14872,plain,
% 2.54/2.78 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(elem!1)) = s(elem!1))),
% 2.54/2.78 inference(monotonicity,[status(thm)],[136])).
% 2.54/2.78 tff(14873,plain,
% 2.54/2.78 ((s(s(elem!1)) = s(elem!1)) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 2.54/2.78 inference(symmetry,[status(thm)],[14872])).
% 2.54/2.78 tff(14874,plain,
% 2.54/2.78 ((s(s(elem!1)) = s(elem!1)) <=> (elem!1 = s(elem!1))),
% 2.54/2.78 inference(monotonicity,[status(thm)],[13835])).
% 2.54/2.78 tff(14875,plain,
% 2.54/2.78 ((s(s(elem!1)) = s(elem!1)) <=> (s(elem!1) = elem!1)),
% 2.54/2.78 inference(transitivity,[status(thm)],[14874, 1162])).
% 2.54/2.78 tff(14876,plain,
% 2.54/2.78 ((s(elem!1) = elem!1) <=> (s(s(elem!1)) = s(elem!1))),
% 2.54/2.78 inference(symmetry,[status(thm)],[14875])).
% 2.54/2.78 tff(14877,plain,
% 2.54/2.78 ((s(elem!1) = elem!1) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 2.54/2.78 inference(transitivity,[status(thm)],[14876, 14873, 2425])).
% 2.54/2.78 tff(14878,plain,
% 2.54/2.78 (s(s(s(elem!1))) = s(s(elem!1))),
% 2.54/2.78 inference(modus_ponens,[status(thm)],[176, 14877])).
% 2.54/2.78 tff(14879,plain,
% 2.54/2.78 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[5403, 14878])).
% 2.54/2.78 tff(14880,plain,
% 2.54/2.78 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 2.54/2.78 inference(monotonicity,[status(thm)],[136])).
% 2.54/2.78 tff(14881,plain,
% 2.54/2.78 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 2.54/2.78 inference(symmetry,[status(thm)],[14880])).
% 2.54/2.78 tff(14882,plain,
% 2.54/2.78 (elem!1 = s(s(elem!1))),
% 2.54/2.78 inference(symmetry,[status(thm)],[13835])).
% 2.54/2.78 tff(14883,plain,
% 2.54/2.78 (elem!1 = s(s(s(s(elem!1))))),
% 2.54/2.78 inference(transitivity,[status(thm)],[14882, 14881])).
% 2.54/2.78 tff(14884,plain,
% 2.54/2.78 (~(s(s(s(z))) = elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[1443, 14883])).
% 2.54/2.78 tff(14885,plain,
% 2.54/2.78 (~(elem!1 = s(s(s(z))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[4555, 14884])).
% 2.54/2.78 tff(14886,plain,
% 2.54/2.78 (~r(z, elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[14192, 4012, 14885, 359, 2859])).
% 2.54/2.78 tff(14887,plain,
% 2.54/2.78 (b(z, elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[835, 14886, 2170])).
% 2.54/2.78 tff(14888,plain,
% 2.54/2.78 (~(s(s(z)) = elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[2398, 176, 5331])).
% 2.54/2.78 tff(14889,plain,
% 2.54/2.78 (b(z, s(s(elem!1)))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[13840, 14886, 136])).
% 2.54/2.78 tff(14890,assumption,(~(s(s(s(s(s(s(z)))))) = elem!1)), introduced(assumption)).
% 2.54/2.78 tff(14891,plain,
% 2.54/2.78 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[12954, 2831, 838, 4012, 204])).
% 2.54/2.78 tff(14892,plain,
% 2.54/2.78 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[1144, 14891, 14890])).
% 2.54/2.78 tff(14893,plain,
% 2.54/2.78 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[2862, 124, 2859, 14892])).
% 2.54/2.78 tff(14894,plain,
% 2.54/2.78 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[4603, 43, 14893, 4577])).
% 2.54/2.78 tff(14895,plain,
% 2.54/2.78 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))),
% 2.54/2.78 inference(rewrite,[status(thm)],[])).
% 2.54/2.78 tff(14896,plain,
% 2.54/2.78 (((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))),
% 2.54/2.78 inference(rewrite,[status(thm)],[])).
% 2.54/2.78 tff(14897,plain,
% 2.54/2.78 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z))))),
% 2.54/2.78 inference(monotonicity,[status(thm)],[14896])).
% 2.54/2.78 tff(14898,plain,
% 2.54/2.78 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))),
% 2.54/2.78 inference(transitivity,[status(thm)],[14897, 14895])).
% 2.54/2.78 tff(14899,plain,
% 2.54/2.78 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))),
% 2.54/2.78 inference(quant_inst,[status(thm)],[])).
% 2.54/2.78 tff(14900,plain,
% 2.54/2.78 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z))),
% 2.54/2.78 inference(modus_ponens,[status(thm)],[14899, 14898])).
% 2.54/2.78 tff(14901,plain,
% 2.54/2.78 (~r(s(z), s(s(s(z))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[14900, 124, 205, 204])).
% 2.54/2.78 tff(14902,plain,
% 2.54/2.78 (b(s(z), s(s(s(z))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[3302, 14901])).
% 2.54/2.78 tff(14903,plain,
% 2.54/2.78 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[2896, 306, 12200, 14902, 14894])).
% 2.54/2.78 tff(14904,plain,
% 2.54/2.78 (r(s(s(s(s(s(s(z)))))), s(z))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[651, 43, 2844, 14903])).
% 2.54/2.78 tff(14905,plain,
% 2.54/2.78 ($false),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[2904, 124, 359, 14892, 14904])).
% 2.54/2.78 tff(14906,plain,((~b(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (s(s(s(s(s(s(z)))))) = elem!1) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~r(s(z), z)) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.78 tff(14907,plain,
% 2.54/2.78 (~b(s(z), elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[14906, 204, 2859, 14890, 838, 4012, 359, 205])).
% 2.54/2.78 tff(14908,plain,
% 2.54/2.78 (r(s(z), elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[1500, 43, 14907, 3094])).
% 2.54/2.78 tff(14909,plain,
% 2.54/2.78 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[12213, 14902, 12200, 2859, 14908])).
% 2.54/2.78 tff(14910,plain,
% 2.54/2.78 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[1144, 14909, 14890])).
% 2.54/2.78 tff(14911,plain,
% 2.54/2.78 (~b(s(s(s(s(s(s(z)))))), z)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[12237, 306, 838, 4012, 14910])).
% 2.54/2.78 tff(14912,plain,
% 2.54/2.78 (r(s(s(s(s(s(s(z)))))), z)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[4232, 14911])).
% 2.54/2.78 tff(14913,plain,
% 2.54/2.78 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[4322, 124, 204, 14912])).
% 2.54/2.78 tff(14914,plain,
% 2.54/2.78 (b(s(s(s(s(s(s(z)))))), s(z))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[651, 43, 2844, 14913])).
% 2.54/2.78 tff(14915,plain,
% 2.54/2.78 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[1392, 124, 205, 14912])).
% 2.54/2.78 tff(14916,plain,
% 2.54/2.78 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[4603, 43, 14915, 4577])).
% 2.54/2.78 tff(14917,plain,
% 2.54/2.78 ($false),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[2896, 306, 12200, 14902, 14916, 14914])).
% 2.54/2.78 tff(14918,plain,((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (s(s(s(s(s(s(z)))))) = elem!1) | (~r(s(s(s(z))), elem!1)) | (s(z) = elem!1) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.78 tff(14919,plain,
% 2.54/2.78 (~r(s(z), z)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[14918, 205, 838, 4012, 14890, 2859, 3094, 359])).
% 2.54/2.78 tff(14920,plain,
% 2.54/2.78 (b(s(z), z)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[221, 14919])).
% 2.54/2.78 tff(14921,plain,
% 2.54/2.78 (~b(s(z), elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[12662, 14920, 4012, 838])).
% 2.54/2.78 tff(14922,plain,
% 2.54/2.78 (r(s(z), elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[1500, 43, 14921, 3094])).
% 2.54/2.78 tff(14923,plain,
% 2.54/2.78 (~r(s(z), s(s(s(z))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[3790, 14922, 2859])).
% 2.54/2.78 tff(14924,plain,
% 2.54/2.78 (b(s(z), s(s(s(z))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[3302, 14923])).
% 2.54/2.78 tff(14925,plain,
% 2.54/2.78 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[12213, 14924, 12200, 2859, 14922])).
% 2.54/2.78 tff(14926,plain,
% 2.54/2.78 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[1144, 14925, 14890])).
% 2.54/2.78 tff(14927,plain,
% 2.54/2.78 (~b(s(s(s(s(s(s(z)))))), z)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[12237, 306, 838, 4012, 14926])).
% 2.54/2.78 tff(14928,plain,
% 2.54/2.78 (r(s(s(s(s(s(s(z)))))), z)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[4232, 14927])).
% 2.54/2.78 tff(14929,plain,
% 2.54/2.78 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[1392, 124, 205, 14928])).
% 2.54/2.78 tff(14930,plain,
% 2.54/2.78 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[4603, 43, 14929, 4577])).
% 2.54/2.78 tff(14931,plain,
% 2.54/2.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.54/2.78 inference(rewrite,[status(thm)],[])).
% 2.54/2.78 tff(14932,plain,
% 2.54/2.78 (((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.54/2.78 inference(rewrite,[status(thm)],[])).
% 2.54/2.78 tff(14933,plain,
% 2.54/2.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))))),
% 2.54/2.78 inference(monotonicity,[status(thm)],[14932])).
% 2.54/2.78 tff(14934,plain,
% 2.54/2.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.54/2.78 inference(transitivity,[status(thm)],[14933, 14931])).
% 2.54/2.78 tff(14935,plain,
% 2.54/2.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.54/2.78 inference(quant_inst,[status(thm)],[])).
% 2.54/2.78 tff(14936,plain,
% 2.54/2.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))),
% 2.54/2.78 inference(modus_ponens,[status(thm)],[14935, 14934])).
% 2.54/2.78 tff(14937,plain,
% 2.54/2.78 (~b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[14936, 306, 2284, 8, 2454, 1330])).
% 2.54/2.78 tff(14938,plain,
% 2.54/2.78 (r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[2829, 43, 2826, 14937])).
% 2.54/2.78 tff(14939,plain,
% 2.54/2.78 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[2896, 306, 2284, 8, 1330])).
% 2.54/2.78 tff(14940,plain,
% 2.54/2.78 (r(s(s(s(s(s(s(z)))))), s(z))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[651, 43, 2844, 14939])).
% 2.54/2.78 tff(14941,plain,
% 2.54/2.78 (~b(s(s(z)), s(z))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[10936, 306, 2284, 8, 2454])).
% 2.54/2.78 tff(14942,plain,
% 2.54/2.78 (r(s(s(z)), s(z))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[2476, 14941])).
% 2.54/2.78 tff(14943,plain,
% 2.54/2.78 ($false),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[2853, 124, 14942, 14940, 14938])).
% 2.54/2.78 tff(14944,plain,((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.79 tff(14945,plain,
% 2.54/2.79 (~b(s(s(z)), s(s(s(z))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[14944, 14924, 12200, 14930])).
% 2.54/2.79 tff(14946,plain,
% 2.54/2.79 (r(s(s(z)), s(s(s(z))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[2514, 14945])).
% 2.54/2.79 tff(14947,plain,
% 2.54/2.79 (~(elem!1 = s(s(s(s(s(s(z)))))))),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[14890, 3893])).
% 2.54/2.79 tff(14948,plain,
% 2.54/2.79 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[2896, 306, 12200, 14924, 14930])).
% 2.54/2.79 tff(14949,plain,
% 2.54/2.79 (r(s(s(s(s(s(s(z)))))), s(z))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[651, 43, 2844, 14948])).
% 2.54/2.79 tff(14950,plain,
% 2.54/2.79 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(z)))))))))),
% 2.54/2.79 inference(rewrite,[status(thm)],[])).
% 2.54/2.79 tff(14951,plain,
% 2.54/2.79 (((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(s(s(z))))))))) <=> ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(z)))))))))),
% 2.54/2.79 inference(rewrite,[status(thm)],[])).
% 2.54/2.79 tff(14952,plain,
% 2.54/2.79 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(z))))))))))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[14951])).
% 2.54/2.79 tff(14953,plain,
% 2.54/2.79 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(z)))))))))),
% 2.54/2.79 inference(transitivity,[status(thm)],[14952, 14950])).
% 2.54/2.79 tff(14954,plain,
% 2.54/2.79 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(s(s(z)))))))))),
% 2.54/2.79 inference(quant_inst,[status(thm)],[])).
% 2.54/2.79 tff(14955,plain,
% 2.54/2.79 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(elem!1, s(s(s(s(s(s(z))))))))),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[14954, 14953])).
% 2.54/2.79 tff(14956,plain,
% 2.54/2.79 (~r(elem!1, s(s(s(s(s(s(z)))))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[14955, 124, 359, 14949])).
% 2.54/2.79 tff(14957,plain,
% 2.54/2.79 ((elem!1 = s(s(s(s(s(s(z))))))) | b(elem!1, s(s(s(s(s(s(z)))))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[3921, 43, 14956])).
% 2.54/2.79 tff(14958,plain,
% 2.54/2.79 (b(elem!1, s(s(s(s(s(s(z)))))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[14957, 14947])).
% 2.54/2.79 tff(14959,plain,
% 2.54/2.79 (r(s(s(s(z))), s(s(elem!1))) <=> r(s(s(s(z))), elem!1)),
% 2.54/2.79 inference(monotonicity,[status(thm)],[1171])).
% 2.54/2.79 tff(14960,plain,
% 2.54/2.79 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(elem!1)))),
% 2.54/2.79 inference(symmetry,[status(thm)],[14959])).
% 2.54/2.79 tff(14961,plain,
% 2.54/2.79 (r(s(s(s(z))), s(s(elem!1)))),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[2859, 14960])).
% 2.54/2.79 tff(14962,plain,
% 2.54/2.79 (b(s(s(elem!1)), z) <=> b(elem!1, z)),
% 2.54/2.79 inference(monotonicity,[status(thm)],[1171])).
% 2.54/2.79 tff(14963,plain,
% 2.54/2.79 (b(elem!1, z) <=> b(s(s(elem!1)), z)),
% 2.54/2.79 inference(symmetry,[status(thm)],[14962])).
% 2.54/2.79 tff(14964,plain,
% 2.54/2.79 (b(s(s(elem!1)), z)),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[4012, 14963])).
% 2.54/2.79 tff(14965,plain,
% 2.54/2.79 (~r(s(s(s(s(s(s(z)))))), z)),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[3203, 3195, 205])).
% 2.54/2.79 tff(14966,plain,
% 2.54/2.79 (b(s(s(s(s(s(s(z)))))), s(s(elem!1))) <=> b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.54/2.79 inference(monotonicity,[status(thm)],[1171])).
% 2.54/2.79 tff(14967,plain,
% 2.54/2.79 (b(s(s(s(s(s(s(z)))))), elem!1) <=> b(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 2.54/2.79 inference(symmetry,[status(thm)],[14966])).
% 2.54/2.79 tff(14968,plain,
% 2.54/2.79 (r(s(s(s(s(s(s(z)))))), s(s(elem!1))) <=> r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.54/2.79 inference(monotonicity,[status(thm)],[1171])).
% 2.54/2.79 tff(14969,plain,
% 2.54/2.79 (r(s(s(s(s(s(s(z)))))), elem!1) <=> r(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 2.54/2.79 inference(symmetry,[status(thm)],[14968])).
% 2.54/2.79 tff(14970,plain,
% 2.54/2.79 (r(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[2858, 14969])).
% 2.54/2.79 tff(14971,plain,
% 2.54/2.79 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))))),
% 2.54/2.79 inference(rewrite,[status(thm)],[])).
% 2.54/2.79 tff(14972,plain,
% 2.54/2.79 (((~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))))),
% 2.54/2.79 inference(rewrite,[status(thm)],[])).
% 2.54/2.79 tff(14973,plain,
% 2.54/2.79 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1))))))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[14972])).
% 2.54/2.79 tff(14974,plain,
% 2.54/2.79 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))))),
% 2.54/2.79 inference(transitivity,[status(thm)],[14973, 14971])).
% 2.54/2.79 tff(14975,plain,
% 2.54/2.79 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 2.54/2.79 inference(quant_inst,[status(thm)],[])).
% 2.54/2.79 tff(14976,plain,
% 2.54/2.79 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1))))),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[14975, 14974])).
% 2.54/2.79 tff(14977,plain,
% 2.54/2.79 (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[14976, 124, 14532, 3195])).
% 2.54/2.79 tff(14978,plain,
% 2.54/2.79 ($false),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[14977, 14970])).
% 2.54/2.79 tff(14979,plain,((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~(s(s(elem!1)) = elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.79 tff(14980,plain,
% 2.54/2.79 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[14979, 3195, 14532, 1171])).
% 2.54/2.79 tff(14981,plain,
% 2.54/2.79 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[1144, 14980, 14890])).
% 2.54/2.79 tff(14982,plain,
% 2.54/2.79 (b(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[14981, 14967])).
% 2.54/2.79 tff(14983,plain,
% 2.54/2.79 (((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))))),
% 2.54/2.79 inference(rewrite,[status(thm)],[])).
% 2.54/2.79 tff(14984,plain,
% 2.54/2.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1))))))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[14983])).
% 2.54/2.79 tff(14985,plain,
% 2.54/2.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))))),
% 2.54/2.79 inference(transitivity,[status(thm)],[14984, 9763])).
% 2.54/2.79 tff(14986,plain,
% 2.54/2.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 2.54/2.79 inference(quant_inst,[status(thm)],[])).
% 2.54/2.79 tff(14987,plain,
% 2.54/2.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1))))),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[14986, 14985])).
% 2.54/2.79 tff(14988,plain,
% 2.54/2.79 ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[14987, 306, 1198, 3968])).
% 2.54/2.79 tff(14989,plain,
% 2.54/2.79 (~b(s(s(s(s(s(s(z)))))), z)),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[14988, 14982])).
% 2.54/2.79 tff(14990,plain,
% 2.54/2.79 ($false),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[856, 43, 554, 14989, 14965])).
% 2.54/2.79 tff(14991,plain,((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~(s(s(elem!1)) = elem!1)) | (s(s(s(s(s(s(z)))))) = elem!1) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.79 tff(14992,plain,
% 2.54/2.79 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[14991, 205, 1171, 14964, 14890, 14961, 1198])).
% 2.54/2.79 tff(14993,plain,
% 2.54/2.79 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[3207, 14992])).
% 2.54/2.79 tff(14994,plain,
% 2.54/2.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(z)))))))))),
% 2.54/2.79 inference(rewrite,[status(thm)],[])).
% 2.54/2.79 tff(14995,plain,
% 2.54/2.79 (((~b(elem!1, z)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(z)))))))))),
% 2.54/2.79 inference(rewrite,[status(thm)],[])).
% 2.54/2.79 tff(14996,plain,
% 2.54/2.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(z))))))))))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[14995])).
% 2.54/2.79 tff(14997,plain,
% 2.54/2.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(z)))))))))),
% 2.54/2.79 inference(transitivity,[status(thm)],[14996, 14994])).
% 2.54/2.79 tff(14998,plain,
% 2.54/2.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(z))))))),
% 2.54/2.79 inference(quant_inst,[status(thm)],[])).
% 2.54/2.79 tff(14999,plain,
% 2.54/2.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(z))))))))),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[14998, 14997])).
% 2.54/2.79 tff(15000,plain,
% 2.54/2.79 (~b(elem!1, s(s(s(z))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[14999, 306, 4012, 14926, 14993, 14958])).
% 2.54/2.79 tff(15001,plain,
% 2.54/2.79 (r(elem!1, s(s(s(z))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[2304, 15000, 2301])).
% 2.54/2.79 tff(15002,plain,
% 2.54/2.79 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), elem!1)))),
% 2.54/2.79 inference(rewrite,[status(thm)],[])).
% 2.54/2.79 tff(15003,plain,
% 2.54/2.79 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), elem!1)))),
% 2.54/2.79 inference(quant_inst,[status(thm)],[])).
% 2.54/2.79 tff(15004,plain,
% 2.54/2.79 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), elem!1))),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[15003, 15002])).
% 2.54/2.79 tff(15005,plain,
% 2.54/2.79 (~r(s(s(z)), elem!1)),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[15004, 124, 15001, 14946])).
% 2.54/2.79 tff(15006,plain,
% 2.54/2.79 (b(s(s(z)), elem!1)),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[5555, 15005, 176, 14888])).
% 2.54/2.79 tff(15007,plain,
% 2.54/2.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 2.54/2.79 inference(rewrite,[status(thm)],[])).
% 2.54/2.79 tff(15008,plain,
% 2.54/2.79 (((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(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(s(z))))))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 2.54/2.79 inference(rewrite,[status(thm)],[])).
% 2.54/2.79 tff(15009,plain,
% 2.54/2.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(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(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[15008])).
% 2.54/2.79 tff(15010,plain,
% 2.54/2.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(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(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 2.54/2.79 inference(transitivity,[status(thm)],[15009, 15007])).
% 2.54/2.79 tff(15011,plain,
% 2.54/2.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(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(s(z)))))))))),
% 2.54/2.79 inference(quant_inst,[status(thm)],[])).
% 2.54/2.79 tff(15012,plain,
% 2.54/2.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[15011, 15010])).
% 2.54/2.79 tff(15013,plain,
% 2.54/2.79 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[15012, 306, 12200, 14924, 14930])).
% 2.54/2.79 tff(15014,plain,
% 2.54/2.79 (r(s(z), s(s(s(s(s(s(z)))))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[5358, 43, 5355, 15013])).
% 2.54/2.79 tff(15015,plain,
% 2.54/2.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 2.54/2.79 inference(rewrite,[status(thm)],[])).
% 2.54/2.79 tff(15016,plain,
% 2.54/2.79 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(s(z))))))))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 2.54/2.79 inference(rewrite,[status(thm)],[])).
% 2.54/2.79 tff(15017,plain,
% 2.54/2.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1))))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[15016])).
% 2.54/2.79 tff(15018,plain,
% 2.54/2.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 2.54/2.79 inference(transitivity,[status(thm)],[15017, 15015])).
% 2.54/2.79 tff(15019,plain,
% 2.54/2.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 2.54/2.79 inference(quant_inst,[status(thm)],[])).
% 2.54/2.79 tff(15020,plain,
% 2.54/2.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1))),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[15019, 15018])).
% 2.54/2.79 tff(15021,plain,
% 2.54/2.79 (~b(z, s(s(s(s(s(s(z)))))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[15020, 306, 838, 4012, 14926])).
% 2.54/2.79 tff(15022,plain,
% 2.54/2.79 ((z = s(s(s(s(s(s(z))))))) | r(z, s(s(s(s(s(s(z)))))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[5445, 43, 15021])).
% 2.54/2.79 tff(15023,plain,
% 2.54/2.79 (r(z, s(s(s(s(s(s(z)))))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[15022, 5435])).
% 2.54/2.79 tff(15024,plain,
% 2.54/2.79 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 2.54/2.79 inference(rewrite,[status(thm)],[])).
% 2.54/2.79 tff(15025,plain,
% 2.54/2.79 (((~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 2.54/2.79 inference(rewrite,[status(thm)],[])).
% 2.54/2.79 tff(15026,plain,
% 2.54/2.79 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z))))))))))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[15025])).
% 2.54/2.79 tff(15027,plain,
% 2.54/2.79 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 2.54/2.79 inference(transitivity,[status(thm)],[15026, 15024])).
% 2.54/2.79 tff(15028,plain,
% 2.54/2.79 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(z))))),
% 2.54/2.79 inference(quant_inst,[status(thm)],[])).
% 2.54/2.79 tff(15029,plain,
% 2.54/2.79 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z))))))))),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[15028, 15027])).
% 2.54/2.79 tff(15030,plain,
% 2.54/2.79 (~r(z, s(z))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[15029, 124, 15023, 15014])).
% 2.54/2.79 tff(15031,plain,
% 2.54/2.79 (b(z, s(z))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[2263, 15030])).
% 2.54/2.79 tff(15032,plain,
% 2.54/2.79 (~b(z, s(s(s(z))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[2298, 306, 12200, 14924, 15031])).
% 2.54/2.79 tff(15033,plain,
% 2.54/2.79 ((z = s(s(s(z)))) | r(z, s(s(s(z))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[2415, 43, 15032])).
% 2.54/2.79 tff(15034,plain,
% 2.54/2.79 (r(z, s(s(s(z))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[15033, 3385])).
% 2.54/2.79 tff(15035,plain,
% 2.54/2.79 (~r(s(s(z)), z)),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[2523, 14946, 15034])).
% 2.54/2.79 tff(15036,plain,
% 2.54/2.79 (b(s(s(z)), z)),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[2531, 15035])).
% 2.54/2.79 tff(15037,plain,
% 2.54/2.79 ($false),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[12229, 306, 838, 4012, 15036, 15006])).
% 2.54/2.79 tff(15038,plain,((~r(s(s(s(z))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~(s(elem!1) = elem!1)) | (elem!1 = s(s(s(z)))) | (s(s(s(s(s(s(z)))))) = elem!1) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (s(z) = elem!1) | (~(s(s(elem!1)) = elem!1)) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.79 tff(15039,plain,
% 2.54/2.79 (~r(s(s(s(z))), z)),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[15038, 14887, 4012, 176, 14885, 14879, 359, 2859, 3094, 13835, 14889])).
% 2.54/2.79 tff(15040,plain,
% 2.54/2.79 (b(s(s(s(z))), z)),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[2197, 15039])).
% 2.54/2.79 tff(15041,plain,
% 2.54/2.79 (~b(elem!1, s(s(s(z))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[14672, 306, 14887, 4012, 15040])).
% 2.54/2.79 tff(15042,plain,
% 2.54/2.80 (r(elem!1, s(s(s(z))))),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[2304, 15041, 14885])).
% 2.54/2.80 tff(15043,plain,
% 2.54/2.80 (~r(s(z), s(s(s(z))))),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[3293, 15042, 359])).
% 2.54/2.80 tff(15044,plain,
% 2.54/2.80 (b(s(z), s(s(s(z))))),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[3302, 15043])).
% 2.54/2.80 tff(15045,plain,
% 2.54/2.80 (~r(s(s(z)), elem!1)),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[12202, 15044, 2859, 359])).
% 2.54/2.80 tff(15046,plain,
% 2.54/2.80 (b(s(s(z)), elem!1)),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[5555, 15045, 176, 14888])).
% 2.54/2.80 tff(15047,plain,
% 2.54/2.80 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[12244, 15046, 4012, 14887])).
% 2.54/2.80 tff(15048,plain,
% 2.54/2.80 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[1144, 15047, 14879])).
% 2.54/2.80 tff(15049,plain,
% 2.54/2.80 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[2862, 124, 2859, 15048])).
% 2.54/2.80 tff(15050,plain,
% 2.54/2.80 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[4603, 43, 15049, 4577])).
% 2.64/2.80 tff(15051,plain,
% 2.64/2.80 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[2896, 306, 12200, 15044, 15050])).
% 2.64/2.80 tff(15052,plain,
% 2.64/2.80 (r(s(s(s(s(s(s(z)))))), s(z))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[651, 43, 2844, 15051])).
% 2.64/2.80 tff(15053,plain,
% 2.64/2.80 ($false),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[2904, 124, 359, 15048, 15052])).
% 2.64/2.80 tff(15054,plain,((~b(elem!1, z)) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~(s(elem!1) = elem!1)) | (s(z) = elem!1) | (~(s(s(s(elem!1))) = s(elem!1))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.64/2.80 tff(15055,plain,
% 2.64/2.80 (~r(s(s(s(z))), elem!1)),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[15054, 14871, 14047, 4287, 8965, 136, 14048])).
% 2.64/2.80 tff(15056,plain,
% 2.64/2.80 (elem!1 = s(elem!1)),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[2571, 14871])).
% 2.64/2.80 tff(15057,plain,
% 2.64/2.80 (r(s(s(s(z))), s(elem!1)) <=> r(s(s(s(z))), elem!1)),
% 2.64/2.80 inference(monotonicity,[status(thm)],[362])).
% 2.64/2.80 tff(15058,plain,
% 2.64/2.80 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(elem!1))),
% 2.64/2.80 inference(symmetry,[status(thm)],[15057])).
% 2.64/2.80 tff(15059,plain,
% 2.64/2.80 ((~r(s(s(s(z))), elem!1)) <=> (~r(s(s(s(z))), s(elem!1)))),
% 2.64/2.80 inference(monotonicity,[status(thm)],[15058])).
% 2.64/2.80 tff(15060,plain,
% 2.64/2.80 (~r(s(s(s(z))), s(elem!1))),
% 2.64/2.80 inference(modus_ponens,[status(thm)],[1484, 15059])).
% 2.64/2.80 tff(15061,plain,
% 2.64/2.80 ((s(s(s(z))) = s(elem!1)) <=> (s(s(s(z))) = s(s(elem!1)))),
% 2.64/2.80 inference(monotonicity,[status(thm)],[2580])).
% 2.64/2.80 tff(15062,plain,
% 2.64/2.80 ((s(s(s(z))) = s(elem!1)) <=> (s(s(elem!1)) = s(s(s(z))))),
% 2.64/2.80 inference(transitivity,[status(thm)],[15061, 7094])).
% 2.64/2.80 tff(15063,plain,
% 2.64/2.80 ((s(s(elem!1)) = s(s(s(z)))) <=> (s(s(s(z))) = s(elem!1))),
% 2.64/2.80 inference(symmetry,[status(thm)],[15062])).
% 2.64/2.80 tff(15064,plain,
% 2.64/2.80 ((~(s(s(elem!1)) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(elem!1)))),
% 2.64/2.80 inference(monotonicity,[status(thm)],[15063])).
% 2.64/2.80 tff(15065,plain,
% 2.64/2.80 (~(s(s(s(z))) = s(elem!1))),
% 2.64/2.80 inference(modus_ponens,[status(thm)],[16, 15064])).
% 2.64/2.80 tff(15066,plain,
% 2.64/2.80 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(z))), elem!1)),
% 2.64/2.80 inference(monotonicity,[status(thm)],[362])).
% 2.64/2.80 tff(15067,plain,
% 2.64/2.80 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(elem!1))),
% 2.64/2.80 inference(symmetry,[status(thm)],[15066])).
% 2.64/2.80 tff(15068,plain,
% 2.64/2.80 ((~b(s(s(s(z))), elem!1)) <=> (~b(s(s(s(z))), s(elem!1)))),
% 2.64/2.80 inference(monotonicity,[status(thm)],[15067])).
% 2.64/2.80 tff(15069,plain,
% 2.64/2.80 (~b(s(s(s(z))), s(elem!1))),
% 2.64/2.80 inference(modus_ponens,[status(thm)],[1, 15068])).
% 2.64/2.80 tff(15070,plain,
% 2.64/2.80 ((s(s(s(z))) = s(elem!1)) | b(s(s(s(z))), s(elem!1)) | r(s(s(s(z))), s(elem!1))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[4132, 43])).
% 2.64/2.80 tff(15071,plain,
% 2.64/2.80 ($false),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[15070, 15069, 15065, 15060])).
% 2.64/2.80 tff(15072,plain,(r(s(s(s(z))), elem!1) | (~(elem!1 = s(elem!1))) | b(s(s(s(z))), elem!1) | (s(s(elem!1)) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.80 tff(15073,plain,
% 2.64/2.80 (b(s(s(s(z))), elem!1)),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[15072, 15056, 15055, 14842])).
% 2.64/2.80 tff(15074,plain,
% 2.64/2.80 (~b(s(s(s(z))), z)),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[2228, 15073, 13280, 838])).
% 2.64/2.80 tff(15075,plain,
% 2.64/2.80 (r(s(s(s(z))), z)),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[2197, 15074])).
% 2.64/2.80 tff(15076,plain,
% 2.64/2.80 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[12298, 15073, 14047, 838])).
% 2.64/2.80 tff(15077,plain,
% 2.64/2.80 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[4289, 15073, 13280, 6, 838, 87, 15076, 5])).
% 2.64/2.80 tff(15078,plain,
% 2.64/2.80 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[1144, 15076, 14843])).
% 2.64/2.80 tff(15079,assumption,(~r(s(s(s(s(s(s(z)))))), s(z))), introduced(assumption)).
% 2.64/2.80 tff(15080,plain,
% 2.64/2.80 (b(s(s(s(s(s(s(z)))))), s(z))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[651, 43, 2844, 15079])).
% 2.64/2.80 tff(15081,plain,
% 2.64/2.80 (b(s(z), s(s(s(s(z)))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[5135, 11730])).
% 2.64/2.80 tff(15082,plain,
% 2.64/2.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.64/2.80 inference(rewrite,[status(thm)],[])).
% 2.64/2.80 tff(15083,plain,
% 2.64/2.80 (((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.64/2.80 inference(rewrite,[status(thm)],[])).
% 2.64/2.80 tff(15084,plain,
% 2.64/2.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 2.64/2.80 inference(monotonicity,[status(thm)],[15083])).
% 2.64/2.80 tff(15085,plain,
% 2.64/2.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.64/2.80 inference(transitivity,[status(thm)],[15084, 15082])).
% 2.64/2.80 tff(15086,plain,
% 2.64/2.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.64/2.80 inference(quant_inst,[status(thm)],[])).
% 2.64/2.80 tff(15087,plain,
% 2.64/2.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 2.64/2.80 inference(modus_ponens,[status(thm)],[15086, 15085])).
% 2.64/2.80 tff(15088,plain,
% 2.64/2.80 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[15087, 306, 12315, 15081, 3620, 15080])).
% 2.64/2.80 tff(15089,plain,
% 2.64/2.80 (r(s(s(s(s(z)))), elem!1)),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[9832, 12316, 9815])).
% 2.64/2.80 tff(15090,plain,
% 2.64/2.80 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[14263, 124, 2858, 15089])).
% 2.64/2.80 tff(15091,plain,
% 2.64/2.80 ($false),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[10662, 15090, 15088])).
% 2.64/2.80 tff(15092,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (s(s(s(s(z)))) = elem!1) | (~r(s(z), s(s(s(z))))) | r(s(s(s(s(s(s(z)))))), s(z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.80 tff(15093,plain,
% 2.64/2.80 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[15092, 15078, 3620, 14837, 1034, 15077, 838, 14047, 15075])).
% 2.64/2.80 tff(15094,plain,
% 2.64/2.80 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[4471, 15093])).
% 2.64/2.80 tff(15095,plain,
% 2.64/2.80 (b(s(s(s(s(s(s(z)))))), s(z))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[651, 43, 2844, 15077])).
% 2.64/2.80 tff(15096,plain,
% 2.64/2.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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)))),
% 2.64/2.80 inference(rewrite,[status(thm)],[])).
% 2.64/2.80 tff(15097,plain,
% 2.64/2.80 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.64/2.80 inference(rewrite,[status(thm)],[])).
% 2.64/2.80 tff(15098,plain,
% 2.64/2.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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))))),
% 2.64/2.80 inference(monotonicity,[status(thm)],[15097])).
% 2.64/2.80 tff(15099,plain,
% 2.64/2.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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)))),
% 2.64/2.80 inference(transitivity,[status(thm)],[15098, 15096])).
% 2.64/2.80 tff(15100,plain,
% 2.64/2.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.64/2.80 inference(quant_inst,[status(thm)],[])).
% 2.64/2.80 tff(15101,plain,
% 2.64/2.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(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))),
% 2.64/2.80 inference(modus_ponens,[status(thm)],[15100, 15099])).
% 2.64/2.80 tff(15102,plain,
% 2.64/2.80 (~b(s(s(s(s(z)))), elem!1)),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[15101, 306, 393, 1470, 762])).
% 2.64/2.80 tff(15103,plain,
% 2.64/2.80 (r(s(s(s(s(z)))), elem!1)),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[9832, 15102, 9815])).
% 2.64/2.80 tff(15104,plain,
% 2.64/2.80 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.64/2.80 inference(rewrite,[status(thm)],[])).
% 2.64/2.80 tff(15105,plain,
% 2.64/2.80 (((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.64/2.80 inference(rewrite,[status(thm)],[])).
% 2.64/2.80 tff(15106,plain,
% 2.64/2.80 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1))))),
% 2.64/2.80 inference(monotonicity,[status(thm)],[15105])).
% 2.64/2.80 tff(15107,plain,
% 2.64/2.80 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.64/2.80 inference(transitivity,[status(thm)],[15106, 15104])).
% 2.64/2.80 tff(15108,plain,
% 2.64/2.80 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 2.64/2.80 inference(quant_inst,[status(thm)],[])).
% 2.64/2.80 tff(15109,plain,
% 2.64/2.80 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1))),
% 2.64/2.80 inference(modus_ponens,[status(thm)],[15108, 15107])).
% 2.64/2.80 tff(15110,plain,
% 2.64/2.80 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[15109, 124, 2858, 15103])).
% 2.64/2.80 tff(15111,plain,
% 2.64/2.80 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[13486, 15110])).
% 2.64/2.80 tff(15112,plain,
% 2.64/2.80 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[14263, 124, 2858, 15103])).
% 2.64/2.80 tff(15113,plain,
% 2.64/2.80 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[10662, 15112])).
% 2.64/2.80 tff(15114,plain,
% 2.64/2.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.64/2.80 inference(rewrite,[status(thm)],[])).
% 2.64/2.80 tff(15115,plain,
% 2.64/2.80 (((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.64/2.80 inference(rewrite,[status(thm)],[])).
% 2.64/2.80 tff(15116,plain,
% 2.64/2.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 2.64/2.80 inference(monotonicity,[status(thm)],[15115])).
% 2.64/2.80 tff(15117,plain,
% 2.64/2.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.64/2.80 inference(transitivity,[status(thm)],[15116, 15114])).
% 2.64/2.80 tff(15118,plain,
% 2.64/2.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 2.64/2.80 inference(quant_inst,[status(thm)],[])).
% 2.64/2.80 tff(15119,plain,
% 2.64/2.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 2.64/2.80 inference(modus_ponens,[status(thm)],[15118, 15117])).
% 2.64/2.80 tff(15120,plain,
% 2.64/2.80 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[15119, 306, 393, 4247, 15113, 15111])).
% 2.64/2.80 tff(15121,plain,
% 2.64/2.80 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[4603, 43, 15120, 4577])).
% 2.64/2.80 tff(15122,plain,
% 2.64/2.80 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[5347, 124, 1034, 15121])).
% 2.64/2.80 tff(15123,plain,
% 2.64/2.80 (b(s(z), s(s(s(s(s(s(z)))))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[5358, 43, 5355, 15122])).
% 2.64/2.80 tff(15124,plain,
% 2.64/2.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 2.64/2.80 inference(rewrite,[status(thm)],[])).
% 2.64/2.80 tff(15125,plain,
% 2.64/2.80 (((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 2.64/2.80 inference(rewrite,[status(thm)],[])).
% 2.64/2.80 tff(15126,plain,
% 2.64/2.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[15125])).
% 2.64/2.81 tff(15127,plain,
% 2.64/2.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 2.64/2.81 inference(transitivity,[status(thm)],[15126, 15124])).
% 2.64/2.81 tff(15128,plain,
% 2.64/2.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.64/2.81 inference(quant_inst,[status(thm)],[])).
% 2.64/2.81 tff(15129,plain,
% 2.64/2.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 2.64/2.81 inference(modus_ponens,[status(thm)],[15128, 15127])).
% 2.64/2.81 tff(15130,plain,
% 2.64/2.81 ($false),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[15129, 306, 3620, 15123, 4247, 15111])).
% 2.64/2.81 tff(15131,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (s(s(s(s(z)))) = elem!1) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.81 tff(15132,plain,
% 2.64/2.81 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[15131, 15095, 3620, 1034, 15078, 14837, 13280, 15094])).
% 2.64/2.81 tff(15133,plain,
% 2.64/2.81 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[10124, 15132])).
% 2.64/2.81 tff(15134,plain,
% 2.64/2.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 2.64/2.81 inference(rewrite,[status(thm)],[])).
% 2.64/2.81 tff(15135,plain,
% 2.64/2.81 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 2.64/2.81 inference(rewrite,[status(thm)],[])).
% 2.64/2.81 tff(15136,plain,
% 2.64/2.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(z))))))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[15135])).
% 2.64/2.81 tff(15137,plain,
% 2.64/2.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 2.64/2.81 inference(transitivity,[status(thm)],[15136, 15134])).
% 2.64/2.81 tff(15138,plain,
% 2.64/2.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.64/2.81 inference(quant_inst,[status(thm)],[])).
% 2.64/2.81 tff(15139,plain,
% 2.64/2.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(z))))),
% 2.64/2.81 inference(modus_ponens,[status(thm)],[15138, 15137])).
% 2.64/2.81 tff(15140,plain,
% 2.64/2.81 ($false),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[15139, 306, 2284, 13651, 5097, 762, 3620])).
% 2.64/2.81 tff(15141,plain,((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.81 tff(15142,plain,
% 2.64/2.81 (~b(s(z), s(s(z)))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[15141, 762, 13651, 2284, 3620])).
% 2.64/2.81 tff(15143,plain,
% 2.64/2.81 (r(s(z), s(s(z)))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[4434, 15142])).
% 2.64/2.81 tff(15144,assumption,(r(s(z), s(s(z)))), introduced(assumption)).
% 2.64/2.81 tff(15145,assumption,(r(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 2.64/2.81 tff(15146,plain,
% 2.64/2.81 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))))),
% 2.64/2.81 inference(rewrite,[status(thm)],[])).
% 2.64/2.81 tff(15147,plain,
% 2.64/2.81 (((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))))),
% 2.64/2.81 inference(rewrite,[status(thm)],[])).
% 2.64/2.81 tff(15148,plain,
% 2.64/2.81 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z))))))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[15147])).
% 2.64/2.81 tff(15149,plain,
% 2.64/2.81 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))))),
% 2.64/2.81 inference(transitivity,[status(thm)],[15148, 15146])).
% 2.64/2.81 tff(15150,plain,
% 2.64/2.81 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))))),
% 2.64/2.81 inference(quant_inst,[status(thm)],[])).
% 2.64/2.81 tff(15151,plain,
% 2.64/2.81 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z))))),
% 2.64/2.81 inference(modus_ponens,[status(thm)],[15150, 15149])).
% 2.64/2.81 tff(15152,plain,
% 2.64/2.81 ($false),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[15151, 124, 1034, 15145, 15144])).
% 2.64/2.81 tff(15153,plain,((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.81 tff(15154,plain,
% 2.64/2.81 (~r(s(s(s(z))), s(s(z)))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[15153, 15143, 1034])).
% 2.64/2.81 tff(15155,plain,
% 2.64/2.81 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(z)))),
% 2.64/2.81 inference(symmetry,[status(thm)],[11691])).
% 2.64/2.81 tff(15156,plain,
% 2.64/2.81 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(z))))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[15155])).
% 2.64/2.81 tff(15157,plain,
% 2.64/2.81 (~(s(s(s(z))) = s(s(z)))),
% 2.64/2.81 inference(modus_ponens,[status(thm)],[2508, 15156])).
% 2.64/2.81 tff(15158,plain,
% 2.64/2.81 (((~![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))))),
% 2.64/2.81 inference(rewrite,[status(thm)],[])).
% 2.64/2.81 tff(15159,plain,
% 2.64/2.81 ((~![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))))),
% 2.64/2.81 inference(quant_inst,[status(thm)],[])).
% 2.64/2.81 tff(15160,plain,
% 2.64/2.81 ((~![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)))),
% 2.64/2.81 inference(modus_ponens,[status(thm)],[15159, 15158])).
% 2.64/2.81 tff(15161,plain,
% 2.64/2.81 ((s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z)))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[15160, 43])).
% 2.64/2.81 tff(15162,plain,
% 2.64/2.81 (b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z)))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[15161, 15157])).
% 2.64/2.81 tff(15163,plain,
% 2.64/2.81 (b(s(s(s(z))), s(s(z)))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[15162, 15154])).
% 2.64/2.81 tff(15164,plain,
% 2.64/2.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(z)))))),
% 2.64/2.81 inference(rewrite,[status(thm)],[])).
% 2.64/2.81 tff(15165,plain,
% 2.64/2.81 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(z)))))),
% 2.64/2.81 inference(rewrite,[status(thm)],[])).
% 2.64/2.81 tff(15166,plain,
% 2.64/2.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(z))))))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[15165])).
% 2.64/2.81 tff(15167,plain,
% 2.64/2.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(z)))))),
% 2.64/2.81 inference(transitivity,[status(thm)],[15166, 15164])).
% 2.64/2.81 tff(15168,plain,
% 2.64/2.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), 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)))),
% 2.64/2.81 inference(quant_inst,[status(thm)],[])).
% 2.64/2.81 tff(15169,plain,
% 2.64/2.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(z))))),
% 2.64/2.81 inference(modus_ponens,[status(thm)],[15168, 15167])).
% 2.64/2.81 tff(15170,plain,
% 2.64/2.81 (~b(s(s(s(s(z)))), elem!1)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[15169, 306, 13651, 1470, 762, 15163])).
% 2.64/2.81 tff(15171,plain,
% 2.64/2.81 (r(s(s(s(s(z)))), elem!1)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[9832, 15170, 9815])).
% 2.64/2.81 tff(15172,plain,
% 2.64/2.81 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[14263, 124, 2858, 15171])).
% 2.64/2.81 tff(15173,plain,
% 2.64/2.81 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[10662, 15172])).
% 2.64/2.81 tff(15174,plain,
% 2.64/2.81 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[15109, 124, 2858, 15171])).
% 2.64/2.81 tff(15175,plain,
% 2.64/2.81 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[13486, 15174])).
% 2.64/2.81 tff(15176,plain,
% 2.64/2.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 2.64/2.81 inference(rewrite,[status(thm)],[])).
% 2.64/2.81 tff(15177,plain,
% 2.64/2.81 (((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 2.64/2.81 inference(rewrite,[status(thm)],[])).
% 2.64/2.81 tff(15178,plain,
% 2.64/2.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[15177])).
% 2.64/2.81 tff(15179,plain,
% 2.64/2.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 2.64/2.81 inference(transitivity,[status(thm)],[15178, 15176])).
% 2.64/2.81 tff(15180,plain,
% 2.64/2.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 2.64/2.81 inference(quant_inst,[status(thm)],[])).
% 2.64/2.81 tff(15181,plain,
% 2.64/2.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))),
% 2.64/2.81 inference(modus_ponens,[status(thm)],[15180, 15179])).
% 2.64/2.81 tff(15182,plain,
% 2.64/2.81 (~b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[15181, 306, 13651, 15173, 15175])).
% 2.64/2.81 tff(15183,plain,
% 2.64/2.81 ((s(s(s(s(s(s(z)))))) = s(s(z))) | r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[4317, 43, 15182])).
% 2.64/2.81 tff(15184,plain,
% 2.64/2.81 (r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[15183, 4310])).
% 2.64/2.81 tff(15185,plain,
% 2.64/2.81 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 2.64/2.81 inference(rewrite,[status(thm)],[])).
% 2.64/2.81 tff(15186,plain,
% 2.64/2.81 (((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(z))))))))) <=> ((~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 2.64/2.81 inference(rewrite,[status(thm)],[])).
% 2.64/2.81 tff(15187,plain,
% 2.64/2.81 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z))))))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[15186])).
% 2.64/2.81 tff(15188,plain,
% 2.64/2.81 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 2.64/2.81 inference(transitivity,[status(thm)],[15187, 15185])).
% 2.64/2.81 tff(15189,plain,
% 2.64/2.81 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 2.64/2.81 inference(quant_inst,[status(thm)],[])).
% 2.64/2.81 tff(15190,plain,
% 2.64/2.81 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z))))),
% 2.64/2.81 inference(modus_ponens,[status(thm)],[15189, 15188])).
% 2.64/2.81 tff(15191,plain,
% 2.64/2.81 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[15190, 124, 15143, 15184])).
% 2.64/2.81 tff(15192,plain,
% 2.64/2.81 (b(s(z), s(s(s(s(s(s(z)))))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[5358, 43, 5355, 15191])).
% 2.64/2.81 tff(15193,plain,
% 2.64/2.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.64/2.81 inference(rewrite,[status(thm)],[])).
% 2.64/2.81 tff(15194,plain,
% 2.64/2.81 (((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.64/2.81 inference(rewrite,[status(thm)],[])).
% 2.64/2.81 tff(15195,plain,
% 2.64/2.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 2.64/2.82 inference(monotonicity,[status(thm)],[15194])).
% 2.64/2.82 tff(15196,plain,
% 2.64/2.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.64/2.82 inference(transitivity,[status(thm)],[15195, 15193])).
% 2.64/2.82 tff(15197,plain,
% 2.64/2.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.64/2.82 inference(quant_inst,[status(thm)],[])).
% 2.64/2.82 tff(15198,plain,
% 2.64/2.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 2.64/2.82 inference(modus_ponens,[status(thm)],[15197, 15196])).
% 2.64/2.82 tff(15199,plain,
% 2.64/2.82 ($false),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[15198, 306, 3620, 15192, 15080, 15173])).
% 2.64/2.82 tff(15200,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | r(s(s(s(s(s(s(z)))))), s(z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (s(s(s(s(z)))) = elem!1) | (~b(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.82 tff(15201,plain,
% 2.64/2.82 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[15200, 15094, 15077, 3620, 15078, 14837, 13280, 1034, 2284])).
% 2.64/2.82 tff(15202,plain,
% 2.64/2.82 (r(s(s(z)), s(s(s(s(z)))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[4510, 15201])).
% 2.64/2.82 tff(15203,plain,
% 2.64/2.82 (~r(s(s(s(z))), s(s(z)))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[13667, 124, 15202, 15133])).
% 2.64/2.82 tff(15204,plain,
% 2.64/2.82 (b(s(s(s(z))), s(s(z)))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[15162, 15203])).
% 2.64/2.82 tff(15205,plain,
% 2.64/2.82 (~r(s(s(z)), s(s(s(z))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[13448, 124, 15202, 15133])).
% 2.64/2.82 tff(15206,plain,
% 2.64/2.82 (b(s(s(z)), s(s(s(z))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[2514, 15205])).
% 2.64/2.82 tff(15207,plain,
% 2.64/2.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(z)))))),
% 2.64/2.82 inference(rewrite,[status(thm)],[])).
% 2.64/2.82 tff(15208,plain,
% 2.64/2.82 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(z)))))),
% 2.64/2.82 inference(rewrite,[status(thm)],[])).
% 2.64/2.82 tff(15209,plain,
% 2.64/2.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(z))))))),
% 2.64/2.82 inference(monotonicity,[status(thm)],[15208])).
% 2.64/2.82 tff(15210,plain,
% 2.64/2.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(z)))))),
% 2.64/2.82 inference(transitivity,[status(thm)],[15209, 15207])).
% 2.64/2.82 tff(15211,plain,
% 2.64/2.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.64/2.82 inference(quant_inst,[status(thm)],[])).
% 2.64/2.82 tff(15212,plain,
% 2.64/2.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(z))))),
% 2.64/2.82 inference(modus_ponens,[status(thm)],[15211, 15210])).
% 2.64/2.82 tff(15213,plain,
% 2.64/2.82 (~b(s(s(s(s(z)))), elem!1)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[15212, 306, 13280, 15206, 15094, 15204])).
% 2.64/2.82 tff(15214,plain,
% 2.64/2.82 (r(s(s(s(s(z)))), elem!1)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[9832, 15213, 14837])).
% 2.64/2.82 tff(15215,plain,
% 2.64/2.82 (~(s(s(z)) = elem!1)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[2398, 14871, 87])).
% 2.64/2.82 tff(15216,plain,
% 2.64/2.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))))),
% 2.64/2.82 inference(rewrite,[status(thm)],[])).
% 2.64/2.82 tff(15217,plain,
% 2.64/2.82 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1))) <=> ((~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))))),
% 2.64/2.82 inference(rewrite,[status(thm)],[])).
% 2.64/2.82 tff(15218,plain,
% 2.64/2.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z))))))),
% 2.64/2.82 inference(monotonicity,[status(thm)],[15217])).
% 2.64/2.82 tff(15219,plain,
% 2.64/2.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))))),
% 2.64/2.82 inference(transitivity,[status(thm)],[15218, 15216])).
% 2.64/2.82 tff(15220,plain,
% 2.64/2.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 2.64/2.82 inference(quant_inst,[status(thm)],[])).
% 2.64/2.82 tff(15221,plain,
% 2.64/2.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z))))),
% 2.64/2.82 inference(modus_ponens,[status(thm)],[15220, 15219])).
% 2.64/2.82 tff(15222,plain,
% 2.64/2.82 (~b(s(s(z)), elem!1)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[15221, 306, 13280, 15206, 15204])).
% 2.64/2.82 tff(15223,plain,
% 2.64/2.82 (r(s(s(z)), elem!1)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[2545, 15222, 15215])).
% 2.64/2.82 tff(15224,plain,
% 2.64/2.82 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.64/2.82 inference(rewrite,[status(thm)],[])).
% 2.64/2.82 tff(15225,plain,
% 2.64/2.82 (((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.64/2.82 inference(rewrite,[status(thm)],[])).
% 2.64/2.82 tff(15226,plain,
% 2.64/2.82 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1))))),
% 2.64/2.82 inference(monotonicity,[status(thm)],[15225])).
% 2.64/2.82 tff(15227,plain,
% 2.64/2.82 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.64/2.82 inference(transitivity,[status(thm)],[15226, 15224])).
% 2.64/2.82 tff(15228,plain,
% 2.64/2.82 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.64/2.82 inference(quant_inst,[status(thm)],[])).
% 2.64/2.82 tff(15229,plain,
% 2.64/2.82 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1))),
% 2.64/2.82 inference(modus_ponens,[status(thm)],[15228, 15227])).
% 2.64/2.82 tff(15230,plain,
% 2.64/2.82 ($false),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[15229, 124, 15202, 15223, 15214])).
% 2.64/2.82 tff(15231,plain,((~r(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, elem!1)) | r(s(s(elem!1)), elem!1) | (elem!1 = s(z)) | b(elem!1, s(z)) | (~(s(s(s(elem!1))) = s(elem!1))) | r(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.64/2.82 tff(15232,plain,
% 2.64/2.82 (~r(s(z), s(s(s(z))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[15231, 14836, 14833, 14680, 6, 14814, 5, 14827, 808])).
% 2.64/2.82 tff(15233,plain,
% 2.64/2.82 (b(s(z), s(s(s(z))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[3302, 15232])).
% 2.64/2.82 tff(15234,plain,
% 2.64/2.82 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[4284, 14828])).
% 2.64/2.82 tff(15235,plain,
% 2.64/2.82 (~b(s(s(s(z))), z)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[2228, 1967, 13280, 838])).
% 2.64/2.82 tff(15236,plain,
% 2.64/2.82 (r(s(s(s(z))), z)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[2197, 15235])).
% 2.64/2.82 tff(15237,plain,
% 2.64/2.82 (~r(s(s(s(s(z)))), z)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[4737, 15236, 12367])).
% 2.64/2.82 tff(15238,plain,
% 2.64/2.82 (b(s(s(s(s(z)))), z)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[695, 15237])).
% 2.64/2.82 tff(15239,plain,
% 2.64/2.82 (~b(s(s(s(s(z)))), elem!1)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[12141, 306, 838, 14047, 15238])).
% 2.64/2.82 tff(15240,plain,
% 2.64/2.82 (r(s(s(s(s(z)))), elem!1)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[9832, 15239, 9815])).
% 2.64/2.82 tff(15241,plain,
% 2.64/2.82 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[12298, 1967, 14047, 838])).
% 2.64/2.82 tff(15242,plain,
% 2.64/2.82 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[1144, 15241, 14890])).
% 2.64/2.82 tff(15243,plain,
% 2.64/2.82 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[14263, 124, 15242, 15240])).
% 2.64/2.82 tff(15244,plain,
% 2.64/2.82 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[10662, 15243])).
% 2.64/2.82 tff(15245,plain,
% 2.64/2.82 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[4289, 1967, 13280, 6, 838, 87, 15241, 5])).
% 2.64/2.82 tff(15246,plain,
% 2.64/2.82 (b(s(s(s(s(s(s(z)))))), s(z))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[651, 43, 2844, 15245])).
% 2.64/2.82 tff(15247,plain,
% 2.64/2.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(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(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.64/2.82 inference(rewrite,[status(thm)],[])).
% 2.64/2.82 tff(15248,plain,
% 2.64/2.82 (((~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(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.64/2.82 inference(rewrite,[status(thm)],[])).
% 2.64/2.82 tff(15249,plain,
% 2.64/2.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(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(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 2.64/2.82 inference(monotonicity,[status(thm)],[15248])).
% 2.64/2.82 tff(15250,plain,
% 2.64/2.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(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(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.64/2.82 inference(transitivity,[status(thm)],[15249, 15247])).
% 2.64/2.82 tff(15251,plain,
% 2.64/2.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.64/2.82 inference(quant_inst,[status(thm)],[])).
% 2.64/2.82 tff(15252,plain,
% 2.64/2.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 2.64/2.82 inference(modus_ponens,[status(thm)],[15251, 15250])).
% 2.64/2.82 tff(15253,plain,
% 2.64/2.82 ($false),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[15252, 306, 2284, 8, 3620, 15246, 15244])).
% 2.64/2.82 tff(15254,plain,((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (s(s(s(s(z)))) = elem!1) | (~b(z, elem!1)) | (s(s(s(s(s(s(z)))))) = elem!1) | r(s(s(elem!1)), elem!1) | (elem!1 = s(z)) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.82 tff(15255,plain,
% 2.64/2.82 (~b(s(s(s(z))), elem!1)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[15254, 14833, 15233, 14836, 14834, 14680, 15234, 6, 14814, 5])).
% 2.64/2.82 tff(15256,plain,
% 2.64/2.82 (r(s(s(s(z))), elem!1)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[1489, 15255, 13281])).
% 2.64/2.82 tff(15257,plain,
% 2.64/2.82 (~r(s(s(z)), elem!1)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[12202, 15256, 14815, 15233])).
% 2.64/2.82 tff(15258,plain,
% 2.64/2.82 (~b(s(z), elem!1)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[2928, 15233, 13280, 14833])).
% 2.64/2.82 tff(15259,plain,
% 2.64/2.82 (r(s(z), elem!1)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[13156, 15258, 14816])).
% 2.64/2.82 tff(15260,plain,
% 2.64/2.82 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[12213, 15256, 15259, 14833, 15233])).
% 2.64/2.82 tff(15261,plain,
% 2.64/2.82 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[1144, 15260, 15234])).
% 2.64/2.82 tff(15262,plain,
% 2.64/2.82 (~b(s(s(z)), elem!1)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[12244, 15261, 14047, 14680])).
% 2.64/2.82 tff(15263,plain,
% 2.64/2.82 (s(s(z)) = elem!1),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[2545, 15262, 15257])).
% 2.64/2.82 tff(15264,plain,
% 2.64/2.82 (s(s(z)) = s(s(elem!1))),
% 2.64/2.82 inference(transitivity,[status(thm)],[15263, 14829])).
% 2.64/2.82 tff(15265,plain,
% 2.64/2.82 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 2.64/2.82 inference(monotonicity,[status(thm)],[15264])).
% 2.64/2.82 tff(15266,plain,
% 2.64/2.82 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 2.64/2.82 inference(symmetry,[status(thm)],[15265])).
% 2.64/2.82 tff(15267,plain,
% 2.64/2.82 (s(elem!1) = s(z)),
% 2.64/2.82 inference(transitivity,[status(thm)],[67, 15266, 546])).
% 2.64/2.82 tff(15268,plain,
% 2.64/2.82 ($false),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[14196, 15267])).
% 2.64/2.82 tff(15269,plain,((~r(s(z), z)) | r(s(s(elem!1)), elem!1) | b(elem!1, s(z)) | r(s(elem!1), elem!1) | r(z, elem!1) | r(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 2.64/2.82 tff(15270,plain,
% 2.64/2.82 (~r(s(z), z)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[15269, 808, 5, 6, 7, 3062])).
% 2.64/2.82 tff(15271,plain,
% 2.64/2.82 (b(s(z), z)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[221, 15270])).
% 2.64/2.82 tff(15272,plain,
% 2.64/2.82 (~b(s(z), elem!1)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[12662, 15271, 14047, 14680])).
% 2.64/2.82 tff(15273,plain,
% 2.64/2.82 (r(s(z), elem!1)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[13156, 15272, 14816])).
% 2.64/2.82 tff(15274,plain,
% 2.64/2.82 (~b(s(s(s(z))), elem!1)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[12298, 2812, 4012, 838])).
% 2.64/2.82 tff(15275,plain,
% 2.64/2.82 (r(s(s(s(z))), elem!1)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[1489, 15274, 1483])).
% 2.64/2.82 tff(15276,plain,
% 2.64/2.82 (~r(s(z), s(s(s(z))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[3790, 15275, 4])).
% 2.64/2.82 tff(15277,plain,
% 2.64/2.82 (~b(s(s(z)), elem!1)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[12244, 2812, 4012, 838])).
% 2.64/2.82 tff(15278,plain,
% 2.64/2.82 (r(s(s(z)), elem!1)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[2545, 15277, 2448])).
% 2.64/2.82 tff(15279,plain,
% 2.64/2.82 (~b(s(z), s(s(s(z))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[12202, 15278, 359, 15275])).
% 2.64/2.82 tff(15280,plain,
% 2.64/2.82 ($false),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[3302, 15279, 15276])).
% 2.64/2.82 tff(15281,plain,((~b(s(s(s(s(s(s(z)))))), elem!1)) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (s(s(z)) = elem!1) | (s(s(s(z))) = elem!1) | (~b(elem!1, z)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.82 tff(15282,plain,
% 2.64/2.82 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[15281, 15273, 14815, 14705, 13281, 14047, 14680])).
% 2.64/2.82 tff(15283,plain,
% 2.64/2.82 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[1144, 15282, 14698])).
% 2.64/2.82 tff(15284,plain,
% 2.64/2.82 (~r(s(s(s(z))), elem!1)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[1481, 206, 4287])).
% 2.64/2.82 tff(15285,plain,
% 2.64/2.82 (b(s(s(s(z))), elem!1)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[1489, 15284, 13281])).
% 2.64/2.82 tff(15286,plain,
% 2.64/2.82 (~b(s(s(s(z))), z)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[2228, 15285, 13280, 838])).
% 2.64/2.82 tff(15287,plain,
% 2.64/2.82 (r(s(s(s(z))), z)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[2197, 15286])).
% 2.64/2.82 tff(15288,plain,
% 2.64/2.82 (~b(s(s(elem!1)), elem!1)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[3002, 15285, 13280, 838, 4270])).
% 2.64/2.82 tff(15289,plain,
% 2.64/2.82 (s(s(elem!1)) = elem!1),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[47, 15288, 6])).
% 2.64/2.82 tff(15290,plain,
% 2.64/2.82 (~(s(s(s(s(z)))) = elem!1)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[9813, 15289])).
% 2.64/2.82 tff(15291,plain,
% 2.64/2.82 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[12298, 15285, 14047, 838])).
% 2.64/2.82 tff(15292,plain,
% 2.64/2.82 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[4289, 15285, 13280, 6, 838, 87, 15291, 5])).
% 2.64/2.82 tff(15293,plain,
% 2.64/2.82 (b(s(s(s(s(s(s(z)))))), s(z))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[651, 43, 2844, 15292])).
% 2.64/2.82 tff(15294,plain,
% 2.64/2.82 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[4284, 15289])).
% 2.64/2.82 tff(15295,plain,
% 2.64/2.82 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[1144, 15294, 15291])).
% 2.64/2.82 tff(15296,plain,
% 2.64/2.82 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[9918, 124, 4, 15295])).
% 2.64/2.82 tff(15297,plain,
% 2.64/2.82 (b(s(z), s(s(s(s(s(s(z)))))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[5358, 43, 5355, 15296])).
% 2.64/2.82 tff(15298,plain,
% 2.64/2.82 (~r(s(s(s(s(z)))), s(z))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[14343, 15290, 13280, 14047, 4287, 206])).
% 2.64/2.82 tff(15299,plain,
% 2.64/2.82 (b(s(s(s(s(z)))), s(z))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[4490, 15298])).
% 2.64/2.82 tff(15300,plain,
% 2.64/2.82 (((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 2.64/2.82 inference(rewrite,[status(thm)],[])).
% 2.64/2.82 tff(15301,plain,
% 2.64/2.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))))),
% 2.64/2.82 inference(monotonicity,[status(thm)],[15300])).
% 2.64/2.82 tff(15302,plain,
% 2.64/2.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 2.64/2.82 inference(transitivity,[status(thm)],[15301, 15124])).
% 2.64/2.82 tff(15303,plain,
% 2.64/2.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 2.64/2.82 inference(quant_inst,[status(thm)],[])).
% 2.64/2.82 tff(15304,plain,
% 2.64/2.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 2.64/2.82 inference(modus_ponens,[status(thm)],[15303, 15302])).
% 2.64/2.82 tff(15305,plain,
% 2.64/2.82 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[15304, 306, 15299, 15297, 15293])).
% 2.64/2.82 tff(15306,plain,
% 2.64/2.82 (r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[13486, 15305])).
% 2.64/2.82 tff(15307,assumption,(r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 2.64/2.82 tff(15308,plain,
% 2.64/2.82 ($false),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[15109, 124, 2858, 14251, 15307])).
% 2.64/2.83 tff(15309,plain,((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.83 tff(15310,plain,
% 2.64/2.83 (~r(s(s(s(s(z)))), elem!1)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[15309, 15295, 15306])).
% 2.64/2.83 tff(15311,plain,
% 2.64/2.83 (b(s(s(s(s(z)))), elem!1)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[9832, 15310, 15290])).
% 2.64/2.83 tff(15312,plain,
% 2.64/2.83 (~b(s(s(s(s(z)))), z)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[12172, 306, 838, 14047, 15311])).
% 2.64/2.83 tff(15313,plain,
% 2.64/2.83 (r(s(s(s(s(z)))), z)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[695, 15312])).
% 2.64/2.83 tff(15314,plain,
% 2.64/2.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.64/2.83 inference(rewrite,[status(thm)],[])).
% 2.64/2.83 tff(15315,plain,
% 2.64/2.83 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.64/2.83 inference(rewrite,[status(thm)],[])).
% 2.64/2.83 tff(15316,plain,
% 2.64/2.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1))))),
% 2.64/2.83 inference(monotonicity,[status(thm)],[15315])).
% 2.64/2.83 tff(15317,plain,
% 2.64/2.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.64/2.83 inference(transitivity,[status(thm)],[15316, 15314])).
% 2.64/2.83 tff(15318,plain,
% 2.64/2.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.64/2.83 inference(quant_inst,[status(thm)],[])).
% 2.64/2.83 tff(15319,plain,
% 2.64/2.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1))),
% 2.64/2.83 inference(modus_ponens,[status(thm)],[15318, 15317])).
% 2.64/2.83 tff(15320,plain,
% 2.64/2.83 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[15319, 306, 838, 14047, 15285, 15311])).
% 2.64/2.83 tff(15321,plain,
% 2.64/2.83 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[10146, 15320])).
% 2.64/2.83 tff(15322,plain,
% 2.64/2.83 ($false),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[4737, 15321, 15313, 15287])).
% 2.64/2.83 tff(15323,plain,((~r(s(s(s(z))), s(z))) | (~b(z, elem!1)) | (~r(s(z), elem!1)) | r(s(s(elem!1)), elem!1) | (elem!1 = s(z)) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.83 tff(15324,plain,
% 2.64/2.83 (~r(s(s(s(z))), s(z))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[15323, 15273, 14680, 6, 14814, 5])).
% 2.64/2.83 tff(15325,plain,
% 2.64/2.83 (b(s(s(s(z))), s(z))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[113, 15324])).
% 2.64/2.83 tff(15326,plain,
% 2.64/2.83 (~r(s(z), s(s(s(z))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[3790, 2859, 4])).
% 2.64/2.83 tff(15327,plain,
% 2.64/2.83 (~b(s(z), s(s(s(z))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[12213, 2859, 4, 2284, 2858])).
% 2.64/2.83 tff(15328,plain,
% 2.64/2.83 ($false),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[3302, 15327, 15326])).
% 2.64/2.83 tff(15329,plain,((~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.83 tff(15330,plain,
% 2.64/2.83 (~r(s(s(s(z))), elem!1)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[15329, 15273, 15325, 15283])).
% 2.64/2.83 tff(15331,plain,
% 2.64/2.83 (b(s(s(s(z))), elem!1)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[1489, 15330, 13281])).
% 2.64/2.83 tff(15332,plain,
% 2.64/2.83 (~b(s(s(s(z))), z)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[2228, 15331, 13280, 14680])).
% 2.64/2.83 tff(15333,plain,
% 2.64/2.83 (r(s(s(s(z))), z)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[2197, 15332])).
% 2.64/2.83 tff(15334,plain,
% 2.64/2.83 (~(s(s(s(s(z)))) = elem!1)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[9813, 14697])).
% 2.64/2.83 tff(15335,plain,
% 2.64/2.83 (~(s(s(z)) = elem!1)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[14704, 13835, 14196])).
% 2.64/2.83 tff(15336,plain,
% 2.64/2.83 (~b(s(z), elem!1)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[12662, 247, 14047, 838])).
% 2.64/2.83 tff(15337,plain,
% 2.64/2.83 (r(s(z), elem!1)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[13156, 15336, 8965])).
% 2.64/2.83 tff(15338,plain,
% 2.64/2.83 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[15281, 15337, 4287, 15335, 13281, 14047, 838])).
% 2.64/2.83 tff(15339,plain,
% 2.64/2.83 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[1144, 15338, 14843])).
% 2.64/2.83 tff(15340,plain,
% 2.64/2.83 (~r(s(s(s(z))), s(z))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[15323, 15337, 838, 6, 87, 5])).
% 2.64/2.83 tff(15341,plain,
% 2.64/2.83 (b(s(s(s(z))), s(z))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[113, 15340])).
% 2.64/2.83 tff(15342,plain,
% 2.64/2.83 (~r(s(s(s(z))), elem!1)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[15329, 15337, 15341, 15339])).
% 2.64/2.83 tff(15343,plain,
% 2.64/2.83 (b(s(s(s(z))), elem!1)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[1489, 15342, 13281])).
% 2.64/2.83 tff(15344,plain,
% 2.64/2.83 (~b(s(s(s(z))), z)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[2228, 15343, 13280, 838])).
% 2.64/2.83 tff(15345,plain,
% 2.64/2.83 (r(s(s(s(z))), z)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[2197, 15344])).
% 2.64/2.83 tff(15346,plain,
% 2.64/2.83 (~b(s(s(s(s(z)))), s(z))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[15231, 1034, 15341, 838, 6, 87, 5, 136, 808])).
% 2.64/2.83 tff(15347,plain,
% 2.64/2.83 (r(s(s(s(s(z)))), s(z))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[4490, 15346])).
% 2.64/2.83 tff(15348,plain,
% 2.64/2.83 (~r(s(s(s(s(z)))), elem!1)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[9849, 124, 4287, 15347])).
% 2.64/2.83 tff(15349,plain,
% 2.64/2.83 (b(s(s(s(s(z)))), elem!1)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[9832, 15348, 14837])).
% 2.64/2.83 tff(15350,plain,
% 2.64/2.83 (~b(s(s(s(s(z)))), z)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[12172, 306, 838, 14047, 15349])).
% 2.64/2.83 tff(15351,plain,
% 2.64/2.83 (r(s(s(s(s(z)))), z)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[695, 15350])).
% 2.64/2.83 tff(15352,plain,
% 2.64/2.83 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[4737, 15351, 15345])).
% 2.64/2.83 tff(15353,plain,
% 2.64/2.83 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[4471, 15352])).
% 2.64/2.83 tff(15354,plain,
% 2.64/2.83 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[9918, 124, 15337, 15339])).
% 2.64/2.83 tff(15355,plain,
% 2.64/2.83 (b(s(z), s(s(s(s(s(s(z)))))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[5358, 43, 5355, 15354])).
% 2.64/2.83 tff(15356,plain,
% 2.64/2.83 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[7174, 124, 15337, 15339])).
% 2.64/2.83 tff(15357,plain,
% 2.64/2.83 (b(s(s(s(s(s(s(z)))))), s(z))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[651, 43, 2844, 15356])).
% 2.64/2.83 tff(15358,plain,
% 2.64/2.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 2.64/2.83 inference(rewrite,[status(thm)],[])).
% 2.64/2.83 tff(15359,plain,
% 2.64/2.83 (((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 2.64/2.83 inference(rewrite,[status(thm)],[])).
% 2.64/2.83 tff(15360,plain,
% 2.64/2.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))))),
% 2.64/2.83 inference(monotonicity,[status(thm)],[15359])).
% 2.64/2.83 tff(15361,plain,
% 2.64/2.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 2.64/2.83 inference(transitivity,[status(thm)],[15360, 15358])).
% 2.64/2.83 tff(15362,plain,
% 2.64/2.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 2.64/2.83 inference(quant_inst,[status(thm)],[])).
% 2.64/2.83 tff(15363,plain,
% 2.64/2.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 2.64/2.83 inference(modus_ponens,[status(thm)],[15362, 15361])).
% 2.64/2.83 tff(15364,plain,
% 2.64/2.83 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[15363, 306, 15341, 15355, 15357])).
% 2.64/2.83 tff(15365,plain,
% 2.64/2.83 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[4603, 43, 15364, 4577])).
% 2.64/2.83 tff(15366,assumption,(b(s(z), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 2.64/2.83 tff(15367,plain,
% 2.64/2.83 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[15363, 306, 2284, 4247, 15366])).
% 2.64/2.83 tff(15368,plain,
% 2.64/2.83 ((s(s(s(s(s(s(z)))))) = s(s(s(z)))) | r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[4603, 43, 15367])).
% 2.64/2.83 tff(15369,plain,
% 2.64/2.83 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[15368, 7213])).
% 2.64/2.83 tff(15370,plain,
% 2.64/2.83 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 2.64/2.83 inference(rewrite,[status(thm)],[])).
% 2.64/2.83 tff(15371,plain,
% 2.64/2.83 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 2.64/2.83 inference(quant_inst,[status(thm)],[])).
% 2.64/2.83 tff(15372,plain,
% 2.64/2.83 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(z))))))))),
% 2.64/2.83 inference(modus_ponens,[status(thm)],[15371, 15370])).
% 2.64/2.83 tff(15373,plain,
% 2.64/2.83 (~r(z, s(s(s(s(s(s(z)))))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[15372, 124, 2518, 15369])).
% 2.64/2.83 tff(15374,plain,
% 2.64/2.83 ((z = s(s(s(s(s(s(z))))))) | b(z, s(s(s(s(s(s(z)))))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[5445, 43, 15373])).
% 2.64/2.83 tff(15375,plain,
% 2.64/2.83 (b(z, s(s(s(s(s(s(z)))))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[15374, 5435])).
% 2.64/2.83 tff(15376,plain,
% 2.64/2.83 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[9934, 306, 2284, 4247, 15366])).
% 2.64/2.83 tff(15377,plain,
% 2.64/2.83 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[3207, 15376])).
% 2.64/2.83 tff(15378,plain,
% 2.64/2.83 (~r(s(s(s(s(s(s(z)))))), z)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[3203, 15377, 205])).
% 2.64/2.83 tff(15379,plain,
% 2.64/2.83 (b(s(s(s(s(s(s(z)))))), z)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[856, 43, 554, 15378])).
% 2.64/2.83 tff(15380,plain,
% 2.64/2.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 2.64/2.83 inference(rewrite,[status(thm)],[])).
% 2.64/2.83 tff(15381,plain,
% 2.64/2.83 (((~b(z, elem!1)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), z))) <=> ((~b(z, elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 2.64/2.83 inference(rewrite,[status(thm)],[])).
% 2.64/2.83 tff(15382,plain,
% 2.64/2.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z))))))))))),
% 2.64/2.83 inference(monotonicity,[status(thm)],[15381])).
% 2.64/2.83 tff(15383,plain,
% 2.64/2.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 2.64/2.83 inference(transitivity,[status(thm)],[15382, 15380])).
% 2.64/2.83 tff(15384,plain,
% 2.64/2.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), z)))),
% 2.64/2.83 inference(quant_inst,[status(thm)],[])).
% 2.64/2.83 tff(15385,plain,
% 2.64/2.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z))))))))),
% 2.64/2.83 inference(modus_ponens,[status(thm)],[15384, 15383])).
% 2.64/2.83 tff(15386,plain,
% 2.64/2.83 ($false),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[15385, 306, 838, 247, 15379, 15366, 15375])).
% 2.64/2.83 tff(15387,plain,((~b(s(s(s(z))), s(z))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.83 tff(15388,plain,
% 2.64/2.83 (~r(z, s(s(s(z))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[15387, 15345, 247, 15341, 15355, 15357, 838])).
% 2.64/2.83 tff(15389,plain,
% 2.64/2.83 (b(z, s(s(s(z))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[11982, 15388])).
% 2.64/2.83 tff(15390,plain,
% 2.64/2.83 (~r(s(s(z)), s(s(s(z))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[7352, 1034, 247, 15357, 15389, 15365])).
% 2.64/2.83 tff(15391,plain,
% 2.64/2.83 (b(s(s(z)), s(s(s(z))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[2514, 15390])).
% 2.64/2.83 tff(15392,plain,
% 2.64/2.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 2.64/2.83 inference(rewrite,[status(thm)],[])).
% 2.64/2.83 tff(15393,plain,
% 2.64/2.83 (((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1))) <=> ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 2.64/2.83 inference(rewrite,[status(thm)],[])).
% 2.64/2.83 tff(15394,plain,
% 2.64/2.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1))))),
% 2.64/2.83 inference(monotonicity,[status(thm)],[15393])).
% 2.64/2.83 tff(15395,plain,
% 2.64/2.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 2.64/2.83 inference(transitivity,[status(thm)],[15394, 15392])).
% 2.64/2.83 tff(15396,plain,
% 2.64/2.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 2.64/2.83 inference(quant_inst,[status(thm)],[])).
% 2.64/2.83 tff(15397,plain,
% 2.64/2.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1))),
% 2.64/2.83 inference(modus_ponens,[status(thm)],[15396, 15395])).
% 2.64/2.83 tff(15398,plain,
% 2.64/2.83 (~b(s(s(z)), elem!1)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[15397, 306, 15341, 13280, 15391, 15355])).
% 2.64/2.83 tff(15399,plain,
% 2.64/2.83 (r(s(s(z)), elem!1)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[2545, 15398, 15335])).
% 2.64/2.83 tff(15400,plain,
% 2.64/2.83 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), elem!1)))),
% 2.64/2.83 inference(rewrite,[status(thm)],[])).
% 2.64/2.83 tff(15401,plain,
% 2.64/2.84 (((~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), elem!1)))),
% 2.64/2.84 inference(rewrite,[status(thm)],[])).
% 2.64/2.84 tff(15402,plain,
% 2.64/2.84 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), elem!1))))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[15401])).
% 2.64/2.84 tff(15403,plain,
% 2.64/2.84 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), elem!1)))),
% 2.64/2.84 inference(transitivity,[status(thm)],[15402, 15400])).
% 2.64/2.84 tff(15404,plain,
% 2.64/2.84 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z)))))),
% 2.64/2.84 inference(quant_inst,[status(thm)],[])).
% 2.64/2.84 tff(15405,plain,
% 2.64/2.84 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), elem!1))),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[15404, 15403])).
% 2.64/2.84 tff(15406,plain,
% 2.64/2.84 (~r(s(z), s(s(z)))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[15405, 124, 15337, 15399])).
% 2.64/2.84 tff(15407,plain,
% 2.64/2.84 (b(s(z), s(s(z)))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[4434, 15406])).
% 2.64/2.84 tff(15408,plain,
% 2.64/2.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.64/2.84 inference(rewrite,[status(thm)],[])).
% 2.64/2.84 tff(15409,plain,
% 2.64/2.84 (((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.64/2.84 inference(rewrite,[status(thm)],[])).
% 2.64/2.84 tff(15410,plain,
% 2.64/2.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1))))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[15409])).
% 2.64/2.84 tff(15411,plain,
% 2.64/2.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.64/2.84 inference(transitivity,[status(thm)],[15410, 15408])).
% 2.64/2.84 tff(15412,plain,
% 2.64/2.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), 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)))),
% 2.64/2.84 inference(quant_inst,[status(thm)],[])).
% 2.64/2.84 tff(15413,plain,
% 2.64/2.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1))),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[15412, 15411])).
% 2.64/2.84 tff(15414,plain,
% 2.64/2.84 ($false),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[15413, 306, 15341, 13280, 15407, 15349, 15353])).
% 2.64/2.84 tff(15415,plain,((~r(s(z), s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(z), z)) | r(s(s(elem!1)), elem!1) | (elem!1 = s(z)) | b(elem!1, s(z)) | (~(s(s(s(elem!1))) = s(elem!1))) | r(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.64/2.84 tff(15416,plain,
% 2.64/2.84 (~r(s(z), s(s(s(z))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[15415, 15271, 14680, 6, 14814, 5, 14696, 808])).
% 2.64/2.84 tff(15417,plain,
% 2.64/2.84 (b(s(z), s(s(s(z))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[3302, 15416])).
% 2.64/2.84 tff(15418,plain,
% 2.64/2.84 (~b(s(s(s(s(z)))), s(z))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[15254, 15417, 15325, 15331, 15334, 14680, 14698, 6, 14814, 5])).
% 2.64/2.84 tff(15419,plain,
% 2.64/2.84 (r(s(s(s(s(z)))), s(z))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[4490, 15418])).
% 2.64/2.84 tff(15420,plain,
% 2.64/2.84 (~r(s(s(s(s(z)))), elem!1)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[9849, 124, 14815, 15419])).
% 2.64/2.84 tff(15421,plain,
% 2.64/2.84 (b(s(s(s(s(z)))), elem!1)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[9832, 15420, 15334])).
% 2.64/2.84 tff(15422,plain,
% 2.64/2.84 (~b(s(s(s(s(z)))), z)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[12172, 306, 14680, 14047, 15421])).
% 2.64/2.84 tff(15423,plain,
% 2.64/2.84 (r(s(s(s(s(z)))), z)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[695, 15422])).
% 2.64/2.84 tff(15424,plain,
% 2.64/2.84 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[4737, 15423, 15333])).
% 2.64/2.84 tff(15425,plain,
% 2.64/2.84 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[4471, 15424])).
% 2.64/2.84 tff(15426,plain,
% 2.64/2.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.64/2.84 inference(rewrite,[status(thm)],[])).
% 2.64/2.84 tff(15427,plain,
% 2.64/2.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), 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)))),
% 2.64/2.84 inference(quant_inst,[status(thm)],[])).
% 2.64/2.84 tff(15428,plain,
% 2.64/2.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1))),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[15427, 15426])).
% 2.64/2.84 tff(15429,plain,
% 2.64/2.84 ($false),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[15428, 306, 15325, 15417, 13280, 15421, 15425])).
% 2.64/2.84 tff(15430,plain,(r(s(elem!1), elem!1) | r(s(s(elem!1)), elem!1) | b(elem!1, s(z)) | r(z, elem!1) | r(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 2.64/2.84 tff(15431,plain,
% 2.64/2.84 (r(s(s(elem!1)), elem!1)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[15430, 808, 5, 14679, 14678])).
% 2.64/2.84 tff(15432,plain,
% 2.64/2.84 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(z))), s(elem!1))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[14116])).
% 2.64/2.84 tff(15433,plain,
% 2.64/2.84 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(z))), s(s(z)))),
% 2.64/2.84 inference(symmetry,[status(thm)],[15432])).
% 2.64/2.84 tff(15434,plain,
% 2.64/2.84 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(z))), s(elem!1))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[19])).
% 2.64/2.84 tff(15435,plain,
% 2.64/2.84 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(z))), s(s(z)))),
% 2.64/2.84 inference(transitivity,[status(thm)],[15434, 15433])).
% 2.64/2.84 tff(15436,plain,
% 2.64/2.84 (b(s(elem!1), s(z))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[7105, 13312, 808, 12588])).
% 2.64/2.84 tff(15437,plain,
% 2.64/2.84 (~b(s(s(s(z))), s(z))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[4206, 13312, 1])).
% 2.64/2.84 tff(15438,plain,
% 2.64/2.84 (~b(s(s(elem!1)), s(z))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[27, 15437, 19])).
% 2.64/2.84 tff(15439,plain,
% 2.64/2.84 (~(elem!1 = s(elem!1))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[2651, 15438, 15436])).
% 2.64/2.84 tff(15440,plain,
% 2.64/2.84 (~(s(elem!1) = elem!1)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[2571, 15439])).
% 2.64/2.84 tff(15441,plain,
% 2.64/2.84 (~(s(s(elem!1)) = s(elem!1))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[195, 15440])).
% 2.64/2.84 tff(15442,plain,
% 2.64/2.84 (b(s(elem!1), elem!1)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[813, 15440, 808])).
% 2.64/2.84 tff(15443,plain,
% 2.64/2.84 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[19])).
% 2.64/2.84 tff(15444,plain,
% 2.64/2.84 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(z)))) = s(s(z)))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[15443, 14])).
% 2.64/2.84 tff(15445,plain,
% 2.64/2.84 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(z)) = s(s(s(s(z)))))),
% 2.64/2.84 inference(transitivity,[status(thm)],[15444, 1707])).
% 2.64/2.84 tff(15446,plain,
% 2.64/2.84 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 2.64/2.84 inference(symmetry,[status(thm)],[15445])).
% 2.64/2.84 tff(15447,plain,
% 2.64/2.84 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[15446])).
% 2.64/2.84 tff(15448,plain,
% 2.64/2.84 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[1612, 15447])).
% 2.64/2.84 tff(15449,plain,
% 2.64/2.84 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[7090, 11840, 12587, 808])).
% 2.64/2.84 tff(15450,plain,
% 2.64/2.84 (~r(s(s(elem!1)), s(elem!1))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[13111, 5076, 4012, 1730, 14725, 15449, 15448, 15439, 15442])).
% 2.64/2.84 tff(15451,plain,
% 2.64/2.84 (b(s(s(elem!1)), s(elem!1))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[994, 15450, 15441])).
% 2.64/2.84 tff(15452,plain,
% 2.64/2.84 (b(s(s(s(z))), s(s(z)))),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[15451, 15435])).
% 2.64/2.84 tff(15453,plain,
% 2.64/2.84 (b(s(s(z)), s(z))),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[15436, 13993])).
% 2.64/2.84 tff(15454,plain,
% 2.64/2.84 (b(z, s(s(elem!1))) <=> b(z, s(s(s(z))))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[19])).
% 2.64/2.84 tff(15455,plain,
% 2.64/2.84 (~r(s(s(s(elem!1))), elem!1)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[7780, 15449, 1730])).
% 2.64/2.84 tff(15456,plain,
% 2.64/2.84 (b(s(s(s(elem!1))), elem!1)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[1636, 15455, 5076])).
% 2.64/2.84 tff(15457,plain,
% 2.64/2.84 (~b(z, s(s(s(elem!1))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[6150, 15456, 4012, 838])).
% 2.64/2.84 tff(15458,plain,
% 2.64/2.84 (r(z, s(s(s(elem!1))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[585, 15457])).
% 2.64/2.84 tff(15459,plain,
% 2.64/2.84 (~r(z, s(s(elem!1)))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[950, 15458, 15449])).
% 2.64/2.84 tff(15460,plain,
% 2.64/2.84 (b(z, s(s(elem!1)))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[460, 15459])).
% 2.64/2.84 tff(15461,plain,
% 2.64/2.84 (b(z, s(s(s(z))))),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[15460, 15454])).
% 2.64/2.84 tff(15462,plain,
% 2.64/2.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.64/2.84 inference(rewrite,[status(thm)],[])).
% 2.64/2.84 tff(15463,plain,
% 2.64/2.84 (((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.64/2.84 inference(rewrite,[status(thm)],[])).
% 2.64/2.84 tff(15464,plain,
% 2.64/2.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z))))))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[15463])).
% 2.64/2.84 tff(15465,plain,
% 2.64/2.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.64/2.84 inference(transitivity,[status(thm)],[15464, 15462])).
% 2.64/2.84 tff(15466,plain,
% 2.64/2.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))))),
% 2.64/2.84 inference(quant_inst,[status(thm)],[])).
% 2.64/2.84 tff(15467,plain,
% 2.64/2.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z))))),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[15466, 15465])).
% 2.64/2.84 tff(15468,plain,
% 2.64/2.84 ($false),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[15467, 306, 13565, 15461, 15453, 11849, 15452])).
% 2.64/2.84 tff(15469,plain,((~(elem!1 = s(z))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | r(s(elem!1), elem!1) | b(s(s(s(z))), elem!1) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.84 tff(15470,plain,
% 2.64/2.84 (~(elem!1 = s(z))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[15469, 1730, 838, 4012, 808, 1, 1470])).
% 2.64/2.84 tff(15471,plain,
% 2.64/2.84 (~(s(z) = elem!1)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[89, 15470])).
% 2.64/2.84 tff(15472,plain,
% 2.64/2.84 (~b(s(s(s(z))), z)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[14674, 838, 4012, 1470])).
% 2.64/2.84 tff(15473,plain,
% 2.64/2.84 (r(s(s(s(z))), z)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[2197, 15472])).
% 2.64/2.84 tff(15474,plain,
% 2.64/2.84 (~b(s(elem!1), z)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[4020, 12630, 4012, 838])).
% 2.64/2.84 tff(15475,plain,
% 2.64/2.84 (r(s(elem!1), z)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[2380, 15474])).
% 2.64/2.84 tff(15476,plain,
% 2.64/2.84 (~r(s(s(s(z))), s(elem!1))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[6878, 124, 15475, 15473])).
% 2.64/2.84 tff(15477,plain,
% 2.64/2.84 (s(s(s(elem!1))) = elem!1),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[13111, 244, 4012, 1730, 360, 653, 150, 366, 816])).
% 2.64/2.84 tff(15478,plain,
% 2.64/2.84 (~(s(s(s(z))) = s(elem!1))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[4128, 15477])).
% 2.64/2.84 tff(15479,plain,
% 2.64/2.84 (b(s(s(s(z))), s(elem!1))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[4132, 43, 15478, 15476])).
% 2.64/2.84 tff(15480,plain,
% 2.64/2.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))))),
% 2.64/2.84 inference(rewrite,[status(thm)],[])).
% 2.64/2.84 tff(15481,plain,
% 2.64/2.84 (((~b(elem!1, z)) | (~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(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))))),
% 2.64/2.84 inference(rewrite,[status(thm)],[])).
% 2.64/2.84 tff(15482,plain,
% 2.64/2.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1)))))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[15481])).
% 2.64/2.84 tff(15483,plain,
% 2.64/2.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))))),
% 2.64/2.84 inference(transitivity,[status(thm)],[15482, 15480])).
% 2.64/2.84 tff(15484,plain,
% 2.64/2.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(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))))))),
% 2.64/2.84 inference(quant_inst,[status(thm)],[])).
% 2.64/2.84 tff(15485,plain,
% 2.64/2.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1)))),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[15484, 15483])).
% 2.64/2.84 tff(15486,plain,
% 2.64/2.84 ($false),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[15485, 306, 4012, 816, 12630, 1470, 15479])).
% 2.64/2.84 tff(15487,plain,((~r(s(s(elem!1)), s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (elem!1 = s(elem!1)) | (~r(s(s(elem!1)), elem!1)) | (elem!1 = s(s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.84 tff(15488,plain,
% 2.64/2.84 (~r(s(s(elem!1)), s(elem!1))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[15487, 5620, 4012, 1470, 838, 5621, 1730, 187, 14605, 144])).
% 2.64/2.84 tff(15489,plain,
% 2.64/2.84 (b(s(s(elem!1)), s(elem!1))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[994, 15488, 196])).
% 2.64/2.84 tff(15490,plain,
% 2.64/2.84 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[12759, 15489, 4012, 12587, 1, 1730, 15471, 5620, 14608, 153])).
% 2.64/2.84 tff(15491,plain,
% 2.64/2.84 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[2974, 15470])).
% 2.64/2.84 tff(15492,plain,
% 2.64/2.84 (r(s(s(s(z))), elem!1)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[1489, 1, 4198])).
% 2.64/2.84 tff(15493,plain,
% 2.64/2.84 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[11484, 124, 1730, 15492])).
% 2.64/2.84 tff(15494,plain,
% 2.64/2.84 ((s(s(s(z))) = s(s(elem!1))) | b(s(s(s(z))), s(s(elem!1)))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[2986, 43, 15493])).
% 2.64/2.84 tff(15495,plain,
% 2.64/2.84 (b(s(s(s(z))), s(s(elem!1)))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[15494, 15491])).
% 2.64/2.84 tff(15496,plain,
% 2.64/2.84 (~r(s(z), elem!1)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[12723, 15489, 15492, 15495, 5620, 1730])).
% 2.64/2.84 tff(15497,plain,
% 2.64/2.84 (b(s(z), elem!1)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[13156, 15496, 15471])).
% 2.64/2.84 tff(15498,plain,
% 2.64/2.84 (~b(s(s(s(elem!1))), elem!1)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[13176, 15497, 4012, 838])).
% 2.64/2.84 tff(15499,plain,
% 2.64/2.84 (s(s(s(elem!1))) = elem!1),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[1636, 15498, 14608])).
% 2.64/2.84 tff(15500,plain,
% 2.64/2.84 (~r(s(elem!1), z)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[7030, 15497, 4012, 838, 12588, 5620])).
% 2.64/2.84 tff(15501,plain,
% 2.64/2.84 (b(s(elem!1), z)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[2380, 15500])).
% 2.64/2.84 tff(15502,plain,
% 2.64/2.84 ($false),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[11496, 15501, 15499, 1, 1730, 15491, 6278, 14605, 5621, 15489, 15490, 12588])).
% 2.64/2.84 tff(15503,plain,((s(s(elem!1)) = elem!1) | b(s(s(s(z))), elem!1) | (~r(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | r(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.64/2.84 tff(15504,plain,
% 2.64/2.84 (s(s(elem!1)) = elem!1),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[15503, 15431, 1, 14047, 14666, 13280, 808])).
% 2.64/2.84 tff(15505,plain,
% 2.64/2.84 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[4284, 15504])).
% 2.64/2.84 tff(15506,plain,
% 2.64/2.84 (~(elem!1 = s(z))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[15469, 15431, 14666, 14047, 808, 1, 13280])).
% 2.64/2.84 tff(15507,plain,
% 2.64/2.84 (~(s(z) = elem!1)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[89, 15506])).
% 2.64/2.84 tff(15508,plain,
% 2.64/2.84 (r(elem!1, s(z))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[97, 15506])).
% 2.64/2.84 tff(15509,plain,
% 2.64/2.84 (~r(s(z), z)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[14918, 15505, 14047, 14676, 14677, 14666, 15507, 15508])).
% 2.64/2.84 tff(15510,plain,
% 2.64/2.84 (b(s(z), z)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[221, 15509])).
% 2.64/2.84 tff(15511,plain,
% 2.64/2.84 (~b(s(z), elem!1)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[12662, 15510, 14047, 14666])).
% 2.64/2.84 tff(15512,plain,
% 2.64/2.84 (r(s(z), elem!1)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[13156, 15511, 15507])).
% 2.64/2.84 tff(15513,plain,
% 2.64/2.84 (~r(s(s(s(z))), s(z))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[1481, 15508, 14677])).
% 2.64/2.84 tff(15514,plain,
% 2.64/2.84 (b(s(s(s(z))), s(z))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[113, 15513])).
% 2.64/2.84 tff(15515,plain,
% 2.64/2.84 (elem!1 = s(s(elem!1))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[1174, 15504])).
% 2.64/2.84 tff(15516,plain,
% 2.64/2.84 (s(s(s(elem!1))) = s(elem!1)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[1168, 15515])).
% 2.64/2.84 tff(15517,plain,
% 2.64/2.84 (b(z, s(s(elem!1)))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[8180, 15504, 14666])).
% 2.64/2.84 tff(15518,plain,
% 2.64/2.84 (~(s(elem!1) = elem!1)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[15038, 15505, 14047, 14666, 14050, 14677, 15508, 14676, 15507, 15504, 15517])).
% 2.64/2.84 tff(15519,plain,
% 2.64/2.84 (b(s(elem!1), elem!1)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[813, 15518, 808])).
% 2.64/2.84 tff(15520,plain,
% 2.64/2.84 (~r(s(z), s(s(s(z))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[14869, 15519, 13280, 14666, 14047, 15514, 15507, 15516])).
% 2.64/2.84 tff(15521,plain,
% 2.64/2.84 (b(s(z), s(s(s(z))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[3302, 15520])).
% 2.64/2.84 tff(15522,plain,
% 2.64/2.84 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[12213, 15521, 14677, 15514, 15512])).
% 2.64/2.84 tff(15523,plain,
% 2.64/2.84 (~(s(s(z)) = elem!1)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[14704, 15504, 14196])).
% 2.64/2.84 tff(15524,plain,
% 2.64/2.84 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[15281, 15512, 14666, 15508, 13281, 14047, 15523])).
% 2.64/2.84 tff(15525,plain,
% 2.64/2.84 ($false),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[1144, 15524, 15522, 15505])).
% 2.64/2.84 tff(15526,plain,(r(s(elem!1), elem!1) | b(s(s(s(z))), elem!1) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.84 tff(15527,plain,
% 2.64/2.84 (r(s(elem!1), elem!1)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[15526, 1, 5])).
% 2.64/2.84 tff(15528,plain,
% 2.64/2.84 (~r(elem!1, z)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[2561, 2859, 14676])).
% 2.64/2.84 tff(15529,plain,
% 2.64/2.84 (~(elem!1 = s(z))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[14813, 6, 13280, 14047, 14666, 15528])).
% 2.64/2.84 tff(15530,plain,
% 2.64/2.84 (~(s(z) = elem!1)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[89, 15529])).
% 2.64/2.84 tff(15531,plain,
% 2.64/2.84 (r(elem!1, s(z))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[97, 15529])).
% 2.64/2.84 tff(15532,plain,
% 2.64/2.84 (~r(s(z), z)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[14831, 206, 838, 4287, 13280])).
% 2.64/2.84 tff(15533,plain,
% 2.64/2.84 (b(s(z), z)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[221, 15532])).
% 2.64/2.84 tff(15534,plain,
% 2.64/2.84 (~r(s(z), elem!1)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[15323, 206, 838, 6, 87, 5])).
% 2.64/2.84 tff(15535,plain,
% 2.64/2.84 (b(s(z), elem!1)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[13156, 15534, 8965])).
% 2.64/2.84 tff(15536,plain,
% 2.64/2.84 ($false),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[12662, 15535, 15533, 14047, 838])).
% 2.64/2.84 tff(15537,plain,((~r(s(s(s(z))), s(z))) | (~b(z, elem!1)) | r(s(s(elem!1)), elem!1) | (elem!1 = s(z)) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.84 tff(15538,plain,
% 2.64/2.84 (~r(s(s(s(z))), s(z))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[15537, 6, 14666, 15529, 5])).
% 2.64/2.84 tff(15539,plain,
% 2.64/2.84 (b(s(s(s(z))), s(z))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[113, 15538])).
% 2.64/2.84 tff(15540,plain,
% 2.64/2.84 (~(s(s(s(s(z)))) = elem!1)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[12307, 12715, 4012, 838, 6, 359, 4198])).
% 2.64/2.84 tff(15541,plain,
% 2.64/2.84 (~r(elem!1, z)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[2561, 2859, 15473])).
% 2.64/2.84 tff(15542,plain,
% 2.64/2.84 (~r(z, elem!1)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[6831, 2859, 15473])).
% 2.64/2.84 tff(15543,plain,
% 2.64/2.84 (~b(s(s(s(s(z)))), z)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[12172, 306, 14683, 4012, 12426])).
% 2.64/2.84 tff(15544,plain,
% 2.64/2.84 (r(s(s(s(s(z)))), z)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[695, 15543])).
% 2.64/2.84 tff(15545,plain,
% 2.64/2.84 (~(elem!1 = s(z))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[14813, 3062, 1470, 4012, 14683, 6])).
% 2.64/2.84 tff(15546,plain,
% 2.64/2.84 (~(s(z) = elem!1)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[89, 15545])).
% 2.64/2.84 tff(15547,plain,
% 2.64/2.84 (~b(s(z), elem!1)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[2928, 8, 1470, 2284])).
% 2.64/2.84 tff(15548,plain,
% 2.64/2.84 (r(s(z), elem!1)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[13156, 15547, 15546])).
% 2.64/2.84 tff(15549,plain,
% 2.64/2.84 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[2974, 15545])).
% 2.64/2.84 tff(15550,plain,
% 2.64/2.84 (b(s(elem!1), s(z))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[2964, 3135, 12588])).
% 2.64/2.84 tff(15551,plain,
% 2.64/2.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))))),
% 2.64/2.84 inference(rewrite,[status(thm)],[])).
% 2.64/2.84 tff(15552,plain,
% 2.64/2.84 (((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(elem!1)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))))),
% 2.64/2.84 inference(rewrite,[status(thm)],[])).
% 2.64/2.84 tff(15553,plain,
% 2.64/2.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1)))))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[15552])).
% 2.64/2.84 tff(15554,plain,
% 2.64/2.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))))),
% 2.64/2.84 inference(transitivity,[status(thm)],[15553, 15551])).
% 2.64/2.84 tff(15555,plain,
% 2.64/2.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(elem!1))))),
% 2.64/2.84 inference(quant_inst,[status(thm)],[])).
% 2.64/2.84 tff(15556,plain,
% 2.64/2.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1)))),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[15555, 15554])).
% 2.64/2.85 tff(15557,plain,
% 2.64/2.85 (~b(s(s(s(z))), s(elem!1))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[15556, 306, 2284, 8, 15550])).
% 2.64/2.85 tff(15558,plain,
% 2.64/2.85 (~(elem!1 = s(elem!1))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[2639, 3135, 359])).
% 2.64/2.85 tff(15559,plain,
% 2.64/2.85 (~(s(elem!1) = elem!1)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[2571, 15558])).
% 2.64/2.85 tff(15560,plain,
% 2.64/2.85 (~(s(s(elem!1)) = s(elem!1))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[195, 15559])).
% 2.64/2.85 tff(15561,plain,
% 2.64/2.85 (~(s(z) = s(elem!1))),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[12588, 4039])).
% 2.64/2.85 tff(15562,plain,
% 2.64/2.85 (~r(s(z), s(elem!1))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[4043, 124, 802, 15548])).
% 2.64/2.85 tff(15563,plain,
% 2.64/2.85 ((s(z) = s(elem!1)) | b(s(z), s(elem!1))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[4047, 43, 15562])).
% 2.64/2.85 tff(15564,plain,
% 2.64/2.85 (b(s(z), s(elem!1))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[15563, 15561])).
% 2.64/2.85 tff(15565,plain,
% 2.64/2.85 (~b(s(s(elem!1)), z)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[3976, 30, 7, 12587, 3062])).
% 2.64/2.85 tff(15566,plain,
% 2.64/2.85 (r(s(s(elem!1)), z)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[476, 15565])).
% 2.64/2.85 tff(15567,plain,
% 2.64/2.85 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[12436, 124, 15566, 15544])).
% 2.64/2.85 tff(15568,plain,
% 2.64/2.85 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[12443, 306, 14683, 4012, 30, 12426])).
% 2.64/2.85 tff(15569,plain,
% 2.64/2.85 (s(s(elem!1)) = s(s(s(s(z))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[12447, 43, 15568, 15567])).
% 2.64/2.85 tff(15570,plain,
% 2.64/2.85 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.64/2.85 inference(symmetry,[status(thm)],[15569])).
% 2.64/2.85 tff(15571,plain,
% 2.64/2.85 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(elem!1)), s(elem!1))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[15570])).
% 2.64/2.85 tff(15572,plain,
% 2.64/2.85 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(s(z)))), s(elem!1))),
% 2.64/2.85 inference(symmetry,[status(thm)],[15571])).
% 2.64/2.85 tff(15573,plain,
% 2.64/2.85 (~b(s(s(s(z))), elem!1)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[3002, 30, 1470, 14683, 2976])).
% 2.64/2.85 tff(15574,plain,
% 2.64/2.85 (r(s(s(s(z))), elem!1)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[1489, 15573, 4198])).
% 2.64/2.85 tff(15575,plain,
% 2.64/2.85 (~r(s(s(s(z))), s(elem!1))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[4110, 124, 802, 15574])).
% 2.64/2.85 tff(15576,assumption,(~b(s(s(s(z))), s(elem!1))), introduced(assumption)).
% 2.64/2.85 tff(15577,plain,
% 2.64/2.85 ((s(s(s(z))) = s(elem!1)) | r(s(s(s(z))), s(elem!1))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[4132, 43, 15576])).
% 2.64/2.85 tff(15578,plain,
% 2.64/2.85 (s(s(s(z))) = s(elem!1)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[15577, 15575])).
% 2.64/2.85 tff(15579,plain,
% 2.64/2.85 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(elem!1))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[15578])).
% 2.64/2.85 tff(15580,plain,
% 2.64/2.85 (b(elem!1, s(elem!1))),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[1470, 15579])).
% 2.64/2.85 tff(15581,plain,
% 2.64/2.85 (~b(s(elem!1), z)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[4020, 15580, 4012, 14683])).
% 2.64/2.85 tff(15582,plain,
% 2.64/2.85 (r(s(elem!1), z)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[2380, 15581])).
% 2.64/2.85 tff(15583,plain,
% 2.64/2.85 (~r(s(s(elem!1)), s(elem!1))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[471, 15582, 15566])).
% 2.64/2.85 tff(15584,plain,
% 2.64/2.85 (b(s(s(elem!1)), s(elem!1))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[994, 15583, 403])).
% 2.64/2.85 tff(15585,plain,
% 2.64/2.85 (b(s(s(s(s(z)))), s(elem!1))),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[15584, 15572])).
% 2.64/2.85 tff(15586,plain,
% 2.64/2.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 2.64/2.85 inference(rewrite,[status(thm)],[])).
% 2.64/2.85 tff(15587,plain,
% 2.64/2.85 (((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 2.64/2.85 inference(rewrite,[status(thm)],[])).
% 2.64/2.85 tff(15588,plain,
% 2.64/2.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[15587])).
% 2.64/2.85 tff(15589,plain,
% 2.64/2.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 2.64/2.85 inference(transitivity,[status(thm)],[15588, 15586])).
% 2.64/2.85 tff(15590,plain,
% 2.64/2.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.64/2.85 inference(quant_inst,[status(thm)],[])).
% 2.64/2.85 tff(15591,plain,
% 2.64/2.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[15590, 15589])).
% 2.64/2.85 tff(15592,plain,
% 2.64/2.85 (~b(s(s(s(s(z)))), s(elem!1))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[15591, 306, 15580, 2647, 12426, 4050])).
% 2.64/2.85 tff(15593,plain,
% 2.64/2.85 ($false),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[15592, 15585])).
% 2.64/2.85 tff(15594,plain,((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(elem!1))) | (s(s(elem!1)) = s(elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))) | b(s(s(s(z))), s(elem!1)) | (~r(s(elem!1), elem!1)) | r(z, elem!1) | r(elem!1, z) | (s(s(s(z))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.85 tff(15595,plain,
% 2.64/2.85 (~b(s(s(elem!1)), elem!1)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[15594, 12426, 15550, 15564, 15560, 4012, 1470, 15557, 802, 7, 3062, 15549])).
% 2.64/2.85 tff(15596,plain,
% 2.64/2.85 (s(s(elem!1)) = elem!1),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[47, 15595, 6])).
% 2.64/2.85 tff(15597,plain,
% 2.64/2.85 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[4284, 15596])).
% 2.64/2.85 tff(15598,plain,
% 2.64/2.85 (~(s(s(z)) = elem!1)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[14704, 15596, 12588])).
% 2.64/2.85 tff(15599,plain,
% 2.64/2.85 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[15281, 15598, 359, 15548, 4198, 4012, 14683])).
% 2.64/2.85 tff(15600,plain,
% 2.64/2.85 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[1144, 15599, 15597])).
% 2.64/2.85 tff(15601,plain,
% 2.64/2.85 (~r(s(s(s(z))), elem!1)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[15329, 15600, 2284, 15548])).
% 2.64/2.85 tff(15602,plain,
% 2.64/2.85 (b(s(s(s(z))), elem!1)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[1489, 15601, 4198])).
% 2.64/2.85 tff(15603,plain,
% 2.64/2.85 (~b(s(s(s(z))), z)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[2228, 15602, 1470, 14683])).
% 2.64/2.85 tff(15604,plain,
% 2.64/2.85 (r(s(s(s(z))), z)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[2197, 15603])).
% 2.64/2.85 tff(15605,plain,
% 2.64/2.85 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[4737, 15604, 15544])).
% 2.64/2.85 tff(15606,plain,
% 2.64/2.85 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[4471, 15605])).
% 2.64/2.85 tff(15607,plain,
% 2.64/2.85 ($false),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[15428, 306, 2284, 8, 1470, 12426, 15606])).
% 2.64/2.85 tff(15608,plain,((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~r(elem!1, s(z))) | (~b(elem!1, z)) | r(s(s(elem!1)), elem!1) | (~r(s(elem!1), elem!1)) | r(z, elem!1) | r(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 2.64/2.85 tff(15609,plain,
% 2.64/2.85 (~b(s(s(s(s(z)))), elem!1)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[15608, 12715, 802, 1470, 2284, 4012, 6, 359, 15542, 15541])).
% 2.64/2.85 tff(15610,plain,
% 2.64/2.85 (r(s(s(s(s(z)))), elem!1)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[9832, 15609, 15540])).
% 2.64/2.85 tff(15611,plain,
% 2.64/2.85 (~r(s(z), s(s(s(s(z)))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[14288, 124, 4, 15610])).
% 2.64/2.85 tff(15612,plain,
% 2.64/2.85 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.64/2.85 inference(rewrite,[status(thm)],[])).
% 2.64/2.85 tff(15613,plain,
% 2.64/2.85 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.64/2.85 inference(quant_inst,[status(thm)],[])).
% 2.64/2.85 tff(15614,plain,
% 2.64/2.85 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[15613, 15612])).
% 2.64/2.85 tff(15615,plain,
% 2.64/2.85 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[15614, 124, 2859, 15610])).
% 2.64/2.85 tff(15616,plain,
% 2.64/2.85 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[4471, 15615])).
% 2.64/2.85 tff(15617,plain,
% 2.64/2.85 (~b(s(z), s(s(s(s(z)))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[12349, 306, 2284, 12715, 15616])).
% 2.64/2.85 tff(15618,plain,
% 2.64/2.85 ($false),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[5135, 15617, 15611])).
% 2.64/2.85 tff(15619,plain,((~r(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | r(s(s(elem!1)), elem!1) | (~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.85 tff(15620,plain,
% 2.64/2.85 (~r(s(z), elem!1)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[15619, 15539, 2859, 14047, 14666, 6, 15531, 802, 13280])).
% 2.64/2.85 tff(15621,plain,
% 2.64/2.85 (b(s(z), elem!1)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[13156, 15620, 15530])).
% 2.64/2.85 tff(15622,plain,
% 2.64/2.85 (~b(s(z), z)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[12662, 15621, 14047, 14666])).
% 2.64/2.85 tff(15623,plain,
% 2.64/2.85 (r(s(z), z)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[221, 15622])).
% 2.64/2.85 tff(15624,plain,
% 2.64/2.85 (s(s(s(s(s(s(z)))))) = elem!1),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[14918, 15623, 14047, 14676, 2859, 14666, 15530, 15531])).
% 2.64/2.85 tff(15625,plain,
% 2.64/2.85 (~(s(s(elem!1)) = elem!1)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[4284, 15624])).
% 2.64/2.85 tff(15626,plain,
% 2.64/2.85 (b(s(s(elem!1)), elem!1)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[47, 15625, 6])).
% 2.64/2.85 tff(15627,plain,
% 2.64/2.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)))),
% 2.64/2.85 inference(rewrite,[status(thm)],[])).
% 2.64/2.85 tff(15628,plain,
% 2.64/2.85 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)))),
% 2.64/2.85 inference(rewrite,[status(thm)],[])).
% 2.64/2.85 tff(15629,plain,
% 2.64/2.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[15628])).
% 2.64/2.85 tff(15630,plain,
% 2.64/2.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)))),
% 2.64/2.85 inference(transitivity,[status(thm)],[15629, 15627])).
% 2.64/2.85 tff(15631,plain,
% 2.64/2.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))))),
% 2.64/2.85 inference(quant_inst,[status(thm)],[])).
% 2.64/2.85 tff(15632,plain,
% 2.64/2.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1))),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[15631, 15630])).
% 2.64/2.85 tff(15633,plain,
% 2.64/2.85 (~b(s(z), s(s(elem!1)))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[15632, 306, 14666, 14047, 15626, 15621])).
% 2.64/2.85 tff(15634,plain,
% 2.64/2.85 (r(s(z), s(s(elem!1)))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[3997, 43, 15633, 79])).
% 2.64/2.85 tff(15635,plain,
% 2.64/2.85 (~r(z, elem!1)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[6831, 2859, 14676])).
% 2.64/2.85 tff(15636,plain,
% 2.64/2.85 (~b(s(s(elem!1)), z)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[3976, 15626, 15635, 14048, 15528])).
% 2.64/2.85 tff(15637,plain,
% 2.64/2.85 (r(s(s(elem!1)), z)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[476, 15636])).
% 2.64/2.85 tff(15638,plain,
% 2.64/2.85 ($false),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[3993, 124, 15637, 15623, 15634])).
% 2.64/2.85 tff(15639,plain,(r(s(s(elem!1)), elem!1) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), elem!1)) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.85 tff(15640,plain,
% 2.64/2.85 (r(s(s(elem!1)), elem!1)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[15639, 2859, 802, 5])).
% 2.64/2.85 tff(15641,plain,
% 2.64/2.85 (r(elem!1, s(z))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[97, 5331])).
% 2.64/2.85 tff(15642,plain,
% 2.64/2.85 (~r(s(s(elem!1)), s(z))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[9725, 15641, 15640])).
% 2.64/2.85 tff(15643,plain,
% 2.64/2.85 (b(s(s(elem!1)), s(z))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[3989, 15642])).
% 2.64/2.85 tff(15644,plain,
% 2.64/2.85 (~r(s(elem!1), s(z))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[2960, 15641, 802])).
% 2.64/2.85 tff(15645,plain,
% 2.64/2.85 (b(s(elem!1), s(z))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[2964, 15644, 14196])).
% 2.64/2.85 tff(15646,plain,
% 2.64/2.85 (~r(s(s(elem!1)), s(elem!1))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[7985, 15640, 802])).
% 2.64/2.85 tff(15647,plain,
% 2.64/2.85 (~(elem!1 = s(elem!1))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[2639, 15644, 15641])).
% 2.64/2.85 tff(15648,plain,
% 2.64/2.85 (~(s(elem!1) = elem!1)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[2571, 15647])).
% 2.64/2.85 tff(15649,plain,
% 2.64/2.85 (~(s(s(elem!1)) = s(elem!1))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[195, 15648])).
% 2.64/2.85 tff(15650,plain,
% 2.64/2.85 (b(s(s(elem!1)), s(elem!1))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[994, 15649, 15646])).
% 2.64/2.85 tff(15651,plain,
% 2.64/2.85 (~b(s(z), s(s(elem!1)))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[4007, 15650, 15645, 15643])).
% 2.64/2.85 tff(15652,plain,
% 2.64/2.85 (r(s(z), s(s(elem!1)))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[3997, 43, 15651, 79])).
% 2.64/2.85 tff(15653,plain,
% 2.64/2.85 (~r(s(z), elem!1)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[13075, 15652, 15640])).
% 2.64/2.85 tff(15654,plain,
% 2.64/2.85 (b(s(z), elem!1)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[13156, 15653, 3094])).
% 2.64/2.85 tff(15655,plain,
% 2.64/2.85 (~b(s(s(s(elem!1))), elem!1)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[13176, 15654, 14047, 14666])).
% 2.64/2.85 tff(15656,plain,
% 2.64/2.85 (s(s(s(z))) = s(elem!1)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[13195, 15654, 802, 15640, 2859, 11319, 15645, 15650])).
% 2.64/2.85 tff(15657,plain,
% 2.64/2.85 (~(s(s(s(elem!1))) = elem!1)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[4128, 15656])).
% 2.64/2.85 tff(15658,plain,
% 2.64/2.85 (r(s(s(s(elem!1))), elem!1)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[1636, 15657, 15655])).
% 2.64/2.85 tff(15659,plain,
% 2.64/2.85 (s(elem!1) = s(s(s(z)))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[7556, 15656])).
% 2.64/2.85 tff(15660,plain,
% 2.64/2.85 (~(s(s(elem!1)) = elem!1)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[2356, 15659])).
% 2.64/2.85 tff(15661,plain,
% 2.64/2.85 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[143, 15660])).
% 2.64/2.85 tff(15662,plain,
% 2.64/2.85 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[13094, 15652, 14047, 14666, 15640, 15641, 3094])).
% 2.64/2.85 tff(15663,plain,
% 2.64/2.85 (~b(s(z), z)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[12662, 15654, 14047, 14666])).
% 2.64/2.85 tff(15664,plain,
% 2.64/2.85 (r(s(z), z)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[221, 15663])).
% 2.64/2.85 tff(15665,plain,
% 2.64/2.85 (s(s(s(s(s(s(z)))))) = elem!1),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[14918, 15664, 14047, 14676, 2859, 14666, 3094, 15641])).
% 2.64/2.85 tff(15666,plain,
% 2.64/2.85 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[5403, 15665])).
% 2.64/2.85 tff(15667,plain,
% 2.64/2.85 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[610, 15666, 15662])).
% 2.64/2.85 tff(15668,plain,
% 2.64/2.85 ($false),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[12859, 15667, 15661, 15640, 15650, 15658, 802])).
% 2.64/2.85 tff(15669,plain,((s(z) = elem!1) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.85 tff(15670,plain,
% 2.64/2.85 (s(z) = elem!1),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[15669, 15527, 14677, 5])).
% 2.64/2.85 tff(15671,plain,
% 2.64/2.85 (elem!1 = s(z)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[89, 15670])).
% 2.64/2.85 tff(15672,plain,
% 2.64/2.85 (s(elem!1) = s(s(z))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[15671])).
% 2.64/2.85 tff(15673,plain,
% 2.64/2.85 (s(s(elem!1)) = s(s(s(z)))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[18, 15671])).
% 2.64/2.85 tff(15674,plain,
% 2.64/2.85 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[15673])).
% 2.64/2.85 tff(15675,plain,
% 2.64/2.85 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(z)))) = s(s(z)))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[15674, 15672])).
% 2.64/2.85 tff(15676,plain,
% 2.64/2.85 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(z)) = s(s(s(s(z)))))),
% 2.64/2.85 inference(transitivity,[status(thm)],[15675, 1707])).
% 2.64/2.85 tff(15677,plain,
% 2.64/2.85 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 2.64/2.85 inference(symmetry,[status(thm)],[15676])).
% 2.64/2.85 tff(15678,plain,
% 2.64/2.85 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[15677])).
% 2.64/2.85 tff(15679,plain,
% 2.64/2.85 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[1612, 15678])).
% 2.64/2.85 tff(15680,plain,
% 2.64/2.85 (r(s(s(elem!1)), elem!1)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[15639, 14677, 15527, 5])).
% 2.64/2.85 tff(15681,plain,
% 2.64/2.85 (~r(s(s(elem!1)), s(elem!1))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[7985, 15680, 15527])).
% 2.64/2.85 tff(15682,plain,
% 2.64/2.85 ((s(s(elem!1)) = s(elem!1)) <=> (s(s(s(z))) = s(elem!1))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[15673])).
% 2.64/2.85 tff(15683,plain,
% 2.64/2.85 ((s(s(elem!1)) = s(elem!1)) <=> (s(elem!1) = s(s(s(z))))),
% 2.64/2.85 inference(transitivity,[status(thm)],[15682, 7552])).
% 2.64/2.85 tff(15684,plain,
% 2.64/2.85 ((s(elem!1) = s(s(s(z)))) <=> (s(s(elem!1)) = s(elem!1))),
% 2.64/2.85 inference(symmetry,[status(thm)],[15683])).
% 2.64/2.85 tff(15685,plain,
% 2.64/2.85 (s(s(z)) = s(elem!1)),
% 2.64/2.85 inference(symmetry,[status(thm)],[15672])).
% 2.64/2.85 tff(15686,plain,
% 2.64/2.85 ((s(s(z)) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[15685])).
% 2.64/2.85 tff(15687,plain,
% 2.64/2.85 ((s(s(z)) = s(s(s(z)))) <=> (s(s(elem!1)) = s(elem!1))),
% 2.64/2.85 inference(transitivity,[status(thm)],[15686, 15684])).
% 2.64/2.85 tff(15688,plain,
% 2.64/2.85 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[15687])).
% 2.64/2.85 tff(15689,plain,
% 2.64/2.85 (~(s(s(elem!1)) = s(elem!1))),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[2508, 15688])).
% 2.64/2.85 tff(15690,plain,
% 2.64/2.85 (b(s(s(elem!1)), s(elem!1))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[994, 15689, 15681])).
% 2.64/2.85 tff(15691,plain,
% 2.64/2.85 ((elem!1 = s(s(s(elem!1)))) <=> (s(z) = s(s(s(elem!1))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[15671])).
% 2.64/2.85 tff(15692,plain,
% 2.64/2.85 ((s(z) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 2.64/2.85 inference(symmetry,[status(thm)],[15691])).
% 2.64/2.85 tff(15693,plain,
% 2.64/2.85 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 2.64/2.85 inference(transitivity,[status(thm)],[15692, 1555])).
% 2.64/2.85 tff(15694,plain,
% 2.64/2.85 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[15693])).
% 2.64/2.85 tff(15695,plain,
% 2.64/2.85 (~(s(s(s(elem!1))) = elem!1)),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[645, 15694])).
% 2.64/2.85 tff(15696,plain,
% 2.64/2.85 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(s(z))) = s(s(s(s(z)))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[15673, 15674])).
% 2.64/2.85 tff(15697,plain,
% 2.64/2.85 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 2.64/2.85 inference(transitivity,[status(thm)],[15696, 339])).
% 2.64/2.85 tff(15698,plain,
% 2.64/2.85 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 2.64/2.85 inference(symmetry,[status(thm)],[15697])).
% 2.64/2.85 tff(15699,plain,
% 2.64/2.85 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[15698])).
% 2.64/2.85 tff(15700,plain,
% 2.64/2.85 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[4470, 15699])).
% 2.64/2.85 tff(15701,plain,
% 2.64/2.85 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[3437, 15700])).
% 2.64/2.85 tff(15702,plain,
% 2.64/2.85 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[15674])).
% 2.64/2.85 tff(15703,plain,
% 2.64/2.85 ((s(s(s(s(elem!1)))) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(s(z)))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[15702, 15672])).
% 2.64/2.85 tff(15704,plain,
% 2.64/2.85 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 2.64/2.85 inference(symmetry,[status(thm)],[15703])).
% 2.64/2.85 tff(15705,plain,
% 2.64/2.85 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(s(s(elem!1)))) = s(elem!1)))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[15704])).
% 2.64/2.85 tff(15706,plain,
% 2.64/2.85 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[6464, 15705])).
% 2.64/2.85 tff(15707,plain,
% 2.64/2.85 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[1284, 15679])).
% 2.64/2.85 tff(15708,plain,
% 2.64/2.85 (b(elem!1, s(s(elem!1)))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[14589, 15671, 13280])).
% 2.64/2.85 tff(15709,plain,
% 2.64/2.85 (~(s(s(s(s(elem!1)))) = elem!1)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[6321, 15671])).
% 2.64/2.85 tff(15710,plain,
% 2.64/2.85 (b(s(elem!1), s(s(elem!1))) <=> b(s(elem!1), s(s(s(z))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[15673])).
% 2.64/2.85 tff(15711,plain,
% 2.64/2.85 (b(s(elem!1), s(s(s(z)))) <=> b(s(elem!1), s(s(elem!1)))),
% 2.64/2.85 inference(symmetry,[status(thm)],[15710])).
% 2.64/2.85 tff(15712,plain,
% 2.64/2.85 (b(s(s(z)), s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[15685])).
% 2.64/2.85 tff(15713,plain,
% 2.64/2.85 (b(s(s(z)), s(s(s(z)))) <=> b(s(elem!1), s(s(elem!1)))),
% 2.64/2.85 inference(transitivity,[status(thm)],[15712, 15711])).
% 2.64/2.85 tff(15714,plain,
% 2.64/2.85 (r(s(elem!1), s(z)) <=> r(s(s(z)), s(z))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[15672])).
% 2.64/2.85 tff(15715,plain,
% 2.64/2.85 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(z))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[15671])).
% 2.64/2.85 tff(15716,plain,
% 2.64/2.85 (r(s(elem!1), s(z))),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[15527, 15715])).
% 2.64/2.85 tff(15717,plain,
% 2.64/2.85 (r(s(s(z)), s(z))),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[15716, 15714])).
% 2.64/2.85 tff(15718,plain,
% 2.64/2.85 (~b(s(s(s(z))), s(z))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[4206, 15670, 1])).
% 2.64/2.85 tff(15719,plain,
% 2.64/2.85 (r(s(s(s(z))), s(z))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[113, 15718])).
% 2.64/2.85 tff(15720,plain,
% 2.64/2.85 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))),
% 2.64/2.85 inference(rewrite,[status(thm)],[])).
% 2.64/2.85 tff(15721,plain,
% 2.64/2.85 (((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))),
% 2.64/2.85 inference(rewrite,[status(thm)],[])).
% 2.64/2.85 tff(15722,plain,
% 2.64/2.85 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z)))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[15721])).
% 2.64/2.85 tff(15723,plain,
% 2.64/2.85 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))),
% 2.64/2.85 inference(transitivity,[status(thm)],[15722, 15720])).
% 2.64/2.85 tff(15724,plain,
% 2.64/2.85 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.64/2.85 inference(quant_inst,[status(thm)],[])).
% 2.64/2.85 tff(15725,plain,
% 2.64/2.85 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z)))),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[15724, 15723])).
% 2.64/2.85 tff(15726,plain,
% 2.64/2.85 (~r(s(s(z)), s(s(s(z))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[15725, 124, 15719, 15717])).
% 2.64/2.85 tff(15727,plain,
% 2.64/2.85 (b(s(s(z)), s(s(s(z))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[2514, 15726])).
% 2.64/2.85 tff(15728,plain,
% 2.64/2.85 (b(s(elem!1), s(s(elem!1)))),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[15727, 15713])).
% 2.64/2.85 tff(15729,plain,
% 2.64/2.85 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[1769, 15728, 15527, 15680, 15709, 15708, 15707, 15690, 15706])).
% 2.64/2.85 tff(15730,plain,
% 2.64/2.85 (~b(s(s(s(elem!1))), elem!1)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[12492, 15729, 14047, 14666, 15701])).
% 2.64/2.85 tff(15731,plain,
% 2.64/2.85 (r(s(s(s(elem!1))), elem!1)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[1636, 15730, 15695])).
% 2.64/2.85 tff(15732,plain,
% 2.64/2.85 (~b(s(s(elem!1)), elem!1)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[32, 15718, 15671])).
% 2.64/2.85 tff(15733,plain,
% 2.64/2.85 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[12869, 15731, 15732, 15679])).
% 2.64/2.85 tff(15734,plain,
% 2.64/2.85 ($false),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[12859, 15733, 15731, 15680, 15690, 15679, 15527])).
% 2.64/2.85 tff(15735,plain,(b(s(s(s(z))), elem!1) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.85 tff(15736,plain,
% 2.64/2.85 (b(s(s(s(z))), elem!1)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[15735, 5])).
% 2.64/2.85 tff(15737,plain,
% 2.64/2.85 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[12298, 15736, 14047, 14666])).
% 2.64/2.85 tff(15738,plain,
% 2.64/2.85 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[4289, 5331, 13280, 14666, 15736, 6, 15737, 5])).
% 2.64/2.85 tff(15739,plain,
% 2.64/2.85 (b(s(s(s(s(s(s(z)))))), s(z))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[651, 43, 2844, 15738])).
% 2.64/2.85 tff(15740,plain,
% 2.64/2.85 (~b(s(s(elem!1)), elem!1)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[3002, 11319, 13280, 14666, 15736])).
% 2.64/2.85 tff(15741,plain,
% 2.64/2.85 (s(s(elem!1)) = elem!1),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[47, 15740, 6])).
% 2.64/2.85 tff(15742,plain,
% 2.64/2.85 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[4284, 15741])).
% 2.64/2.86 tff(15743,plain,
% 2.64/2.86 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[1144, 15742, 15737])).
% 2.64/2.86 tff(15744,plain,
% 2.64/2.86 (~r(s(s(s(z))), s(z))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[15537, 5331, 14666, 6, 5])).
% 2.64/2.86 tff(15745,plain,
% 2.64/2.86 (b(s(s(s(z))), s(z))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[113, 15744])).
% 2.64/2.86 tff(15746,plain,
% 2.64/2.86 ($false),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[13205, 306, 838, 4012, 2284, 2831, 1967])).
% 2.64/2.86 tff(15747,plain,((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.86 tff(15748,plain,
% 2.64/2.86 (~b(s(z), elem!1)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[15747, 15745, 14047, 14666, 15736])).
% 2.64/2.86 tff(15749,plain,
% 2.64/2.86 (r(s(z), elem!1)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[13156, 15748, 3094])).
% 2.64/2.86 tff(15750,plain,
% 2.64/2.86 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[9918, 124, 15749, 15743])).
% 2.64/2.86 tff(15751,plain,
% 2.64/2.86 (b(s(z), s(s(s(s(s(s(z)))))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[5358, 43, 5355, 15750])).
% 2.64/2.86 tff(15752,plain,
% 2.64/2.86 (~(s(s(s(s(z)))) = elem!1)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[9813, 15741])).
% 2.64/2.86 tff(15753,plain,
% 2.64/2.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))))),
% 2.64/2.86 inference(rewrite,[status(thm)],[])).
% 2.64/2.86 tff(15754,plain,
% 2.64/2.86 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z)))))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))))),
% 2.64/2.86 inference(rewrite,[status(thm)],[])).
% 2.64/2.86 tff(15755,plain,
% 2.64/2.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(z, s(s(s(z)))))))),
% 2.64/2.86 inference(monotonicity,[status(thm)],[15754])).
% 2.64/2.86 tff(15756,plain,
% 2.64/2.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(z, s(s(s(z))))))),
% 2.64/2.86 inference(transitivity,[status(thm)],[15755, 15753])).
% 2.64/2.86 tff(15757,plain,
% 2.64/2.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))))),
% 2.64/2.86 inference(quant_inst,[status(thm)],[])).
% 2.64/2.86 tff(15758,plain,
% 2.64/2.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z)))))),
% 2.64/2.86 inference(modus_ponens,[status(thm)],[15757, 15756])).
% 2.64/2.86 tff(15759,plain,
% 2.64/2.86 (~b(z, s(s(s(z))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[15758, 306, 14666, 14047, 15736])).
% 2.64/2.86 tff(15760,plain,
% 2.64/2.86 (r(z, s(s(s(z))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[11982, 15759])).
% 2.64/2.86 tff(15761,plain,
% 2.64/2.86 (~b(s(z), z)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[15387, 15739, 15760, 15751, 14676, 15745, 14666])).
% 2.64/2.86 tff(15762,plain,
% 2.64/2.86 (r(s(z), z)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[221, 15761])).
% 2.64/2.86 tff(15763,plain,
% 2.64/2.86 (~r(s(s(s(s(z)))), s(z))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[12145, 15762, 14666, 15752, 14047, 15641])).
% 2.64/2.86 tff(15764,plain,
% 2.64/2.86 (b(s(s(s(s(z)))), s(z))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[4490, 15763])).
% 2.64/2.86 tff(15765,plain,
% 2.64/2.86 (~b(s(z), s(s(s(z))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[15254, 15764, 14666, 15736, 15752, 15742, 15745, 6, 5331, 5])).
% 2.64/2.86 tff(15766,plain,
% 2.64/2.86 (r(s(z), s(s(s(z))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[3302, 15765])).
% 2.64/2.86 tff(15767,plain,
% 2.64/2.86 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[15092, 15766, 14666, 15752, 15738, 15743, 15764, 14047, 14676])).
% 2.64/2.86 tff(15768,plain,
% 2.64/2.86 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[4471, 15767])).
% 2.64/2.86 tff(15769,plain,
% 2.64/2.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 2.64/2.86 inference(rewrite,[status(thm)],[])).
% 2.64/2.86 tff(15770,plain,
% 2.64/2.86 (((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(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(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 2.64/2.86 inference(rewrite,[status(thm)],[])).
% 2.64/2.86 tff(15771,plain,
% 2.64/2.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))))),
% 2.64/2.86 inference(monotonicity,[status(thm)],[15770])).
% 2.64/2.86 tff(15772,plain,
% 2.64/2.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 2.64/2.86 inference(transitivity,[status(thm)],[15771, 15769])).
% 2.64/2.86 tff(15773,plain,
% 2.64/2.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(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))))))),
% 2.64/2.86 inference(quant_inst,[status(thm)],[])).
% 2.64/2.86 tff(15774,plain,
% 2.64/2.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 2.64/2.86 inference(modus_ponens,[status(thm)],[15773, 15772])).
% 2.64/2.86 tff(15775,plain,
% 2.64/2.86 ($false),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[15774, 306, 15745, 15768, 15764, 15751, 15739])).
% 2.64/2.86 tff(15776,plain,((s(z) = elem!1) | r(s(s(elem!1)), elem!1) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.86 tff(15777,plain,
% 2.64/2.86 (s(z) = elem!1),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[15776, 6, 5])).
% 2.64/2.86 tff(15778,plain,
% 2.64/2.86 (s(s(z)) = s(elem!1)),
% 2.64/2.86 inference(monotonicity,[status(thm)],[15777])).
% 2.64/2.86 tff(15779,plain,
% 2.64/2.86 (r(s(s(z)), z) <=> r(s(elem!1), z)),
% 2.64/2.86 inference(monotonicity,[status(thm)],[15778])).
% 2.64/2.86 tff(15780,plain,
% 2.64/2.86 (r(s(elem!1), z) <=> r(s(s(z)), z)),
% 2.64/2.86 inference(symmetry,[status(thm)],[15779])).
% 2.64/2.86 tff(15781,plain,
% 2.64/2.86 ((~r(s(elem!1), z)) <=> (~r(s(s(z)), z))),
% 2.64/2.86 inference(monotonicity,[status(thm)],[15780])).
% 2.64/2.86 tff(15782,plain,
% 2.64/2.86 (r(s(z), z) <=> r(elem!1, z)),
% 2.64/2.86 inference(monotonicity,[status(thm)],[15777])).
% 2.64/2.86 tff(15783,plain,
% 2.64/2.86 (r(elem!1, z) <=> r(s(z), z)),
% 2.64/2.86 inference(symmetry,[status(thm)],[15782])).
% 2.64/2.86 tff(15784,plain,
% 2.64/2.86 (elem!1 = s(z)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[89, 15777])).
% 2.64/2.86 tff(15785,plain,
% 2.64/2.86 (r(elem!1, z)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[14813, 15784, 13280, 14047, 14666, 6])).
% 2.64/2.86 tff(15786,plain,
% 2.64/2.86 (r(s(z), z)),
% 2.64/2.86 inference(modus_ponens,[status(thm)],[15785, 15783])).
% 2.64/2.86 tff(15787,plain,
% 2.64/2.86 (r(s(elem!1), s(z)) <=> r(s(elem!1), elem!1)),
% 2.64/2.86 inference(monotonicity,[status(thm)],[15777])).
% 2.64/2.86 tff(15788,plain,
% 2.64/2.86 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(z))),
% 2.64/2.86 inference(symmetry,[status(thm)],[15787])).
% 2.64/2.86 tff(15789,plain,
% 2.64/2.86 (~r(z, elem!1)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[14578, 6, 5])).
% 2.64/2.86 tff(15790,plain,
% 2.64/2.86 (r(elem!1, z)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[15430, 808, 5, 15789, 6])).
% 2.64/2.86 tff(15791,plain,
% 2.64/2.86 (s(elem!1) = elem!1),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[2389, 15790, 13280, 14666, 15736, 6, 808])).
% 2.64/2.86 tff(15792,plain,
% 2.64/2.86 (s(s(elem!1)) = elem!1),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[180, 15791])).
% 2.64/2.86 tff(15793,plain,
% 2.64/2.86 (~(s(s(s(s(z)))) = elem!1)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[9813, 15792])).
% 2.64/2.86 tff(15794,plain,
% 2.64/2.86 (~r(s(s(s(s(z)))), z)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[9834, 15793, 13280, 14676, 15790, 15736])).
% 2.64/2.86 tff(15795,plain,
% 2.64/2.86 (b(s(s(s(s(z)))), z)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[695, 15794])).
% 2.64/2.86 tff(15796,plain,
% 2.64/2.86 (~b(s(s(s(s(z)))), elem!1)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[12141, 306, 14666, 14047, 15795])).
% 2.64/2.86 tff(15797,plain,
% 2.64/2.86 (r(s(s(s(s(z)))), elem!1)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[9832, 15796, 15793])).
% 2.64/2.86 tff(15798,plain,
% 2.64/2.86 ((s(s(elem!1)) = s(z)) <=> (elem!1 = s(z))),
% 2.64/2.86 inference(monotonicity,[status(thm)],[15792])).
% 2.64/2.86 tff(15799,plain,
% 2.64/2.86 ((~(s(s(elem!1)) = s(z))) <=> (~(elem!1 = s(z)))),
% 2.64/2.86 inference(monotonicity,[status(thm)],[15798])).
% 2.64/2.86 tff(15800,plain,
% 2.64/2.86 (~(elem!1 = s(z))),
% 2.64/2.86 inference(modus_ponens,[status(thm)],[80, 15799])).
% 2.64/2.86 tff(15801,plain,
% 2.64/2.86 (~r(s(s(s(z))), s(z))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[15537, 15800, 14666, 6, 5])).
% 2.64/2.86 tff(15802,plain,
% 2.64/2.86 (b(s(s(s(z))), s(z))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[113, 15801])).
% 2.64/2.86 tff(15803,plain,
% 2.64/2.86 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[4284, 15792])).
% 2.64/2.86 tff(15804,plain,
% 2.64/2.86 (elem!1 = s(s(elem!1))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[1174, 15792])).
% 2.64/2.86 tff(15805,plain,
% 2.64/2.86 (s(s(s(elem!1))) = s(elem!1)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[1168, 15804])).
% 2.64/2.86 tff(15806,plain,
% 2.64/2.86 (~r(s(z), z)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[2654, 15791, 15790, 5])).
% 2.64/2.86 tff(15807,plain,
% 2.64/2.86 (b(s(z), z)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[221, 15806])).
% 2.64/2.86 tff(15808,plain,
% 2.64/2.86 (~r(s(z), s(s(s(z))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[15415, 15800, 14666, 6, 15807, 5, 15805, 808])).
% 2.64/2.86 tff(15809,plain,
% 2.64/2.86 (b(s(z), s(s(s(z))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[3302, 15808])).
% 2.64/2.86 tff(15810,plain,
% 2.64/2.86 (~b(s(s(s(s(z)))), s(z))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[15254, 15809, 14666, 15736, 15793, 15803, 15802, 6, 15800, 5])).
% 2.64/2.86 tff(15811,plain,
% 2.64/2.86 (r(s(s(s(s(z)))), s(z))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[4490, 15810])).
% 2.64/2.86 tff(15812,plain,
% 2.64/2.86 ((s(s(elem!1)) = s(z)) <=> (s(z) = elem!1)),
% 2.64/2.86 inference(transitivity,[status(thm)],[15798, 3092])).
% 2.64/2.86 tff(15813,plain,
% 2.64/2.86 ((~(s(s(elem!1)) = s(z))) <=> (~(s(z) = elem!1))),
% 2.64/2.86 inference(monotonicity,[status(thm)],[15812])).
% 2.64/2.86 tff(15814,plain,
% 2.64/2.86 (~(s(z) = elem!1)),
% 2.64/2.86 inference(modus_ponens,[status(thm)],[80, 15813])).
% 2.64/2.86 tff(15815,plain,
% 2.64/2.86 (~b(s(z), elem!1)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[12662, 15807, 14047, 14666])).
% 2.64/2.86 tff(15816,plain,
% 2.64/2.86 (r(s(z), elem!1)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[1500, 43, 15815, 15814])).
% 2.64/2.86 tff(15817,plain,
% 2.64/2.86 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))),
% 2.64/2.86 inference(rewrite,[status(thm)],[])).
% 2.64/2.86 tff(15818,plain,
% 2.64/2.86 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))),
% 2.64/2.86 inference(quant_inst,[status(thm)],[])).
% 2.64/2.86 tff(15819,plain,
% 2.64/2.86 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z)))),
% 2.64/2.86 inference(modus_ponens,[status(thm)],[15818, 15817])).
% 2.64/2.86 tff(15820,plain,
% 2.64/2.86 ($false),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[15819, 124, 15816, 15811, 15797])).
% 2.64/2.86 tff(15821,plain,(r(s(elem!1), elem!1) | r(s(s(elem!1)), elem!1) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.86 tff(15822,plain,
% 2.64/2.86 (r(s(elem!1), elem!1)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[15821, 6, 5])).
% 2.64/2.86 tff(15823,plain,
% 2.64/2.86 (r(s(elem!1), s(z))),
% 2.64/2.86 inference(modus_ponens,[status(thm)],[15822, 15788])).
% 2.64/2.86 tff(15824,plain,
% 2.64/2.86 (~r(s(elem!1), z)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[2634, 15823, 15786])).
% 2.64/2.86 tff(15825,plain,
% 2.64/2.86 (~r(s(s(z)), z)),
% 2.64/2.86 inference(modus_ponens,[status(thm)],[15824, 15781])).
% 2.64/2.86 tff(15826,plain,
% 2.64/2.86 (r(s(s(z)), s(z)) <=> r(s(s(z)), elem!1)),
% 2.64/2.86 inference(monotonicity,[status(thm)],[15777])).
% 2.64/2.86 tff(15827,plain,
% 2.64/2.86 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(z))),
% 2.64/2.86 inference(symmetry,[status(thm)],[15826])).
% 2.64/2.86 tff(15828,plain,
% 2.64/2.86 (r(s(s(z)), elem!1) <=> r(s(elem!1), elem!1)),
% 2.64/2.86 inference(monotonicity,[status(thm)],[15778])).
% 2.64/2.86 tff(15829,plain,
% 2.64/2.86 (r(s(elem!1), elem!1) <=> r(s(s(z)), elem!1)),
% 2.64/2.86 inference(symmetry,[status(thm)],[15828])).
% 2.64/2.86 tff(15830,plain,
% 2.64/2.86 (r(s(elem!1), elem!1) <=> r(s(s(z)), s(z))),
% 2.64/2.86 inference(transitivity,[status(thm)],[15829, 15827])).
% 2.64/2.86 tff(15831,plain,
% 2.64/2.86 (r(s(s(z)), s(z))),
% 2.64/2.86 inference(modus_ponens,[status(thm)],[15822, 15830])).
% 2.64/2.86 tff(15832,plain,
% 2.64/2.86 (b(z, s(z))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[2281, 15785, 5, 14666])).
% 2.64/2.86 tff(15833,plain,
% 2.64/2.86 (b(s(z), s(s(s(z))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[9887, 15777, 13280])).
% 2.64/2.86 tff(15834,plain,
% 2.64/2.86 (r(s(s(s(s(s(s(z)))))), s(z)) <=> r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.64/2.86 inference(monotonicity,[status(thm)],[15777])).
% 2.64/2.86 tff(15835,plain,
% 2.64/2.86 (r(s(s(s(s(s(s(z)))))), elem!1) <=> r(s(s(s(s(s(s(z)))))), s(z))),
% 2.64/2.86 inference(symmetry,[status(thm)],[15834])).
% 2.64/2.86 tff(15836,plain,
% 2.64/2.86 (elem!1 = s(z)),
% 2.64/2.86 inference(symmetry,[status(thm)],[15777])).
% 2.64/2.86 tff(15837,plain,
% 2.64/2.86 ((s(s(s(s(s(s(z)))))) = elem!1) <=> (s(s(s(s(s(s(z)))))) = s(z))),
% 2.64/2.86 inference(monotonicity,[status(thm)],[15836])).
% 2.64/2.86 tff(15838,plain,
% 2.64/2.86 ((s(s(s(s(s(s(z)))))) = s(z)) <=> (s(s(s(s(s(s(z)))))) = elem!1)),
% 2.64/2.86 inference(symmetry,[status(thm)],[15837])).
% 2.64/2.86 tff(15839,plain,
% 2.64/2.86 ((~(s(s(s(s(s(s(z)))))) = s(z))) <=> (~(s(s(s(s(s(s(z)))))) = elem!1))),
% 2.64/2.86 inference(monotonicity,[status(thm)],[15838])).
% 2.64/2.86 tff(15840,plain,
% 2.64/2.86 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 2.64/2.86 inference(modus_ponens,[status(thm)],[2844, 15839])).
% 2.64/2.86 tff(15841,plain,
% 2.64/2.86 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[1144, 15840, 15737])).
% 2.64/2.86 tff(15842,plain,
% 2.64/2.86 (r(s(s(s(s(s(s(z)))))), s(z))),
% 2.64/2.86 inference(modus_ponens,[status(thm)],[15841, 15835])).
% 2.64/2.86 tff(15843,plain,
% 2.64/2.86 (~b(s(s(z)), z)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[4331, 15842, 15833, 15832, 15786, 15831])).
% 2.64/2.86 tff(15844,plain,
% 2.64/2.86 ($false),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[2531, 15843, 15825])).
% 2.64/2.86 tff(15845,plain,(r(s(s(elem!1)), elem!1) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.86 tff(15846,plain,
% 2.64/2.86 (r(s(s(elem!1)), elem!1)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[15845, 5])).
% 2.64/2.86 tff(15847,plain,
% 2.64/2.86 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), s(s(elem!1)))),
% 2.64/2.86 inference(monotonicity,[status(thm)],[183])).
% 2.64/2.86 tff(15848,plain,
% 2.64/2.86 (r(s(s(elem!1)), s(s(elem!1))) <=> r(s(s(elem!1)), elem!1)),
% 2.64/2.86 inference(symmetry,[status(thm)],[15847])).
% 2.64/2.86 tff(15849,plain,
% 2.64/2.86 ((~r(s(s(elem!1)), s(s(elem!1)))) <=> (~r(s(s(elem!1)), elem!1))),
% 2.64/2.86 inference(monotonicity,[status(thm)],[15848])).
% 2.64/2.86 tff(15850,plain,
% 2.64/2.86 (~r(s(s(elem!1)), s(s(elem!1)))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[13229, 124, 1730])).
% 2.64/2.86 tff(15851,plain,
% 2.64/2.86 (~r(s(s(elem!1)), elem!1)),
% 2.64/2.86 inference(modus_ponens,[status(thm)],[15850, 15849])).
% 2.64/2.86 tff(15852,plain,
% 2.64/2.86 ($false),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[1730, 15851])).
% 2.64/2.86 tff(15853,plain,((~(elem!1 = s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.86 tff(15854,plain,
% 2.64/2.86 (~(elem!1 = s(s(elem!1)))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[15853, 15846])).
% 2.64/2.86 tff(15855,plain,
% 2.64/2.86 (~(s(s(elem!1)) = elem!1)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[1174, 15854])).
% 2.64/2.86 tff(15856,plain,
% 2.64/2.86 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[143, 15855])).
% 2.64/2.86 tff(15857,plain,
% 2.64/2.86 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[152, 15856])).
% 2.64/2.86 tff(15858,plain,
% 2.64/2.86 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[159, 15857])).
% 2.64/2.86 tff(15859,plain,
% 2.64/2.86 (~r(s(s(elem!1)), s(z))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[9725, 15641, 15846])).
% 2.64/2.86 tff(15860,plain,
% 2.64/2.86 (b(s(s(elem!1)), s(z))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[3989, 15859])).
% 2.64/2.86 tff(15861,plain,
% 2.64/2.86 (~(s(elem!1) = elem!1)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[180, 15855])).
% 2.64/2.86 tff(15862,plain,
% 2.64/2.86 (~(s(s(elem!1)) = s(elem!1))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[195, 15861])).
% 2.64/2.86 tff(15863,plain,
% 2.64/2.86 (~(elem!1 = s(s(elem!1)))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[15853, 1730])).
% 2.64/2.86 tff(15864,plain,
% 2.64/2.86 (~(s(s(elem!1)) = elem!1)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[1174, 15863])).
% 2.64/2.86 tff(15865,plain,
% 2.64/2.86 (~(s(elem!1) = elem!1)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[180, 15864])).
% 2.64/2.86 tff(15866,plain,
% 2.64/2.86 (b(s(elem!1), elem!1)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[813, 808, 15865])).
% 2.64/2.86 tff(15867,plain,
% 2.64/2.86 (~b(s(elem!1), z)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[3111, 306, 838, 4012, 15866])).
% 2.64/2.86 tff(15868,plain,
% 2.64/2.86 (r(s(elem!1), z)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[2380, 15867])).
% 2.64/2.86 tff(15869,plain,
% 2.64/2.86 (~r(s(elem!1), s(s(s(z))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[2387, 124, 15868, 205])).
% 2.64/2.86 tff(15870,plain,
% 2.64/2.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)))),
% 2.64/2.86 inference(rewrite,[status(thm)],[])).
% 2.64/2.86 tff(15871,plain,
% 2.64/2.86 (((~b(z, elem!1)) | (~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(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)))),
% 2.64/2.86 inference(rewrite,[status(thm)],[])).
% 2.64/2.86 tff(15872,plain,
% 2.64/2.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1))))),
% 2.64/2.86 inference(monotonicity,[status(thm)],[15871])).
% 2.64/2.86 tff(15873,plain,
% 2.64/2.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)))),
% 2.64/2.86 inference(transitivity,[status(thm)],[15872, 15870])).
% 2.64/2.86 tff(15874,plain,
% 2.64/2.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~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))))))),
% 2.64/2.86 inference(quant_inst,[status(thm)],[])).
% 2.64/2.86 tff(15875,plain,
% 2.64/2.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1))),
% 2.64/2.86 inference(modus_ponens,[status(thm)],[15874, 15873])).
% 2.64/2.86 tff(15876,plain,
% 2.64/2.86 (~b(s(elem!1), s(s(s(z))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[15875, 306, 838, 4012, 15866, 1967])).
% 2.64/2.86 tff(15877,plain,
% 2.64/2.86 ((s(elem!1) = s(s(s(z)))) | r(s(elem!1), s(s(s(z))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[2367, 43, 15876])).
% 2.64/2.86 tff(15878,plain,
% 2.64/2.86 (s(elem!1) = s(s(s(z)))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[15877, 15869])).
% 2.64/2.86 tff(15879,plain,
% 2.64/2.86 (s(s(elem!1)) = s(s(s(s(z))))),
% 2.64/2.86 inference(monotonicity,[status(thm)],[15878])).
% 2.64/2.86 tff(15880,plain,
% 2.64/2.86 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 2.64/2.86 inference(monotonicity,[status(thm)],[15879])).
% 2.64/2.86 tff(15881,plain,
% 2.64/2.86 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 2.64/2.86 inference(symmetry,[status(thm)],[15880])).
% 2.64/2.86 tff(15882,plain,
% 2.64/2.86 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 2.64/2.86 inference(monotonicity,[status(thm)],[15881])).
% 2.64/2.86 tff(15883,plain,
% 2.64/2.86 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(s(z))))), elem!1)),
% 2.64/2.86 inference(symmetry,[status(thm)],[15882])).
% 2.64/2.86 tff(15884,plain,
% 2.64/2.86 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[7090, 808, 12587, 15864])).
% 2.64/2.86 tff(15885,plain,
% 2.64/2.86 (~r(s(s(s(elem!1))), elem!1)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[7780, 15884, 1730])).
% 2.64/2.86 tff(15886,plain,
% 2.64/2.86 (~r(s(s(s(z))), s(elem!1))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[6878, 124, 15868, 205])).
% 2.64/2.86 tff(15887,plain,
% 2.64/2.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))),
% 2.64/2.86 inference(rewrite,[status(thm)],[])).
% 2.64/2.86 tff(15888,plain,
% 2.64/2.86 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1)))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))),
% 2.64/2.86 inference(rewrite,[status(thm)],[])).
% 2.64/2.86 tff(15889,plain,
% 2.64/2.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1)))))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[15888])).
% 2.64/2.87 tff(15890,plain,
% 2.64/2.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))),
% 2.64/2.87 inference(transitivity,[status(thm)],[15889, 15887])).
% 2.64/2.87 tff(15891,plain,
% 2.64/2.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))),
% 2.64/2.87 inference(quant_inst,[status(thm)],[])).
% 2.64/2.87 tff(15892,plain,
% 2.64/2.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1)))),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[15891, 15890])).
% 2.64/2.87 tff(15893,plain,
% 2.64/2.87 (~b(s(s(s(z))), s(elem!1))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[15892, 306, 838, 4012, 15866, 1967])).
% 2.64/2.87 tff(15894,plain,
% 2.64/2.87 ((s(s(s(z))) = s(elem!1)) | r(s(s(s(z))), s(elem!1))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[4132, 43, 15893])).
% 2.64/2.87 tff(15895,plain,
% 2.64/2.87 (s(s(s(z))) = s(elem!1)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[15894, 15886])).
% 2.64/2.87 tff(15896,plain,
% 2.64/2.87 (~(s(s(s(elem!1))) = elem!1)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[4128, 15895])).
% 2.64/2.87 tff(15897,plain,
% 2.64/2.87 (b(s(s(s(elem!1))), elem!1)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[1636, 15896, 15885])).
% 2.64/2.87 tff(15898,plain,
% 2.64/2.87 (b(s(s(s(s(s(z))))), elem!1)),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[15897, 15883])).
% 2.64/2.87 tff(15899,plain,
% 2.64/2.87 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[15880, 15878])).
% 2.64/2.87 tff(15900,plain,
% 2.64/2.87 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[143, 15864])).
% 2.64/2.87 tff(15901,plain,
% 2.64/2.87 (~b(z, s(elem!1))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[11332, 306, 838, 4012, 15866])).
% 2.64/2.87 tff(15902,plain,
% 2.64/2.87 (r(z, s(elem!1))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[275, 15901])).
% 2.64/2.87 tff(15903,plain,
% 2.64/2.87 (~b(z, s(s(s(elem!1))))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[6150, 15897, 4012, 838])).
% 2.64/2.87 tff(15904,plain,
% 2.64/2.87 (r(z, s(s(s(elem!1))))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[585, 15903])).
% 2.64/2.87 tff(15905,plain,
% 2.64/2.87 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[5741, 15904, 15902])).
% 2.64/2.87 tff(15906,plain,
% 2.64/2.87 (b(s(s(s(elem!1))), s(elem!1))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[664, 15905, 15900])).
% 2.64/2.87 tff(15907,plain,
% 2.64/2.87 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[15906, 15899])).
% 2.64/2.87 tff(15908,plain,
% 2.64/2.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.64/2.87 inference(rewrite,[status(thm)],[])).
% 2.64/2.87 tff(15909,plain,
% 2.64/2.87 (((~b(z, elem!1)) | (~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)))))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.64/2.87 inference(rewrite,[status(thm)],[])).
% 2.64/2.87 tff(15910,plain,
% 2.64/2.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[15909])).
% 2.64/2.87 tff(15911,plain,
% 2.64/2.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.64/2.87 inference(transitivity,[status(thm)],[15910, 15908])).
% 2.64/2.87 tff(15912,plain,
% 2.64/2.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~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))))))),
% 2.64/2.87 inference(quant_inst,[status(thm)],[])).
% 2.64/2.87 tff(15913,plain,
% 2.64/2.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[15912, 15911])).
% 2.64/2.87 tff(15914,plain,
% 2.64/2.87 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[15913, 306, 838, 4012, 1967, 15907])).
% 2.64/2.87 tff(15915,plain,
% 2.64/2.87 ($false),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[15914, 15898])).
% 2.64/2.87 tff(15916,plain,(r(s(elem!1), elem!1) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.87 tff(15917,plain,
% 2.64/2.87 (r(s(elem!1), elem!1)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[15916, 14666, 14047, 15736, 14676, 15846])).
% 2.64/2.87 tff(15918,plain,
% 2.64/2.87 (~r(s(s(elem!1)), s(elem!1))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[7985, 15917, 15846])).
% 2.64/2.87 tff(15919,plain,
% 2.64/2.87 (b(s(s(elem!1)), s(elem!1))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[994, 15918, 15862])).
% 2.64/2.87 tff(15920,plain,
% 2.64/2.87 (~r(s(elem!1), s(z))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[2960, 15641, 15917])).
% 2.64/2.87 tff(15921,plain,
% 2.64/2.87 (b(s(elem!1), s(z))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[2964, 15920, 14196])).
% 2.64/2.87 tff(15922,plain,
% 2.64/2.87 (~b(s(z), s(s(elem!1)))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[4007, 15921, 15919, 15860])).
% 2.64/2.87 tff(15923,plain,
% 2.64/2.87 (r(s(z), s(s(elem!1)))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[3997, 43, 15922, 79])).
% 2.64/2.87 tff(15924,plain,
% 2.64/2.87 (~r(s(z), elem!1)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[13075, 15923, 15846])).
% 2.64/2.87 tff(15925,plain,
% 2.64/2.87 (b(s(z), elem!1)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[13156, 15924, 3094])).
% 2.64/2.87 tff(15926,plain,
% 2.64/2.87 (~b(s(z), z)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[12662, 15925, 14047, 14666])).
% 2.64/2.87 tff(15927,plain,
% 2.64/2.87 (r(s(z), z)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[221, 15926])).
% 2.64/2.87 tff(15928,plain,
% 2.64/2.87 (~b(s(s(s(z))), s(z))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[15747, 15925, 14047, 14666, 15736])).
% 2.64/2.87 tff(15929,plain,
% 2.64/2.87 (r(s(s(s(z))), s(z))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[113, 15928])).
% 2.64/2.87 tff(15930,plain,
% 2.64/2.87 ($false),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[14831, 15929, 15927, 14666, 15641, 13280])).
% 2.64/2.87 tff(15931,plain,((s(z) = elem!1) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.87 tff(15932,plain,
% 2.64/2.87 (s(z) = elem!1),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[15931, 5])).
% 2.64/2.87 tff(15933,plain,
% 2.64/2.87 (elem!1 = s(z)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[89, 15932])).
% 2.64/2.87 tff(15934,plain,
% 2.64/2.87 ((elem!1 = s(s(s(elem!1)))) <=> (s(z) = s(s(s(elem!1))))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[15933])).
% 2.64/2.87 tff(15935,plain,
% 2.64/2.87 ((s(z) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 2.64/2.87 inference(symmetry,[status(thm)],[15934])).
% 2.64/2.87 tff(15936,plain,
% 2.64/2.87 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 2.64/2.87 inference(transitivity,[status(thm)],[15935, 1555])).
% 2.64/2.87 tff(15937,plain,
% 2.64/2.87 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[15936])).
% 2.64/2.87 tff(15938,plain,
% 2.64/2.87 (~(s(s(s(elem!1))) = elem!1)),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[645, 15937])).
% 2.64/2.87 tff(15939,plain,
% 2.64/2.87 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[3437, 15857])).
% 2.64/2.87 tff(15940,plain,
% 2.64/2.87 (~(s(s(s(s(elem!1)))) = elem!1)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[6321, 15933])).
% 2.64/2.87 tff(15941,plain,
% 2.64/2.87 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[1284, 15856])).
% 2.64/2.87 tff(15942,plain,
% 2.64/2.87 (b(elem!1, s(s(elem!1)))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[14589, 15933, 13280])).
% 2.64/2.87 tff(15943,plain,
% 2.64/2.87 (~(s(elem!1) = s(s(elem!1)))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[4689, 15862])).
% 2.64/2.87 tff(15944,plain,
% 2.64/2.87 (~r(s(elem!1), s(s(elem!1)))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[1680, 124, 15917, 15846])).
% 2.64/2.87 tff(15945,plain,
% 2.64/2.87 (b(s(elem!1), s(s(elem!1)))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[1684, 43, 15944, 15943])).
% 2.64/2.87 tff(15946,plain,
% 2.64/2.87 (s(elem!1) = s(s(z))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[15933])).
% 2.64/2.87 tff(15947,plain,
% 2.64/2.87 (s(s(elem!1)) = s(s(s(z)))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[15946])).
% 2.64/2.87 tff(15948,plain,
% 2.64/2.87 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[15947])).
% 2.64/2.87 tff(15949,plain,
% 2.64/2.87 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[15948])).
% 2.64/2.87 tff(15950,plain,
% 2.64/2.87 ((s(s(s(s(elem!1)))) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(s(z)))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[15949, 15946])).
% 2.64/2.87 tff(15951,plain,
% 2.64/2.87 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 2.64/2.87 inference(symmetry,[status(thm)],[15950])).
% 2.64/2.87 tff(15952,plain,
% 2.64/2.87 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(s(s(elem!1)))) = s(elem!1)))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[15951])).
% 2.64/2.87 tff(15953,plain,
% 2.64/2.87 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[6464, 15952])).
% 2.64/2.87 tff(15954,plain,
% 2.64/2.87 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[1769, 15953, 15846, 15917, 15945, 15942, 15941, 15919, 15940])).
% 2.64/2.87 tff(15955,plain,
% 2.64/2.87 (~b(s(s(s(elem!1))), elem!1)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[12492, 15954, 14047, 14666, 15939])).
% 2.64/2.87 tff(15956,plain,
% 2.64/2.87 (r(s(s(s(elem!1))), elem!1)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[1636, 15955, 15938])).
% 2.64/2.87 tff(15957,plain,
% 2.64/2.87 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[7780, 15956, 15846])).
% 2.64/2.87 tff(15958,plain,
% 2.64/2.87 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[12859, 15956, 15846, 15919, 15856, 15917])).
% 2.64/2.87 tff(15959,plain,
% 2.64/2.87 ($false),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[610, 15958, 15957, 15858])).
% 2.64/2.87 tff(15960,plain,(b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.87 tff(15961,plain,
% 2.64/2.87 (r(s(s(elem!1)), elem!1)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[10311, 2, 3, 7])).
% 2.64/2.87 tff(15962,plain,
% 2.64/2.87 (~(elem!1 = s(s(elem!1)))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[15853, 15961])).
% 2.64/2.87 tff(15963,plain,
% 2.64/2.87 (~(s(s(elem!1)) = elem!1)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[1174, 15962])).
% 2.64/2.87 tff(15964,plain,
% 2.64/2.87 (~(s(elem!1) = elem!1)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[180, 15963])).
% 2.64/2.87 tff(15965,plain,
% 2.64/2.87 (~(s(s(elem!1)) = s(elem!1))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[195, 15964])).
% 2.64/2.87 tff(15966,plain,
% 2.64/2.87 (s(s(s(z))) = elem!1),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[1489, 1484, 1])).
% 2.64/2.87 tff(15967,plain,
% 2.64/2.87 (s(s(s(s(z)))) = s(elem!1)),
% 2.64/2.87 inference(monotonicity,[status(thm)],[15966])).
% 2.64/2.87 tff(15968,plain,
% 2.64/2.87 (r(s(s(s(s(z)))), elem!1) <=> r(s(elem!1), elem!1)),
% 2.64/2.87 inference(monotonicity,[status(thm)],[15967])).
% 2.64/2.87 tff(15969,plain,
% 2.64/2.87 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(z)))), elem!1)),
% 2.64/2.87 inference(monotonicity,[status(thm)],[15966])).
% 2.64/2.87 tff(15970,plain,
% 2.64/2.87 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(elem!1), elem!1)),
% 2.64/2.87 inference(transitivity,[status(thm)],[15969, 15968])).
% 2.64/2.87 tff(15971,plain,
% 2.64/2.87 (r(z, s(s(s(z)))) <=> r(z, elem!1)),
% 2.64/2.87 inference(monotonicity,[status(thm)],[15966])).
% 2.64/2.87 tff(15972,plain,
% 2.64/2.87 (r(z, elem!1) <=> r(z, s(s(s(z))))),
% 2.64/2.87 inference(symmetry,[status(thm)],[15971])).
% 2.64/2.87 tff(15973,plain,
% 2.64/2.87 ((~r(z, elem!1)) <=> (~r(z, s(s(s(z)))))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[15972])).
% 2.64/2.87 tff(15974,plain,
% 2.64/2.87 (~r(z, s(s(s(z))))),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[7, 15973])).
% 2.64/2.87 tff(15975,plain,
% 2.64/2.87 (b(z, s(s(s(z))))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[11982, 15974])).
% 2.64/2.87 tff(15976,plain,
% 2.64/2.87 ((~(s(s(s(z))) = elem!1)) | b(s(s(s(z))), s(z))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[4551, 15960])).
% 2.64/2.87 tff(15977,plain,
% 2.64/2.87 (b(s(s(s(z))), s(z))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[15976, 15966])).
% 2.64/2.87 tff(15978,plain,
% 2.64/2.87 (~(s(z) = elem!1)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[10054, 15960])).
% 2.64/2.87 tff(15979,plain,
% 2.64/2.87 (~(elem!1 = s(z))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[3096, 15978])).
% 2.64/2.87 tff(15980,plain,
% 2.64/2.87 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[2974, 15979])).
% 2.64/2.87 tff(15981,plain,
% 2.64/2.87 (~r(s(z), s(s(elem!1)))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[13075, 1730, 4])).
% 2.64/2.87 tff(15982,plain,
% 2.64/2.87 (b(s(z), s(s(elem!1)))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[3997, 43, 79, 15981])).
% 2.64/2.87 tff(15983,plain,
% 2.64/2.87 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[13104, 306, 7138, 15982, 8828])).
% 2.64/2.87 tff(15984,plain,
% 2.64/2.87 ($false),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[2986, 43, 15983, 12638, 15980])).
% 2.64/2.87 tff(15985,plain,((~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.87 tff(15986,plain,
% 2.64/2.87 (~r(s(s(s(z))), elem!1)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[15985, 15961, 4])).
% 2.64/2.87 tff(15987,plain,
% 2.64/2.87 (s(s(s(z))) = elem!1),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[1489, 15986, 1])).
% 2.64/2.87 tff(15988,plain,
% 2.64/2.87 (r(s(s(s(z))), z) <=> r(elem!1, z)),
% 2.64/2.87 inference(monotonicity,[status(thm)],[15987])).
% 2.64/2.87 tff(15989,plain,
% 2.64/2.87 (r(s(s(s(z))), z)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[2219, 15986, 2, 1])).
% 2.64/2.87 tff(15990,plain,
% 2.64/2.87 (r(elem!1, z)),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[15989, 15988])).
% 2.64/2.87 tff(15991,plain,
% 2.64/2.87 (~r(s(z), z)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[1049, 15990, 4])).
% 2.64/2.87 tff(15992,plain,
% 2.64/2.87 (b(s(z), z)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[221, 15991])).
% 2.64/2.87 tff(15993,plain,
% 2.64/2.87 (~r(s(z), s(s(elem!1)))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[13075, 15961, 4])).
% 2.64/2.87 tff(15994,plain,
% 2.64/2.87 (b(s(z), s(s(elem!1)))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[3997, 43, 79, 15993])).
% 2.64/2.87 tff(15995,plain,
% 2.64/2.87 (~r(s(s(elem!1)), z)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[7786, 15990, 15961])).
% 2.64/2.87 tff(15996,plain,
% 2.64/2.87 (b(s(s(elem!1)), z)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[476, 15995])).
% 2.64/2.87 tff(15997,plain,
% 2.64/2.87 (~r(s(s(elem!1)), s(z))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[8826, 15961, 4])).
% 2.64/2.87 tff(15998,plain,
% 2.64/2.87 (b(s(s(elem!1)), s(z))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[3989, 15997])).
% 2.64/2.87 tff(15999,plain,
% 2.64/2.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))))),
% 2.64/2.87 inference(rewrite,[status(thm)],[])).
% 2.64/2.87 tff(16000,plain,
% 2.64/2.87 (((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))))),
% 2.64/2.87 inference(rewrite,[status(thm)],[])).
% 2.64/2.87 tff(16001,plain,
% 2.64/2.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z)))))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[16000])).
% 2.64/2.87 tff(16002,plain,
% 2.64/2.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))))),
% 2.64/2.87 inference(transitivity,[status(thm)],[16001, 15999])).
% 2.64/2.87 tff(16003,plain,
% 2.64/2.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))))),
% 2.64/2.87 inference(quant_inst,[status(thm)],[])).
% 2.64/2.87 tff(16004,plain,
% 2.64/2.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z)))),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[16003, 16002])).
% 2.64/2.87 tff(16005,plain,
% 2.64/2.87 (~b(elem!1, s(s(elem!1)))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[16004, 306, 15994, 15960, 15998])).
% 2.64/2.87 tff(16006,plain,
% 2.64/2.87 (r(elem!1, s(s(elem!1)))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[516, 16005, 15962])).
% 2.64/2.87 tff(16007,plain,
% 2.64/2.87 (~r(z, s(s(elem!1)))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[978, 15990, 16006])).
% 2.64/2.87 tff(16008,plain,
% 2.64/2.87 (b(z, s(s(elem!1)))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[460, 16007])).
% 2.64/2.87 tff(16009,plain,
% 2.64/2.87 ((s(s(s(z))) = z) <=> (elem!1 = z)),
% 2.64/2.87 inference(monotonicity,[status(thm)],[15987])).
% 2.64/2.87 tff(16010,plain,
% 2.64/2.87 ((s(s(s(z))) = z) <=> (z = elem!1)),
% 2.64/2.87 inference(transitivity,[status(thm)],[16009, 161])).
% 2.64/2.87 tff(16011,plain,
% 2.64/2.87 ((~(s(s(s(z))) = z)) <=> (~(z = elem!1))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[16010])).
% 2.64/2.87 tff(16012,plain,
% 2.64/2.87 (~(z = elem!1)),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[169, 16011])).
% 2.64/2.87 tff(16013,plain,
% 2.64/2.87 (b(z, elem!1)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[835, 16012, 7])).
% 2.64/2.87 tff(16014,plain,
% 2.64/2.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)))),
% 2.64/2.87 inference(rewrite,[status(thm)],[])).
% 2.64/2.87 tff(16015,plain,
% 2.64/2.87 (((~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)))),
% 2.64/2.87 inference(rewrite,[status(thm)],[])).
% 2.64/2.87 tff(16016,plain,
% 2.64/2.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z))))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[16015])).
% 2.64/2.87 tff(16017,plain,
% 2.64/2.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)))),
% 2.64/2.87 inference(transitivity,[status(thm)],[16016, 16014])).
% 2.64/2.87 tff(16018,plain,
% 2.64/2.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)))),
% 2.64/2.87 inference(quant_inst,[status(thm)],[])).
% 2.64/2.87 tff(16019,plain,
% 2.64/2.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z))),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[16018, 16017])).
% 2.64/2.87 tff(16020,plain,
% 2.64/2.87 ($false),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[16019, 306, 16013, 16008, 15996, 15994, 15992])).
% 2.64/2.87 tff(16021,plain,(b(elem!1, z) | (~r(s(z), elem!1)) | r(z, elem!1) | b(s(s(s(z))), elem!1) | b(elem!1, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.87 tff(16022,plain,
% 2.64/2.87 (b(elem!1, z)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[16021, 4, 7, 1, 3])).
% 2.64/2.87 tff(16023,plain,
% 2.64/2.87 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))))),
% 2.64/2.87 inference(rewrite,[status(thm)],[])).
% 2.64/2.87 tff(16024,plain,
% 2.64/2.87 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))))),
% 2.64/2.87 inference(quant_inst,[status(thm)],[])).
% 2.64/2.87 tff(16025,plain,
% 2.64/2.87 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z))))),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[16024, 16023])).
% 2.64/2.87 tff(16026,plain,
% 2.64/2.87 (~r(s(s(s(z))), s(s(z)))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[16025, 124, 2859, 2478])).
% 2.64/2.87 tff(16027,plain,
% 2.64/2.87 (b(s(s(s(z))), s(s(z)))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[15162, 16026])).
% 2.64/2.87 tff(16028,plain,
% 2.64/2.87 (b(s(z), s(s(s(z))))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[3302, 15326])).
% 2.64/2.87 tff(16029,plain,
% 2.64/2.87 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))))),
% 2.64/2.87 inference(rewrite,[status(thm)],[])).
% 2.64/2.87 tff(16030,plain,
% 2.64/2.87 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))))),
% 2.64/2.87 inference(quant_inst,[status(thm)],[])).
% 2.64/2.87 tff(16031,plain,
% 2.64/2.87 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z)))),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[16030, 16029])).
% 2.64/2.87 tff(16032,plain,
% 2.64/2.87 (~r(s(s(z)), s(z))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[16031, 124, 4, 2478])).
% 2.64/2.87 tff(16033,plain,
% 2.64/2.87 (b(s(s(z)), s(z))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[2476, 16032])).
% 2.64/2.87 tff(16034,plain,
% 2.64/2.87 (~r(s(z), s(s(z)))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[15405, 124, 4, 2478])).
% 2.64/2.87 tff(16035,plain,
% 2.64/2.87 (b(s(z), s(s(z)))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[4434, 16034])).
% 2.64/2.87 tff(16036,plain,
% 2.64/2.87 ($false),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[14004, 16035, 16033, 16028, 16027])).
% 2.64/2.87 tff(16037,plain,((~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.87 tff(16038,plain,
% 2.64/2.87 (~r(s(s(z)), elem!1)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[16037, 2859, 4])).
% 2.64/2.87 tff(16039,plain,
% 2.64/2.87 (b(z, elem!1)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[835, 12587, 7])).
% 2.64/2.87 tff(16040,plain,
% 2.64/2.87 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[12213, 16028, 4, 7138, 2859])).
% 2.64/2.87 tff(16041,plain,
% 2.64/2.87 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[1144, 4918, 8026])).
% 2.64/2.87 tff(16042,plain,
% 2.64/2.87 (~(s(s(z)) = elem!1)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[14704, 1171, 12588])).
% 2.64/2.87 tff(16043,plain,
% 2.64/2.87 (b(s(s(z)), elem!1)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[2545, 16042, 5546])).
% 2.64/2.87 tff(16044,plain,
% 2.64/2.87 ($false),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[12244, 16043, 16041, 4012, 838])).
% 2.64/2.87 tff(16045,plain,((~(s(s(elem!1)) = elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | r(s(s(z)), elem!1) | r(s(s(s(s(s(s(z)))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.64/2.87 tff(16046,plain,
% 2.64/2.87 (~(s(s(elem!1)) = elem!1)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[16045, 16040, 16039, 4012, 16038])).
% 2.64/2.87 tff(16047,plain,
% 2.64/2.87 (b(s(s(elem!1)), elem!1)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[47, 16046, 6])).
% 2.64/2.87 tff(16048,plain,
% 2.64/2.87 ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), z))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[8234, 15960])).
% 2.64/2.87 tff(16049,plain,
% 2.64/2.87 (~b(s(z), z)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[16048, 16039, 4012])).
% 2.64/2.87 tff(16050,plain,
% 2.64/2.87 (r(s(z), z)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[221, 16049])).
% 2.64/2.87 tff(16051,plain,
% 2.64/2.87 (~r(elem!1, z)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[1049, 16050, 4])).
% 2.64/2.87 tff(16052,plain,
% 2.64/2.87 (~b(s(s(elem!1)), z)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[3976, 16047, 7, 12587, 16051])).
% 2.64/2.87 tff(16053,plain,
% 2.64/2.87 (r(s(s(elem!1)), z)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[476, 16052])).
% 2.64/2.87 tff(16054,plain,
% 2.64/2.87 (b(s(s(z)), s(z)) <=> b(elem!1, s(z))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[2392])).
% 2.64/2.87 tff(16055,plain,
% 2.64/2.87 (b(elem!1, s(z)) <=> b(s(s(z)), s(z))),
% 2.64/2.87 inference(symmetry,[status(thm)],[16054])).
% 2.64/2.87 tff(16056,plain,
% 2.64/2.87 (b(s(s(z)), s(z))),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[15960, 16055])).
% 2.64/2.87 tff(16057,plain,
% 2.64/2.87 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(z)))), elem!1)),
% 2.64/2.87 inference(monotonicity,[status(thm)],[2392])).
% 2.64/2.87 tff(16058,plain,
% 2.64/2.87 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(z)))),
% 2.64/2.87 inference(symmetry,[status(thm)],[16057])).
% 2.64/2.87 tff(16059,plain,
% 2.64/2.87 (s(s(s(z))) = s(elem!1)),
% 2.64/2.87 inference(monotonicity,[status(thm)],[2392])).
% 2.64/2.87 tff(16060,plain,
% 2.64/2.87 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[16059])).
% 2.64/2.87 tff(16061,plain,
% 2.64/2.87 (s(s(elem!1)) = s(s(s(s(z))))),
% 2.64/2.87 inference(symmetry,[status(thm)],[16060])).
% 2.64/2.87 tff(16062,plain,
% 2.64/2.87 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 2.64/2.87 inference(monotonicity,[status(thm)],[16061])).
% 2.64/2.87 tff(16063,plain,
% 2.64/2.87 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(z)))), s(s(z)))),
% 2.64/2.87 inference(transitivity,[status(thm)],[16062, 16058])).
% 2.64/2.87 tff(16064,plain,
% 2.64/2.87 (b(s(s(s(s(z)))), s(s(z)))),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[30, 16063])).
% 2.64/2.87 tff(16065,plain,
% 2.64/2.87 (r(s(s(s(s(z)))), z) <=> r(s(s(elem!1)), z)),
% 2.64/2.87 inference(monotonicity,[status(thm)],[16060])).
% 2.64/2.87 tff(16066,plain,
% 2.64/2.87 (r(s(s(elem!1)), z) <=> r(s(s(s(s(z)))), z)),
% 2.64/2.87 inference(symmetry,[status(thm)],[16065])).
% 2.64/2.87 tff(16067,plain,
% 2.64/2.87 (r(s(s(s(s(z)))), z)),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[465, 16066])).
% 2.64/2.87 tff(16068,plain,
% 2.64/2.87 ($false),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[3463, 16067, 16064, 8, 2284, 204, 16056])).
% 2.64/2.87 tff(16069,plain,((~(s(s(z)) = elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.88 tff(16070,plain,
% 2.64/2.88 (~(s(s(z)) = elem!1)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[16069, 16053, 7138, 16050, 16028, 16047])).
% 2.64/2.88 tff(16071,plain,
% 2.64/2.88 (b(s(s(z)), elem!1)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[2545, 16070, 16038])).
% 2.64/2.88 tff(16072,plain,
% 2.64/2.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.64/2.88 inference(rewrite,[status(thm)],[])).
% 2.64/2.88 tff(16073,plain,
% 2.64/2.88 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1))))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.64/2.88 inference(rewrite,[status(thm)],[])).
% 2.64/2.88 tff(16074,plain,
% 2.64/2.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1))))))),
% 2.64/2.88 inference(monotonicity,[status(thm)],[16073])).
% 2.64/2.88 tff(16075,plain,
% 2.64/2.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.64/2.88 inference(transitivity,[status(thm)],[16074, 16072])).
% 2.64/2.88 tff(16076,plain,
% 2.64/2.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.64/2.88 inference(quant_inst,[status(thm)],[])).
% 2.64/2.88 tff(16077,plain,
% 2.64/2.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1))))),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[16076, 16075])).
% 2.64/2.88 tff(16078,plain,
% 2.64/2.88 (~b(s(s(z)), s(s(elem!1)))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[16077, 306, 16039, 4012, 16047, 16071])).
% 2.64/2.88 tff(16079,assumption,(s(s(z)) = s(s(elem!1))), introduced(assumption)).
% 2.64/2.88 tff(16080,plain,
% 2.64/2.88 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 2.64/2.88 inference(monotonicity,[status(thm)],[16079])).
% 2.64/2.88 tff(16081,plain,
% 2.64/2.88 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 2.64/2.88 inference(symmetry,[status(thm)],[16080])).
% 2.64/2.88 tff(16082,plain,
% 2.64/2.88 (s(elem!1) = s(z)),
% 2.64/2.88 inference(transitivity,[status(thm)],[67, 16081, 546])).
% 2.64/2.88 tff(16083,plain,
% 2.64/2.88 ($false),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[2249, 16082])).
% 2.64/2.88 tff(16084,plain,((~(s(s(z)) = s(s(elem!1)))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.88 tff(16085,plain,
% 2.64/2.88 (~(s(s(z)) = s(s(elem!1)))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[16084, 12588])).
% 2.64/2.88 tff(16086,plain,
% 2.64/2.88 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1))) | r(s(s(z)), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1))) | r(s(s(z)), s(s(elem!1))))),
% 2.64/2.88 inference(rewrite,[status(thm)],[])).
% 2.64/2.88 tff(16087,plain,
% 2.64/2.88 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1))) | r(s(s(z)), s(s(elem!1))))),
% 2.64/2.88 inference(quant_inst,[status(thm)],[])).
% 2.64/2.88 tff(16088,plain,
% 2.64/2.88 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1))) | r(s(s(z)), s(s(elem!1)))),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[16087, 16086])).
% 2.64/2.88 tff(16089,plain,
% 2.64/2.88 (r(s(s(z)), s(s(elem!1)))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[16088, 43, 16085, 16078])).
% 2.64/2.88 tff(16090,plain,
% 2.64/2.88 (~b(s(s(z)), z)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[12229, 306, 16039, 4012, 16071])).
% 2.64/2.88 tff(16091,plain,
% 2.64/2.88 (r(s(s(z)), z)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[2531, 16090])).
% 2.64/2.88 tff(16092,plain,
% 2.64/2.88 (~b(z, s(s(elem!1)))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[4030, 306, 16039, 4012, 16047])).
% 2.64/2.88 tff(16093,plain,
% 2.64/2.88 (r(z, s(s(elem!1)))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[460, 16092])).
% 2.64/2.88 tff(16094,plain,
% 2.64/2.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(elem!1)))))),
% 2.64/2.88 inference(rewrite,[status(thm)],[])).
% 2.64/2.88 tff(16095,plain,
% 2.64/2.88 (((~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z))) <=> ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(elem!1)))))),
% 2.64/2.88 inference(rewrite,[status(thm)],[])).
% 2.64/2.88 tff(16096,plain,
% 2.64/2.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(elem!1))))))),
% 2.64/2.88 inference(monotonicity,[status(thm)],[16095])).
% 2.64/2.88 tff(16097,plain,
% 2.64/2.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(elem!1)))))),
% 2.64/2.88 inference(transitivity,[status(thm)],[16096, 16094])).
% 2.64/2.88 tff(16098,plain,
% 2.64/2.88 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)))),
% 2.64/2.88 inference(quant_inst,[status(thm)],[])).
% 2.64/2.88 tff(16099,plain,
% 2.64/2.88 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(elem!1))))),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[16098, 16097])).
% 2.64/2.88 tff(16100,plain,
% 2.64/2.88 ($false),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[16099, 124, 16093, 16091, 16089])).
% 2.64/2.88 tff(16101,plain,((~r(s(s(s(z))), elem!1)) | (~b(elem!1, z)) | r(z, elem!1) | r(s(s(elem!1)), elem!1) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.88 tff(16102,plain,
% 2.64/2.88 (~r(s(s(s(z))), elem!1)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[16101, 6, 7, 4012, 4])).
% 2.64/2.88 tff(16103,plain,
% 2.64/2.88 (s(s(s(z))) = elem!1),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[1489, 16102, 1])).
% 2.64/2.88 tff(16104,plain,
% 2.64/2.88 (~(s(s(s(elem!1))) = elem!1)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[4105, 16103, 12588])).
% 2.64/2.88 tff(16105,plain,
% 2.64/2.88 (elem!1 = s(s(s(z)))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[12937, 16103])).
% 2.64/2.88 tff(16106,plain,
% 2.64/2.88 ((~(s(s(elem!1)) = elem!1)) | (~(elem!1 = s(s(s(z)))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[10068, 15980])).
% 2.64/2.88 tff(16107,plain,
% 2.64/2.88 (~(s(s(elem!1)) = elem!1)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[16106, 16105])).
% 2.64/2.88 tff(16108,plain,
% 2.64/2.88 (b(s(s(elem!1)), elem!1)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[47, 16107, 6])).
% 2.64/2.88 tff(16109,plain,
% 2.64/2.88 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[143, 16107])).
% 2.64/2.88 tff(16110,plain,
% 2.64/2.88 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[152, 16109])).
% 2.64/2.88 tff(16111,plain,
% 2.64/2.88 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[159, 16110])).
% 2.64/2.88 tff(16112,plain,
% 2.64/2.88 (~b(z, s(s(elem!1)))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[4030, 306, 838, 4012, 30])).
% 2.64/2.88 tff(16113,plain,
% 2.64/2.88 (r(z, s(s(elem!1)))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[460, 16112])).
% 2.64/2.88 tff(16114,plain,
% 2.64/2.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.64/2.88 inference(rewrite,[status(thm)],[])).
% 2.64/2.88 tff(16115,plain,
% 2.64/2.88 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.64/2.88 inference(rewrite,[status(thm)],[])).
% 2.64/2.88 tff(16116,plain,
% 2.64/2.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1))))),
% 2.64/2.88 inference(monotonicity,[status(thm)],[16115])).
% 2.64/2.88 tff(16117,plain,
% 2.64/2.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.64/2.88 inference(transitivity,[status(thm)],[16116, 16114])).
% 2.64/2.88 tff(16118,plain,
% 2.64/2.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.64/2.88 inference(quant_inst,[status(thm)],[])).
% 2.64/2.88 tff(16119,plain,
% 2.64/2.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1))),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[16118, 16117])).
% 2.64/2.88 tff(16120,plain,
% 2.64/2.88 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[16119, 306, 838, 4012, 30, 1664])).
% 2.64/2.88 tff(16121,plain,
% 2.64/2.88 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[610, 16120, 739])).
% 2.64/2.88 tff(16122,plain,
% 2.64/2.88 (~b(z, s(s(s(elem!1))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[6148, 306, 838, 4012, 1664])).
% 2.64/2.88 tff(16123,plain,
% 2.64/2.88 (r(z, s(s(s(elem!1))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[585, 16122])).
% 2.64/2.88 tff(16124,plain,
% 2.64/2.88 ($false),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[950, 16123, 16121, 16113])).
% 2.64/2.88 tff(16125,plain,((~b(s(s(s(elem!1))), elem!1)) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.88 tff(16126,plain,
% 2.64/2.88 (~b(s(s(s(elem!1))), elem!1)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[16125, 16111, 16039, 4012, 16108])).
% 2.64/2.88 tff(16127,plain,
% 2.64/2.88 (r(s(s(s(elem!1))), elem!1)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[1636, 16126, 16104])).
% 2.64/2.88 tff(16128,plain,
% 2.64/2.88 (~r(s(z), s(s(s(elem!1))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[3013, 124, 16127, 4])).
% 2.64/2.88 tff(16129,plain,
% 2.64/2.88 (b(s(z), s(s(s(elem!1))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[3017, 43, 645, 16128])).
% 2.64/2.88 tff(16130,plain,
% 2.64/2.88 (s(s(s(s(z)))) = s(elem!1)),
% 2.64/2.88 inference(monotonicity,[status(thm)],[16103])).
% 2.64/2.88 tff(16131,plain,
% 2.64/2.88 (b(s(z), s(s(s(s(z))))) <=> b(s(z), s(elem!1))),
% 2.64/2.88 inference(monotonicity,[status(thm)],[16130])).
% 2.64/2.88 tff(16132,plain,
% 2.64/2.88 (r(s(z), s(s(s(s(z))))) <=> r(s(z), s(elem!1))),
% 2.64/2.88 inference(monotonicity,[status(thm)],[16130])).
% 2.64/2.88 tff(16133,plain,
% 2.64/2.88 (r(s(z), s(elem!1)) <=> r(s(z), s(s(s(s(z)))))),
% 2.64/2.88 inference(symmetry,[status(thm)],[16132])).
% 2.64/2.88 tff(16134,plain,
% 2.64/2.88 ((~r(s(z), s(elem!1))) <=> (~r(s(z), s(s(s(s(z))))))),
% 2.64/2.88 inference(monotonicity,[status(thm)],[16133])).
% 2.64/2.88 tff(16135,plain,
% 2.64/2.88 (r(s(elem!1), elem!1)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[14695, 16109, 7, 6, 4012, 16051])).
% 2.64/2.88 tff(16136,plain,
% 2.64/2.88 (~r(s(z), s(elem!1))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[4043, 124, 16135, 4])).
% 2.64/2.88 tff(16137,plain,
% 2.64/2.88 (~r(s(z), s(s(s(s(z)))))),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[16136, 16134])).
% 2.64/2.88 tff(16138,plain,
% 2.64/2.88 (b(s(z), s(s(s(s(z)))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[5135, 16137])).
% 2.64/2.88 tff(16139,plain,
% 2.64/2.88 (b(s(z), s(elem!1))),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[16138, 16131])).
% 2.64/2.88 tff(16140,plain,
% 2.64/2.88 (~r(s(elem!1), s(z))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[9506, 124, 16135, 4])).
% 2.64/2.88 tff(16141,plain,
% 2.64/2.88 (b(s(elem!1), s(z))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[2964, 16140, 12588])).
% 2.64/2.88 tff(16142,plain,
% 2.64/2.88 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[9032, 124, 16135, 16127])).
% 2.64/2.88 tff(16143,plain,
% 2.64/2.88 (b(s(s(s(elem!1))), s(elem!1))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[664, 16142, 16109])).
% 2.64/2.88 tff(16144,plain,
% 2.64/2.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 2.64/2.88 inference(rewrite,[status(thm)],[])).
% 2.64/2.88 tff(16145,plain,
% 2.64/2.88 (((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 2.64/2.88 inference(rewrite,[status(thm)],[])).
% 2.64/2.88 tff(16146,plain,
% 2.64/2.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 2.64/2.88 inference(monotonicity,[status(thm)],[16145])).
% 2.64/2.88 tff(16147,plain,
% 2.64/2.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 2.64/2.88 inference(transitivity,[status(thm)],[16146, 16144])).
% 2.64/2.88 tff(16148,plain,
% 2.64/2.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(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))))))),
% 2.64/2.88 inference(quant_inst,[status(thm)],[])).
% 2.64/2.88 tff(16149,plain,
% 2.64/2.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[16148, 16147])).
% 2.64/2.88 tff(16150,plain,
% 2.64/2.88 ($false),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[16149, 306, 16143, 16141, 16139, 16129])).
% 2.64/2.88 tff(16151,plain,(r(s(s(elem!1)), elem!1) | (~r(s(z), elem!1)) | (~b(elem!1, z)) | r(z, elem!1) | b(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.64/2.88 tff(16152,plain,
% 2.64/2.88 (r(s(s(elem!1)), elem!1)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[16151, 4, 16022, 7, 1])).
% 2.64/2.88 tff(16153,plain,
% 2.64/2.88 (~r(s(s(elem!1)), s(z))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[8826, 16152, 4])).
% 2.64/2.88 tff(16154,plain,
% 2.64/2.88 (b(s(s(elem!1)), s(z))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[3989, 16153])).
% 2.64/2.88 tff(16155,plain,
% 2.64/2.88 (~r(s(z), s(s(elem!1)))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[13075, 16152, 4])).
% 2.64/2.88 tff(16156,plain,
% 2.64/2.88 (b(s(z), s(s(elem!1)))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[3997, 43, 79, 16155])).
% 2.64/2.88 tff(16157,plain,
% 2.64/2.88 (~(z = elem!1)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[11005, 16022])).
% 2.64/2.88 tff(16158,plain,
% 2.64/2.88 (~(s(elem!1) = s(z))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[2689, 16157])).
% 2.64/2.88 tff(16159,plain,
% 2.64/2.88 (~r(s(s(s(z))), elem!1)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[15985, 16152, 4])).
% 2.64/2.88 tff(16160,plain,
% 2.64/2.88 (s(s(s(z))) = elem!1),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[1489, 16159, 1])).
% 2.64/2.88 tff(16161,plain,
% 2.64/2.88 (s(s(s(s(z)))) = s(elem!1)),
% 2.64/2.88 inference(monotonicity,[status(thm)],[16160])).
% 2.64/2.88 tff(16162,plain,
% 2.64/2.88 (r(s(s(s(s(z)))), elem!1) <=> r(s(elem!1), elem!1)),
% 2.64/2.88 inference(monotonicity,[status(thm)],[16161])).
% 2.64/2.88 tff(16163,plain,
% 2.64/2.88 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(z)))), elem!1)),
% 2.64/2.88 inference(monotonicity,[status(thm)],[16160])).
% 2.64/2.88 tff(16164,plain,
% 2.64/2.88 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(elem!1), elem!1)),
% 2.64/2.88 inference(transitivity,[status(thm)],[16163, 16162])).
% 2.64/2.88 tff(16165,plain,
% 2.64/2.88 (~(elem!1 = s(s(elem!1)))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[15853, 16152])).
% 2.64/2.88 tff(16166,plain,
% 2.64/2.88 (~(s(s(elem!1)) = elem!1)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[1174, 16165])).
% 2.64/2.88 tff(16167,plain,
% 2.64/2.88 (elem!1 = s(s(s(z)))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[12937, 16160])).
% 2.64/2.88 tff(16168,plain,
% 2.64/2.88 (~b(s(s(elem!1)), elem!1)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[7610, 306, 16156, 15960, 16154])).
% 2.64/2.88 tff(16169,plain,
% 2.64/2.88 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[12791, 16168, 16157, 16152, 16154, 16167, 16156, 16166])).
% 2.64/2.88 tff(16170,plain,
% 2.64/2.88 (r(s(elem!1), elem!1)),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[16169, 16164])).
% 2.64/2.88 tff(16171,plain,
% 2.64/2.88 (~r(s(elem!1), s(z))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[9506, 124, 16170, 4])).
% 2.64/2.88 tff(16172,plain,
% 2.64/2.88 (b(s(elem!1), s(z))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[2964, 16171, 16158])).
% 2.64/2.88 tff(16173,plain,
% 2.64/2.88 (~(s(elem!1) = elem!1)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[180, 16166])).
% 2.64/2.88 tff(16174,plain,
% 2.64/2.88 (~(s(s(elem!1)) = s(elem!1))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[195, 16173])).
% 2.64/2.88 tff(16175,plain,
% 2.64/2.88 (~r(s(s(elem!1)), s(elem!1))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[7983, 124, 16170, 16152])).
% 2.64/2.88 tff(16176,plain,
% 2.64/2.88 (b(s(s(elem!1)), s(elem!1))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[994, 16175, 16174])).
% 2.64/2.88 tff(16177,plain,
% 2.64/2.88 ($false),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[4007, 16176, 16172, 16156, 16154])).
% 2.64/2.88 tff(16178,plain,((~r(s(z), elem!1)) | b(s(s(s(z))), elem!1) | r(z, elem!1) | b(elem!1, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.88 tff(16179,plain,
% 2.64/2.88 (~r(s(z), elem!1)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[16178, 7, 1, 3])).
% 2.64/2.88 tff(16180,plain,
% 2.64/2.88 (b(s(z), elem!1) | r(s(z), elem!1)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[13156, 15978])).
% 2.64/2.88 tff(16181,plain,
% 2.64/2.88 (b(s(z), elem!1)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[16180, 16179])).
% 2.64/2.88 tff(16182,plain,
% 2.64/2.88 ((s(s(s(z))) = z) <=> (elem!1 = z)),
% 2.64/2.88 inference(monotonicity,[status(thm)],[15966])).
% 2.64/2.88 tff(16183,plain,
% 2.64/2.88 ((s(s(s(z))) = z) <=> (z = elem!1)),
% 2.64/2.88 inference(transitivity,[status(thm)],[16182, 161])).
% 2.64/2.88 tff(16184,plain,
% 2.64/2.88 ((~(s(s(s(z))) = z)) <=> (~(z = elem!1))),
% 2.64/2.88 inference(monotonicity,[status(thm)],[16183])).
% 2.64/2.88 tff(16185,plain,
% 2.64/2.88 (~(z = elem!1)),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[169, 16184])).
% 2.64/2.88 tff(16186,plain,
% 2.64/2.88 (b(z, elem!1)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[835, 16185, 7])).
% 2.64/2.88 tff(16187,plain,
% 2.64/2.88 (b(s(z), s(s(s(z)))) <=> b(s(z), elem!1)),
% 2.64/2.88 inference(monotonicity,[status(thm)],[1430])).
% 2.64/2.88 tff(16188,plain,
% 2.64/2.88 (b(s(z), elem!1) <=> b(s(z), s(s(s(z))))),
% 2.64/2.88 inference(symmetry,[status(thm)],[16187])).
% 2.64/2.88 tff(16189,plain,
% 2.64/2.88 (b(s(z), s(s(s(z))))),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[2831, 16188])).
% 2.64/2.88 tff(16190,plain,
% 2.64/2.88 ($false),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[3300, 16189])).
% 2.64/2.88 tff(16191,plain,((~(s(s(s(z))) = elem!1)) | b(s(z), s(s(s(z)))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.88 tff(16192,plain,
% 2.64/2.88 (b(s(z), s(s(s(z))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[16191, 15966, 16181])).
% 2.64/2.88 tff(16193,plain,
% 2.64/2.88 (r(s(s(s(z))), z) <=> r(elem!1, z)),
% 2.64/2.88 inference(monotonicity,[status(thm)],[15966])).
% 2.64/2.88 tff(16194,plain,
% 2.64/2.88 (r(s(s(s(z))), z)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[2219, 1484, 2, 1])).
% 2.64/2.88 tff(16195,plain,
% 2.64/2.88 (r(elem!1, z)),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[16194, 16193])).
% 2.64/2.88 tff(16196,plain,
% 2.64/2.88 (~b(s(z), z)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[4956, 16195, 16192, 3, 16186, 15977, 2])).
% 2.64/2.88 tff(16197,plain,
% 2.64/2.88 (r(s(z), z)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[221, 16196])).
% 2.64/2.88 tff(16198,plain,
% 2.64/2.88 ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~r(s(z), z)) | (~b(z, s(s(s(z)))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[10286, 15960])).
% 2.64/2.88 tff(16199,plain,
% 2.64/2.88 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[16198, 16197, 16181, 15977, 15975])).
% 2.64/2.88 tff(16200,plain,
% 2.64/2.88 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[10146, 16199])).
% 2.64/2.88 tff(16201,plain,
% 2.64/2.88 (r(s(elem!1), elem!1)),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[16200, 15970])).
% 2.64/2.88 tff(16202,plain,
% 2.64/2.88 (~r(s(s(elem!1)), s(elem!1))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[7983, 124, 16201, 15961])).
% 2.64/2.88 tff(16203,plain,
% 2.64/2.88 (~r(s(s(elem!1)), z)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[7786, 16195, 15961])).
% 2.64/2.88 tff(16204,plain,
% 2.64/2.88 (b(s(s(elem!1)), z)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[476, 16203])).
% 2.64/2.88 tff(16205,plain,
% 2.64/2.88 (b(s(s(s(s(z)))), z) <=> b(s(elem!1), z)),
% 2.64/2.88 inference(monotonicity,[status(thm)],[15967])).
% 2.64/2.88 tff(16206,plain,
% 2.64/2.88 (~r(s(s(s(s(z)))), z)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[4737, 16200, 16194])).
% 2.64/2.88 tff(16207,plain,
% 2.64/2.88 (b(s(s(s(s(z)))), z)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[695, 16206])).
% 2.64/2.88 tff(16208,plain,
% 2.64/2.88 (b(s(elem!1), z)),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[16207, 16205])).
% 2.64/2.88 tff(16209,plain,
% 2.64/2.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(z))))),
% 2.64/2.88 inference(rewrite,[status(thm)],[])).
% 2.64/2.88 tff(16210,plain,
% 2.64/2.88 (((~b(elem!1, s(z))) | (~b(z, 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, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(z))))),
% 2.64/2.88 inference(rewrite,[status(thm)],[])).
% 2.64/2.88 tff(16211,plain,
% 2.64/2.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(z)))))),
% 2.64/2.88 inference(monotonicity,[status(thm)],[16210])).
% 2.64/2.88 tff(16212,plain,
% 2.64/2.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(z))))),
% 2.64/2.88 inference(transitivity,[status(thm)],[16211, 16209])).
% 2.64/2.88 tff(16213,plain,
% 2.64/2.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.64/2.88 inference(quant_inst,[status(thm)],[])).
% 2.64/2.88 tff(16214,plain,
% 2.64/2.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(z)))),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[16213, 16212])).
% 2.64/2.88 tff(16215,plain,
% 2.64/2.88 (~b(s(s(elem!1)), s(elem!1))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[16214, 306, 16186, 16208, 16204, 15960])).
% 2.64/2.88 tff(16216,plain,
% 2.64/2.88 ($false),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[994, 16215, 16202, 15965])).
% 2.64/2.88 tff(16217,plain,(r(s(s(s(z))), elem!1) | b(elem!1, s(s(s(z)))) | b(elem!1, z) | r(z, elem!1) | b(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.64/2.88 tff(16218,plain,
% 2.64/2.88 (r(s(s(s(z))), elem!1)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[16217, 2, 3, 7, 1])).
% 2.64/2.88 tff(16219,plain,
% 2.64/2.88 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 2.64/2.88 inference(monotonicity,[status(thm)],[1502])).
% 2.64/2.88 tff(16220,plain,
% 2.64/2.88 ((~(s(s(s(s(z)))) = z)) <=> (~(s(s(s(s(z)))) = elem!1))),
% 2.64/2.88 inference(monotonicity,[status(thm)],[16219])).
% 2.64/2.88 tff(16221,plain,
% 2.64/2.88 (~(s(s(s(s(z)))) = elem!1)),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[291, 16220])).
% 2.64/2.88 tff(16222,plain,
% 2.64/2.88 (~b(s(s(s(elem!1))), elem!1)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[2215, 1502, 1])).
% 2.64/2.88 tff(16223,plain,
% 2.64/2.88 (r(s(s(s(elem!1))), elem!1)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[1636, 3171, 16222])).
% 2.64/2.88 tff(16224,plain,
% 2.64/2.88 (r(s(s(s(z))), z)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[1631, 16223, 1619])).
% 2.64/2.88 tff(16225,plain,
% 2.64/2.88 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[152, 15900])).
% 2.64/2.88 tff(16226,plain,
% 2.64/2.88 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[159, 16225])).
% 2.64/2.88 tff(16227,plain,
% 2.64/2.88 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[7780, 16223, 1730])).
% 2.64/2.88 tff(16228,plain,
% 2.64/2.88 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[610, 16227, 16226])).
% 2.64/2.88 tff(16229,plain,
% 2.64/2.88 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[7010, 16223, 1730])).
% 2.64/2.88 tff(16230,plain,
% 2.64/2.88 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[891, 16229, 16225])).
% 2.64/2.88 tff(16231,plain,
% 2.64/2.88 (r(s(s(s(s(z)))), z)),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[14251, 4731])).
% 2.64/2.88 tff(16232,plain,
% 2.64/2.88 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[4737, 16231, 205])).
% 2.64/2.88 tff(16233,plain,
% 2.64/2.88 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[4471, 16232])).
% 2.64/2.89 tff(16234,plain,
% 2.64/2.89 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.64/2.89 inference(modus_ponens,[status(thm)],[16233, 1724])).
% 2.64/2.89 tff(16235,plain,
% 2.64/2.89 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.64/2.89 inference(modus_ponens,[status(thm)],[16234, 4728])).
% 2.64/2.89 tff(16236,plain,
% 2.64/2.89 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[1284, 15900])).
% 2.64/2.89 tff(16237,plain,
% 2.64/2.89 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.64/2.89 inference(modus_ponens,[status(thm)],[14251, 4732])).
% 2.64/2.89 tff(16238,plain,
% 2.64/2.89 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[1754, 124, 1730, 16237])).
% 2.64/2.89 tff(16239,plain,
% 2.64/2.89 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[1302, 16238, 16236])).
% 2.64/2.89 tff(16240,plain,
% 2.64/2.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.64/2.89 inference(rewrite,[status(thm)],[])).
% 2.64/2.89 tff(16241,plain,
% 2.64/2.89 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.64/2.89 inference(rewrite,[status(thm)],[])).
% 2.64/2.89 tff(16242,plain,
% 2.64/2.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(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(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 2.64/2.89 inference(monotonicity,[status(thm)],[16241])).
% 2.64/2.89 tff(16243,plain,
% 2.64/2.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(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(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.64/2.89 inference(transitivity,[status(thm)],[16242, 16240])).
% 2.64/2.89 tff(16244,plain,
% 2.64/2.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(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(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.64/2.89 inference(quant_inst,[status(thm)],[])).
% 2.64/2.89 tff(16245,plain,
% 2.64/2.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 2.64/2.89 inference(modus_ponens,[status(thm)],[16244, 16243])).
% 2.64/2.89 tff(16246,plain,
% 2.64/2.89 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[16245, 306, 1590, 601, 16239])).
% 2.64/2.89 tff(16247,plain,
% 2.64/2.89 ($false),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[16246, 16235])).
% 2.64/2.89 tff(16248,plain,((~r(s(s(s(s(z)))), elem!1)) | (~(z = elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.89 tff(16249,plain,
% 2.64/2.89 (~r(s(s(s(s(z)))), elem!1)),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[16248, 1502, 16230, 16228, 16224, 1730])).
% 2.64/2.89 tff(16250,plain,
% 2.64/2.89 (b(s(s(s(s(z)))), elem!1)),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[9832, 16249, 16221])).
% 2.64/2.89 tff(16251,plain,
% 2.64/2.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 2.64/2.89 inference(rewrite,[status(thm)],[])).
% 2.64/2.89 tff(16252,plain,
% 2.64/2.89 (((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 2.64/2.89 inference(rewrite,[status(thm)],[])).
% 2.64/2.89 tff(16253,plain,
% 2.64/2.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), elem!1))))),
% 2.64/2.89 inference(monotonicity,[status(thm)],[16252])).
% 2.64/2.89 tff(16254,plain,
% 2.64/2.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 2.64/2.89 inference(transitivity,[status(thm)],[16253, 16251])).
% 2.64/2.89 tff(16255,plain,
% 2.64/2.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.64/2.89 inference(quant_inst,[status(thm)],[])).
% 2.64/2.89 tff(16256,plain,
% 2.64/2.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), elem!1))),
% 2.64/2.89 inference(modus_ponens,[status(thm)],[16255, 16254])).
% 2.64/2.89 tff(16257,plain,
% 2.64/2.89 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[16256, 306, 2831, 15960, 2812, 12426])).
% 2.64/2.89 tff(16258,plain,
% 2.64/2.89 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[10662, 16257])).
% 2.64/2.89 tff(16259,plain,
% 2.64/2.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 2.64/2.89 inference(rewrite,[status(thm)],[])).
% 2.64/2.89 tff(16260,plain,
% 2.64/2.89 (((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 2.64/2.89 inference(rewrite,[status(thm)],[])).
% 2.64/2.89 tff(16261,plain,
% 2.64/2.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1))))),
% 2.64/2.89 inference(monotonicity,[status(thm)],[16260])).
% 2.64/2.89 tff(16262,plain,
% 2.64/2.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 2.64/2.89 inference(transitivity,[status(thm)],[16261, 16259])).
% 2.64/2.89 tff(16263,plain,
% 2.64/2.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 2.64/2.89 inference(quant_inst,[status(thm)],[])).
% 2.64/2.89 tff(16264,plain,
% 2.64/2.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1))),
% 2.64/2.89 inference(modus_ponens,[status(thm)],[16263, 16262])).
% 2.64/2.89 tff(16265,plain,
% 2.64/2.89 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[16264, 306, 2831, 15960, 2812])).
% 2.64/2.89 tff(16266,plain,
% 2.64/2.89 (r(s(s(s(s(s(s(z)))))), s(z))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[651, 43, 2844, 16265])).
% 2.64/2.89 tff(16267,plain,
% 2.64/2.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.64/2.89 inference(rewrite,[status(thm)],[])).
% 2.64/2.89 tff(16268,plain,
% 2.64/2.89 (((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.64/2.89 inference(rewrite,[status(thm)],[])).
% 2.64/2.89 tff(16269,plain,
% 2.64/2.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1))))),
% 2.64/2.89 inference(monotonicity,[status(thm)],[16268])).
% 2.64/2.89 tff(16270,plain,
% 2.64/2.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.64/2.89 inference(transitivity,[status(thm)],[16269, 16267])).
% 2.64/2.89 tff(16271,plain,
% 2.64/2.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 2.64/2.89 inference(quant_inst,[status(thm)],[])).
% 2.64/2.89 tff(16272,plain,
% 2.64/2.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1))),
% 2.64/2.89 inference(modus_ponens,[status(thm)],[16271, 16270])).
% 2.64/2.89 tff(16273,plain,
% 2.64/2.89 (~b(s(z), s(s(s(s(z)))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[16272, 306, 2831, 15960, 12426])).
% 2.64/2.89 tff(16274,plain,
% 2.64/2.89 (r(s(z), s(s(s(s(z)))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[5135, 16273])).
% 2.64/2.89 tff(16275,plain,
% 2.64/2.89 ($false),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[753, 124, 16274, 16266, 16258])).
% 2.64/2.89 tff(16276,plain,((~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.89 tff(16277,plain,
% 2.64/2.89 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[16276, 16250, 2831])).
% 2.64/2.89 tff(16278,plain,
% 2.64/2.89 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[1144, 16277, 3170])).
% 2.64/2.89 tff(16279,plain,
% 2.64/2.89 (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[8458, 124, 1730, 16278])).
% 2.64/2.89 tff(16280,plain,
% 2.64/2.89 (b(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[3247, 43, 3244, 16279])).
% 2.64/2.89 tff(16281,plain,
% 2.64/2.89 (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[4745, 124, 16223, 16278])).
% 2.64/2.89 tff(16282,plain,
% 2.64/2.89 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.64/2.89 inference(modus_ponens,[status(thm)],[16281, 4742])).
% 2.64/2.89 tff(16283,plain,
% 2.64/2.89 (b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[2880, 16282, 1502])).
% 2.64/2.89 tff(16284,plain,
% 2.64/2.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 2.64/2.89 inference(rewrite,[status(thm)],[])).
% 2.64/2.89 tff(16285,plain,
% 2.64/2.89 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), 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(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 2.64/2.89 inference(rewrite,[status(thm)],[])).
% 2.64/2.89 tff(16286,plain,
% 2.64/2.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(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(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))))),
% 2.64/2.89 inference(monotonicity,[status(thm)],[16285])).
% 2.64/2.89 tff(16287,plain,
% 2.64/2.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(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(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 2.64/2.89 inference(transitivity,[status(thm)],[16286, 16284])).
% 2.64/2.89 tff(16288,plain,
% 2.64/2.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(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(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 2.64/2.89 inference(quant_inst,[status(thm)],[])).
% 2.64/2.89 tff(16289,plain,
% 2.64/2.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))),
% 2.64/2.89 inference(modus_ponens,[status(thm)],[16288, 16287])).
% 2.64/2.89 tff(16290,plain,
% 2.64/2.89 ($false),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[16289, 306, 16230, 16228, 16283, 16280])).
% 2.64/2.89 tff(16291,plain,((~(z = elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | b(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.64/2.89 tff(16292,plain,
% 2.64/2.89 (~(z = elem!1)),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[16291, 15961, 16181, 1])).
% 2.64/2.89 tff(16293,plain,
% 2.64/2.89 (~(elem!1 = z)),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[2172, 16292])).
% 2.64/2.89 tff(16294,plain,
% 2.64/2.89 (r(elem!1, z)),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[174, 16293, 2])).
% 2.64/2.89 tff(16295,plain,
% 2.64/2.89 (~r(s(s(s(z))), z)),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[2561, 16294, 16218])).
% 2.64/2.89 tff(16296,plain,
% 2.64/2.89 (b(s(s(s(z))), z)),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[2197, 16295])).
% 2.64/2.89 tff(16297,plain,
% 2.64/2.89 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[11484, 124, 15961, 16218])).
% 2.64/2.89 tff(16298,plain,
% 2.64/2.89 (b(s(s(s(z))), s(s(elem!1)))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[2986, 43, 16297, 15980])).
% 2.64/2.89 tff(16299,plain,
% 2.64/2.89 (~r(s(s(elem!1)), z)),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[7786, 16294, 15961])).
% 2.64/2.89 tff(16300,plain,
% 2.64/2.89 (b(s(s(elem!1)), z)),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[476, 16299])).
% 2.64/2.89 tff(16301,plain,
% 2.64/2.89 (~b(z, s(s(elem!1)))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[12693, 16296, 16298, 16300])).
% 2.64/2.89 tff(16302,plain,
% 2.64/2.89 (r(z, s(s(elem!1)))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[460, 16301])).
% 2.64/2.89 tff(16303,plain,
% 2.64/2.89 (~r(elem!1, s(s(elem!1)))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[978, 16302, 16294])).
% 2.64/2.89 tff(16304,plain,
% 2.64/2.89 (b(elem!1, s(s(elem!1)))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[516, 16303, 15962])).
% 2.64/2.89 tff(16305,plain,
% 2.64/2.89 (b(z, elem!1)),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[835, 16292, 7])).
% 2.64/2.89 tff(16306,plain,
% 2.64/2.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.64/2.89 inference(rewrite,[status(thm)],[])).
% 2.64/2.89 tff(16307,plain,
% 2.64/2.89 (((~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1))))) <=> ((~b(z, elem!1)) | (~b(elem!1, 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)))))),
% 2.64/2.90 inference(rewrite,[status(thm)],[])).
% 2.64/2.90 tff(16308,plain,
% 2.64/2.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 2.64/2.90 inference(monotonicity,[status(thm)],[16307])).
% 2.64/2.90 tff(16309,plain,
% 2.64/2.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.64/2.90 inference(transitivity,[status(thm)],[16308, 16306])).
% 2.64/2.90 tff(16310,plain,
% 2.64/2.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.64/2.90 inference(quant_inst,[status(thm)],[])).
% 2.64/2.90 tff(16311,plain,
% 2.64/2.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1))))),
% 2.64/2.90 inference(modus_ponens,[status(thm)],[16310, 16309])).
% 2.64/2.90 tff(16312,plain,
% 2.64/2.90 ($false),
% 2.64/2.90 inference(unit_resolution,[status(thm)],[16311, 306, 16305, 16304, 16300, 16298, 16296])).
% 2.64/2.90 tff(16313,plain,(b(elem!1, z) | r(z, elem!1) | b(s(s(s(z))), elem!1) | b(elem!1, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.90 tff(16314,plain,
% 2.64/2.90 (b(elem!1, z)),
% 2.64/2.90 inference(unit_resolution,[status(thm)],[16313, 7, 1, 3])).
% 2.64/2.90 tff(16315,plain,
% 2.64/2.90 (~(z = elem!1)),
% 2.64/2.90 inference(unit_resolution,[status(thm)],[11005, 16314])).
% 2.64/2.90 tff(16316,plain,
% 2.64/2.90 (b(z, elem!1)),
% 2.64/2.90 inference(unit_resolution,[status(thm)],[835, 16315, 7])).
% 2.64/2.90 tff(16317,plain,
% 2.64/2.90 (~b(s(z), z)),
% 2.64/2.90 inference(unit_resolution,[status(thm)],[12662, 16316, 16181, 16314])).
% 2.64/2.90 tff(16318,plain,
% 2.64/2.90 (r(s(z), z)),
% 2.64/2.90 inference(unit_resolution,[status(thm)],[221, 16317])).
% 2.64/2.90 tff(16319,plain,
% 2.64/2.90 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.64/2.90 inference(unit_resolution,[status(thm)],[12954, 16318, 16181, 16314, 16316])).
% 2.64/2.90 tff(16320,plain,
% 2.64/2.90 (~b(s(s(s(elem!1))), elem!1)),
% 2.64/2.90 inference(unit_resolution,[status(thm)],[13176, 16316, 16181, 16314])).
% 2.64/2.90 tff(16321,plain,
% 2.64/2.90 ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z)))),
% 2.64/2.90 inference(unit_resolution,[status(thm)],[4380, 15960])).
% 2.64/2.90 tff(16322,plain,
% 2.64/2.90 (~b(s(s(elem!1)), s(z))),
% 2.64/2.90 inference(unit_resolution,[status(thm)],[16321, 30, 2831])).
% 2.64/2.90 tff(16323,plain,
% 2.64/2.90 (r(s(s(elem!1)), s(z))),
% 2.64/2.90 inference(unit_resolution,[status(thm)],[3989, 16322])).
% 2.64/2.90 tff(16324,plain,
% 2.64/2.90 (~b(z, s(z))),
% 2.64/2.90 inference(unit_resolution,[status(thm)],[8305, 306, 838, 4012, 2831])).
% 2.64/2.90 tff(16325,plain,
% 2.64/2.90 (r(z, s(z))),
% 2.64/2.90 inference(unit_resolution,[status(thm)],[2263, 16324])).
% 2.64/2.90 tff(16326,plain,
% 2.64/2.90 (~b(s(s(elem!1)), z)),
% 2.64/2.90 inference(unit_resolution,[status(thm)],[3974, 306, 838, 4012, 30])).
% 2.64/2.90 tff(16327,plain,
% 2.64/2.90 (r(s(s(elem!1)), z)),
% 2.64/2.90 inference(unit_resolution,[status(thm)],[476, 16326])).
% 2.64/2.90 tff(16328,plain,
% 2.64/2.90 ($false),
% 2.64/2.90 inference(unit_resolution,[status(thm)],[4657, 124, 16327, 16325, 16323])).
% 2.64/2.90 tff(16329,plain,((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.90 tff(16330,plain,
% 2.74/2.90 (~b(s(s(elem!1)), elem!1)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[16329, 16316, 16314, 16181])).
% 2.74/2.90 tff(16331,plain,
% 2.74/2.90 (~b(s(z), z)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[12662, 838, 2831, 4012])).
% 2.74/2.90 tff(16332,plain,
% 2.74/2.90 (r(s(z), z)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[221, 16331])).
% 2.74/2.90 tff(16333,plain,
% 2.74/2.90 (~b(s(s(s(s(z)))), z)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[12172, 306, 838, 4012, 12426])).
% 2.74/2.90 tff(16334,plain,
% 2.74/2.90 (r(s(s(s(s(z)))), z)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[695, 16333])).
% 2.74/2.90 tff(16335,plain,
% 2.74/2.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.74/2.90 inference(rewrite,[status(thm)],[])).
% 2.74/2.90 tff(16336,plain,
% 2.74/2.90 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.74/2.90 inference(rewrite,[status(thm)],[])).
% 2.74/2.90 tff(16337,plain,
% 2.74/2.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1))))),
% 2.74/2.90 inference(monotonicity,[status(thm)],[16336])).
% 2.74/2.90 tff(16338,plain,
% 2.74/2.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.74/2.90 inference(transitivity,[status(thm)],[16337, 16335])).
% 2.74/2.90 tff(16339,plain,
% 2.74/2.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 2.74/2.90 inference(quant_inst,[status(thm)],[])).
% 2.74/2.90 tff(16340,plain,
% 2.74/2.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1))),
% 2.74/2.90 inference(modus_ponens,[status(thm)],[16339, 16338])).
% 2.74/2.90 tff(16341,plain,
% 2.74/2.90 (~b(s(s(s(s(z)))), s(z))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[16340, 306, 838, 4012, 2831, 12426])).
% 2.74/2.90 tff(16342,plain,
% 2.74/2.90 (r(s(s(s(s(z)))), s(z))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[4490, 16341])).
% 2.74/2.90 tff(16343,plain,
% 2.74/2.90 ($false),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[10160, 16342, 16334, 16332])).
% 2.74/2.90 tff(16344,plain,((~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.90 tff(16345,plain,
% 2.74/2.90 (~b(s(s(s(s(z)))), elem!1)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[16344, 16316, 16314, 16181])).
% 2.74/2.90 tff(16346,plain,
% 2.74/2.90 (r(s(s(s(s(z)))), elem!1)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[9832, 10291, 14202])).
% 2.74/2.90 tff(16347,plain,
% 2.74/2.90 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[1144, 4918, 4269])).
% 2.74/2.90 tff(16348,plain,
% 2.74/2.90 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[14263, 124, 16347, 16346])).
% 2.74/2.90 tff(16349,plain,
% 2.74/2.90 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[10662, 16348])).
% 2.74/2.90 tff(16350,plain,
% 2.74/2.90 (~(elem!1 = s(s(s(z))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[16106, 1171])).
% 2.74/2.90 tff(16351,plain,
% 2.74/2.90 (~(s(s(s(z))) = elem!1)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[12937, 16350])).
% 2.74/2.90 tff(16352,plain,
% 2.74/2.90 (r(s(s(s(z))), elem!1)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[1489, 16351, 1])).
% 2.74/2.90 tff(16353,plain,
% 2.74/2.90 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 2.74/2.90 inference(rewrite,[status(thm)],[])).
% 2.74/2.90 tff(16354,plain,
% 2.74/2.90 (((~r(s(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(s(z))))))))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 2.74/2.90 inference(rewrite,[status(thm)],[])).
% 2.74/2.90 tff(16355,plain,
% 2.74/2.90 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(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(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))))),
% 2.74/2.90 inference(monotonicity,[status(thm)],[16354])).
% 2.74/2.90 tff(16356,plain,
% 2.74/2.90 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(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(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 2.74/2.90 inference(transitivity,[status(thm)],[16355, 16353])).
% 2.74/2.90 tff(16357,plain,
% 2.74/2.90 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(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(s(z)))))))))),
% 2.74/2.90 inference(quant_inst,[status(thm)],[])).
% 2.74/2.90 tff(16358,plain,
% 2.74/2.90 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 2.74/2.90 inference(modus_ponens,[status(thm)],[16357, 16356])).
% 2.74/2.90 tff(16359,plain,
% 2.74/2.90 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[16358, 124, 16352, 16347])).
% 2.74/2.90 tff(16360,plain,
% 2.74/2.90 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[3207, 16359])).
% 2.74/2.90 tff(16361,plain,
% 2.74/2.90 (r(elem!1, s(s(s(z))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[2304, 16350, 3])).
% 2.74/2.90 tff(16362,plain,
% 2.74/2.90 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[15614, 124, 2859, 14251])).
% 2.74/2.90 tff(16363,plain,
% 2.74/2.90 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[15309, 14251, 2858])).
% 2.74/2.90 tff(16364,plain,
% 2.74/2.90 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[13486, 16363])).
% 2.74/2.90 tff(16365,plain,
% 2.74/2.90 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[16358, 124, 2859, 2858])).
% 2.74/2.90 tff(16366,plain,
% 2.74/2.90 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[3207, 16365])).
% 2.74/2.90 tff(16367,plain,
% 2.74/2.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 2.74/2.90 inference(rewrite,[status(thm)],[])).
% 2.74/2.90 tff(16368,plain,
% 2.74/2.90 (((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 2.74/2.90 inference(rewrite,[status(thm)],[])).
% 2.74/2.90 tff(16369,plain,
% 2.74/2.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))))),
% 2.74/2.90 inference(monotonicity,[status(thm)],[16368])).
% 2.74/2.90 tff(16370,plain,
% 2.74/2.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 2.74/2.90 inference(transitivity,[status(thm)],[16369, 16367])).
% 2.74/2.90 tff(16371,plain,
% 2.74/2.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.74/2.90 inference(quant_inst,[status(thm)],[])).
% 2.74/2.90 tff(16372,plain,
% 2.74/2.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 2.74/2.90 inference(modus_ponens,[status(thm)],[16371, 16370])).
% 2.74/2.90 tff(16373,plain,
% 2.74/2.90 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[16372, 306, 1531, 16366, 12206, 16364])).
% 2.74/2.90 tff(16374,plain,
% 2.74/2.90 ($false),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[4471, 16373, 16362])).
% 2.74/2.90 tff(16375,plain,((~r(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.90 tff(16376,plain,
% 2.74/2.90 (~b(s(s(s(z))), z)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[16375, 16352, 16346, 16347])).
% 2.74/2.90 tff(16377,plain,
% 2.74/2.90 (r(s(s(s(z))), z)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[2197, 16376])).
% 2.74/2.90 tff(16378,plain,
% 2.74/2.90 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[12318, 16377, 4012, 838, 16361, 10291])).
% 2.74/2.90 tff(16379,plain,
% 2.74/2.90 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[4471, 16378])).
% 2.74/2.90 tff(16380,plain,
% 2.74/2.90 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.74/2.90 inference(rewrite,[status(thm)],[])).
% 2.74/2.90 tff(16381,plain,
% 2.74/2.90 (((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.74/2.90 inference(rewrite,[status(thm)],[])).
% 2.74/2.90 tff(16382,plain,
% 2.74/2.90 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1))))),
% 2.74/2.90 inference(monotonicity,[status(thm)],[16381])).
% 2.74/2.90 tff(16383,plain,
% 2.74/2.90 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.74/2.90 inference(transitivity,[status(thm)],[16382, 16380])).
% 2.74/2.90 tff(16384,plain,
% 2.74/2.90 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 2.74/2.90 inference(quant_inst,[status(thm)],[])).
% 2.74/2.90 tff(16385,plain,
% 2.74/2.90 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1))),
% 2.74/2.90 inference(modus_ponens,[status(thm)],[16384, 16383])).
% 2.74/2.90 tff(16386,plain,
% 2.74/2.90 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[16385, 124, 16352, 16346])).
% 2.74/2.90 tff(16387,plain,
% 2.74/2.90 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[4481, 16386])).
% 2.74/2.90 tff(16388,plain,
% 2.74/2.90 (~r(s(s(s(z))), s(z))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[211, 16377, 204])).
% 2.74/2.90 tff(16389,plain,
% 2.74/2.90 (b(s(s(s(z))), s(z))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[113, 16388])).
% 2.74/2.90 tff(16390,plain,
% 2.74/2.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 2.74/2.90 inference(rewrite,[status(thm)],[])).
% 2.74/2.90 tff(16391,plain,
% 2.74/2.90 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 2.74/2.90 inference(rewrite,[status(thm)],[])).
% 2.74/2.90 tff(16392,plain,
% 2.74/2.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))))),
% 2.74/2.90 inference(monotonicity,[status(thm)],[16391])).
% 2.74/2.90 tff(16393,plain,
% 2.74/2.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 2.74/2.90 inference(transitivity,[status(thm)],[16392, 16390])).
% 2.74/2.90 tff(16394,plain,
% 2.74/2.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 2.74/2.90 inference(quant_inst,[status(thm)],[])).
% 2.74/2.90 tff(16395,plain,
% 2.74/2.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 2.74/2.90 inference(modus_ponens,[status(thm)],[16394, 16393])).
% 2.74/2.90 tff(16396,plain,
% 2.74/2.90 ($false),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[16395, 306, 16389, 16387, 16379, 16360, 16349])).
% 2.74/2.90 tff(16397,plain,((~(s(s(elem!1)) = elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~r(s(z), z)) | b(s(s(s(z))), elem!1) | b(elem!1, s(s(s(z)))) | b(s(s(s(s(z)))), elem!1) | b(s(s(s(s(s(s(z)))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.90 tff(16398,plain,
% 2.74/2.90 (~(s(s(elem!1)) = elem!1)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[16397, 16314, 16316, 16318, 1, 3, 16345, 16319])).
% 2.74/2.90 tff(16399,plain,
% 2.74/2.90 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[7780, 1627, 7974])).
% 2.74/2.90 tff(16400,plain,
% 2.74/2.90 (r(s(elem!1), elem!1)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[7090, 16399, 2170, 91])).
% 2.74/2.90 tff(16401,plain,
% 2.74/2.90 (~r(s(s(elem!1)), s(elem!1))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[7985, 16400, 7974])).
% 2.74/2.90 tff(16402,plain,
% 2.74/2.90 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[12869, 1627, 6481, 144])).
% 2.74/2.90 tff(16403,plain,
% 2.74/2.90 (~b(s(s(elem!1)), s(elem!1))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[12859, 16400, 7974, 1627, 144, 16402])).
% 2.74/2.90 tff(16404,plain,
% 2.74/2.90 ($false),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[994, 16403, 16401, 196])).
% 2.74/2.90 tff(16405,plain,((~r(s(s(s(elem!1))), elem!1)) | (z = elem!1) | (s(s(elem!1)) = elem!1) | b(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.90 tff(16406,plain,
% 2.74/2.90 (~r(s(s(s(elem!1))), elem!1)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[16405, 16315, 16398, 16330])).
% 2.74/2.90 tff(16407,plain,
% 2.74/2.90 (s(s(s(elem!1))) = elem!1),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[1636, 16406, 16320])).
% 2.74/2.90 tff(16408,plain,
% 2.74/2.90 (~(s(elem!1) = s(z))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[2689, 16315])).
% 2.74/2.90 tff(16409,plain,
% 2.74/2.90 (~(s(s(s(z))) = elem!1)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[4105, 16407, 16408])).
% 2.74/2.90 tff(16410,plain,
% 2.74/2.90 (~(s(s(s(s(z)))) = s(elem!1))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[14363, 16409])).
% 2.74/2.90 tff(16411,plain,
% 2.74/2.90 (s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))),
% 2.74/2.90 inference(transitivity,[status(thm)],[4273, 4097])).
% 2.74/2.90 tff(16412,plain,
% 2.74/2.90 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(s(elem!1))))),
% 2.74/2.90 inference(monotonicity,[status(thm)],[16411])).
% 2.74/2.90 tff(16413,plain,
% 2.74/2.90 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 2.74/2.90 inference(transitivity,[status(thm)],[2823, 16412, 139])).
% 2.74/2.90 tff(16414,plain,
% 2.74/2.90 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(elem!1)))),
% 2.74/2.90 inference(monotonicity,[status(thm)],[16413])).
% 2.74/2.90 tff(16415,plain,
% 2.74/2.90 (s(s(s(s(z)))) = s(elem!1)),
% 2.74/2.90 inference(transitivity,[status(thm)],[497, 16414, 66])).
% 2.74/2.90 tff(16416,assumption,(~(s(s(s(s(z)))) = s(elem!1))), introduced(assumption)).
% 2.74/2.90 tff(16417,plain,
% 2.74/2.90 ($false),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[16416, 16415])).
% 2.74/2.90 tff(16418,plain,((~(s(s(s(s(s(s(z)))))) = elem!1)) | (s(s(s(s(z)))) = s(elem!1)) | (~(s(s(s(elem!1))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.91 tff(16419,plain,
% 2.74/2.91 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[16418, 16410, 16407])).
% 2.74/2.91 tff(16420,plain,
% 2.74/2.91 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[1144, 16419, 16319])).
% 2.74/2.91 tff(16421,plain,
% 2.74/2.91 (r(s(s(elem!1)), elem!1)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[47, 16398, 16330])).
% 2.74/2.91 tff(16422,plain,
% 2.74/2.91 (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[8458, 124, 16421, 16420])).
% 2.74/2.91 tff(16423,plain,
% 2.74/2.91 (~(s(s(s(s(s(s(z)))))) = s(s(elem!1)))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[7206, 16407])).
% 2.74/2.91 tff(16424,plain,
% 2.74/2.91 (b(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[3247, 43, 16423, 16422])).
% 2.74/2.91 tff(16425,plain,
% 2.74/2.91 (r(s(s(s(z))), elem!1)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[1489, 16409, 1])).
% 2.74/2.91 tff(16426,plain,
% 2.74/2.91 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[2862, 124, 16425, 16420])).
% 2.74/2.91 tff(16427,plain,
% 2.74/2.91 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[4603, 43, 16426, 4577])).
% 2.74/2.91 tff(16428,plain,
% 2.74/2.91 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[11484, 124, 16421, 16425])).
% 2.74/2.91 tff(16429,plain,
% 2.74/2.91 (b(s(s(s(z))), s(s(elem!1)))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[2986, 43, 16428, 15980])).
% 2.74/2.91 tff(16430,plain,
% 2.74/2.91 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.74/2.91 inference(rewrite,[status(thm)],[])).
% 2.74/2.91 tff(16431,plain,
% 2.74/2.91 (((~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(z)))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.74/2.91 inference(rewrite,[status(thm)],[])).
% 2.74/2.91 tff(16432,plain,
% 2.74/2.91 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 2.74/2.91 inference(monotonicity,[status(thm)],[16431])).
% 2.74/2.91 tff(16433,plain,
% 2.74/2.91 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.74/2.91 inference(transitivity,[status(thm)],[16432, 16430])).
% 2.74/2.91 tff(16434,plain,
% 2.74/2.91 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.74/2.91 inference(quant_inst,[status(thm)],[])).
% 2.74/2.91 tff(16435,plain,
% 2.74/2.91 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 2.74/2.91 inference(modus_ponens,[status(thm)],[16434, 16433])).
% 2.74/2.91 tff(16436,plain,
% 2.74/2.91 (~r(s(s(elem!1)), s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[16435, 124, 16421, 16425])).
% 2.74/2.91 tff(16437,plain,
% 2.74/2.91 (s(s(s(z))) = s(s(elem!1))),
% 2.74/2.91 inference(modus_ponens,[status(thm)],[20, 7095])).
% 2.74/2.91 tff(16438,plain,
% 2.74/2.91 ($false),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[15980, 16437])).
% 2.74/2.91 tff(16439,plain,(~(s(s(elem!1)) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.91 tff(16440,plain,
% 2.74/2.91 (b(s(s(elem!1)), s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[7962, 43, 16439, 16436])).
% 2.74/2.91 tff(16441,plain,
% 2.74/2.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))))),
% 2.74/2.91 inference(rewrite,[status(thm)],[])).
% 2.74/2.91 tff(16442,plain,
% 2.74/2.91 (((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))) <=> ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))))),
% 2.74/2.91 inference(rewrite,[status(thm)],[])).
% 2.74/2.91 tff(16443,plain,
% 2.74/2.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1))))))),
% 2.74/2.91 inference(monotonicity,[status(thm)],[16442])).
% 2.74/2.91 tff(16444,plain,
% 2.74/2.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))))),
% 2.74/2.91 inference(transitivity,[status(thm)],[16443, 16441])).
% 2.74/2.91 tff(16445,plain,
% 2.74/2.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 2.74/2.91 inference(quant_inst,[status(thm)],[])).
% 2.74/2.91 tff(16446,plain,
% 2.74/2.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1))))),
% 2.74/2.91 inference(modus_ponens,[status(thm)],[16445, 16444])).
% 2.74/2.91 tff(16447,plain,
% 2.74/2.91 ($false),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[16446, 306, 16440, 16429, 16427, 16424])).
% 2.74/2.91 tff(16448,plain,(r(z, elem!1) | b(s(s(s(z))), elem!1) | b(elem!1, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.91 tff(16449,plain,
% 2.74/2.91 (r(z, elem!1)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[16448, 1, 3])).
% 2.74/2.91 tff(16450,plain,
% 2.74/2.91 (~r(z, s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[14175, 124, 374, 4200])).
% 2.74/2.91 tff(16451,plain,
% 2.74/2.91 (b(z, s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[11982, 16450])).
% 2.74/2.91 tff(16452,plain,
% 2.74/2.91 (~r(s(s(s(z))), z)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[6831, 4200, 374])).
% 2.74/2.91 tff(16453,plain,
% 2.74/2.91 (b(s(s(s(z))), z)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[2197, 16452])).
% 2.74/2.91 tff(16454,plain,
% 2.74/2.91 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[4471, 16362])).
% 2.74/2.91 tff(16455,plain,
% 2.74/2.91 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[16385, 124, 2859, 14251])).
% 2.74/2.91 tff(16456,plain,
% 2.74/2.91 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[4481, 16455])).
% 2.74/2.91 tff(16457,plain,
% 2.74/2.91 ($false),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[10722, 16456, 14270, 859, 16454])).
% 2.74/2.91 tff(16458,plain,((~r(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.91 tff(16459,plain,
% 2.74/2.91 (~r(s(s(s(s(z)))), elem!1)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[16458, 4200, 859, 374])).
% 2.74/2.91 tff(16460,plain,
% 2.74/2.91 (b(s(s(s(s(z)))), elem!1)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[9832, 16459, 9815])).
% 2.74/2.91 tff(16461,plain,
% 2.74/2.91 (r(s(z), elem!1)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[16180, 2715])).
% 2.74/2.91 tff(16462,plain,
% 2.74/2.91 ($false),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[7152, 16461, 2715, 374, 1483, 1])).
% 2.74/2.91 tff(16463,plain,(b(s(z), elem!1) | (~r(z, elem!1)) | (s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.91 tff(16464,plain,
% 2.74/2.91 (b(s(z), elem!1)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[16463, 1, 1483, 374])).
% 2.74/2.91 tff(16465,plain,
% 2.74/2.91 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[16276, 16464, 16460])).
% 2.74/2.91 tff(16466,plain,
% 2.74/2.91 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[1144, 16465, 14890])).
% 2.74/2.91 tff(16467,plain,
% 2.74/2.91 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[2862, 124, 4200, 16466])).
% 2.74/2.91 tff(16468,plain,
% 2.74/2.91 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[5462, 16466, 374, 1531])).
% 2.74/2.91 tff(16469,plain,
% 2.74/2.91 ($false),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[4603, 43, 16468, 16467, 4577])).
% 2.74/2.91 tff(16470,plain,(b(s(s(s(z))), elem!1) | (~r(z, elem!1)) | (~b(s(s(s(z))), z)) | (s(s(s(s(s(s(z)))))) = elem!1) | (s(s(s(s(z)))) = elem!1) | (~b(z, s(s(s(z))))) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.91 tff(16471,plain,
% 2.74/2.91 ($false),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[16470, 10291, 4918, 374, 1, 16453, 16451, 1483])).
% 2.74/2.91 tff(16472,plain,((~(s(s(elem!1)) = elem!1)) | (~r(z, elem!1)) | b(s(s(s(z))), elem!1) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.91 tff(16473,plain,
% 2.74/2.91 (s(s(s(z))) = elem!1),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[16472, 1171, 1, 374])).
% 2.74/2.91 tff(16474,plain,
% 2.74/2.91 ($false),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[12937, 16473, 16350])).
% 2.74/2.91 tff(16475,plain,((~(s(s(elem!1)) = elem!1)) | b(s(s(s(z))), elem!1) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.91 tff(16476,plain,
% 2.74/2.91 (~(s(s(elem!1)) = elem!1)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[16475, 1, 16449])).
% 2.74/2.91 tff(16477,plain,
% 2.74/2.91 (~(s(elem!1) = elem!1)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[180, 16476])).
% 2.74/2.91 tff(16478,plain,
% 2.74/2.91 (~(s(s(elem!1)) = s(elem!1))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[195, 16477])).
% 2.74/2.91 tff(16479,plain,
% 2.74/2.91 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[143, 16476])).
% 2.74/2.91 tff(16480,plain,
% 2.74/2.91 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[152, 16479])).
% 2.74/2.91 tff(16481,plain,
% 2.74/2.91 (r(elem!1, z)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[174, 13979, 2])).
% 2.74/2.91 tff(16482,plain,
% 2.74/2.91 (~r(z, s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[3392, 16361, 16481])).
% 2.74/2.91 tff(16483,plain,
% 2.74/2.91 (b(z, s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[11982, 16482])).
% 2.74/2.91 tff(16484,plain,
% 2.74/2.91 (~r(s(s(s(z))), z)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[2312, 16361, 16481])).
% 2.74/2.91 tff(16485,plain,
% 2.74/2.91 (b(s(s(s(z))), z)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[2197, 16484])).
% 2.74/2.91 tff(16486,plain,
% 2.74/2.91 (b(s(s(s(z))), elem!1)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[16470, 16485, 374, 4918, 10291, 16483, 16351])).
% 2.74/2.91 tff(16487,plain,
% 2.74/2.91 (~r(s(s(s(z))), z)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[2312, 3313, 16481])).
% 2.74/2.91 tff(16488,plain,
% 2.74/2.91 (b(s(s(s(z))), z)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[2197, 16487])).
% 2.74/2.91 tff(16489,plain,
% 2.74/2.91 (b(s(z), z)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[221, 14507])).
% 2.74/2.91 tff(16490,plain,
% 2.74/2.91 (~r(s(z), s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[3347, 4, 3313])).
% 2.74/2.91 tff(16491,plain,
% 2.74/2.91 (b(s(z), s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[3302, 16490])).
% 2.74/2.91 tff(16492,plain,
% 2.74/2.91 ($false),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[4943, 16491, 16489, 16481, 3, 16488, 2])).
% 2.74/2.91 tff(16493,plain,((~r(s(z), elem!1)) | b(elem!1, s(s(s(z)))) | b(elem!1, z) | (~r(elem!1, s(s(s(z))))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.91 tff(16494,plain,
% 2.74/2.91 (~r(s(z), elem!1)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[16493, 16361, 2, 3, 374])).
% 2.74/2.91 tff(16495,plain,
% 2.74/2.91 (b(s(z), elem!1)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[16180, 16494])).
% 2.74/2.91 tff(16496,plain,
% 2.74/2.91 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[5462, 2858, 374, 1531])).
% 2.74/2.91 tff(16497,plain,
% 2.74/2.91 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[4603, 43, 16496, 4577])).
% 2.74/2.91 tff(16498,plain,
% 2.74/2.91 ($false),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[4610, 124, 3313, 2858, 16497])).
% 2.74/2.91 tff(16499,plain,((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(z, elem!1)) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.91 tff(16500,plain,
% 2.74/2.91 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[16499, 16361, 374, 16485])).
% 2.74/2.91 tff(16501,plain,
% 2.74/2.91 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[1144, 16500, 4918])).
% 2.74/2.91 tff(16502,plain,
% 2.74/2.91 ((~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z)))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[5377, 15960])).
% 2.74/2.91 tff(16503,plain,
% 2.74/2.91 (~r(s(z), s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[16502, 16501, 16486, 16495])).
% 2.74/2.91 tff(16504,plain,
% 2.74/2.91 (b(s(z), s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[3302, 16503])).
% 2.74/2.91 tff(16505,plain,
% 2.74/2.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)))),
% 2.74/2.91 inference(rewrite,[status(thm)],[])).
% 2.74/2.91 tff(16506,plain,
% 2.74/2.91 (((~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)))),
% 2.74/2.91 inference(rewrite,[status(thm)],[])).
% 2.74/2.91 tff(16507,plain,
% 2.74/2.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1))))),
% 2.74/2.91 inference(monotonicity,[status(thm)],[16506])).
% 2.74/2.91 tff(16508,plain,
% 2.74/2.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)))),
% 2.74/2.91 inference(transitivity,[status(thm)],[16507, 16505])).
% 2.74/2.91 tff(16509,plain,
% 2.74/2.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 2.74/2.91 inference(quant_inst,[status(thm)],[])).
% 2.74/2.91 tff(16510,plain,
% 2.74/2.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1))),
% 2.74/2.91 inference(modus_ponens,[status(thm)],[16509, 16508])).
% 2.74/2.91 tff(16511,plain,
% 2.74/2.91 ($false),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[16510, 306, 16504, 16495, 16486, 15960])).
% 2.74/2.91 tff(16512,plain,((~(s(s(elem!1)) = elem!1)) | (~r(z, elem!1)) | b(elem!1, z) | b(elem!1, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.91 tff(16513,plain,
% 2.74/2.91 (~(s(s(elem!1)) = elem!1)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[16512, 2, 3, 16449])).
% 2.74/2.91 tff(16514,plain,
% 2.74/2.91 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[143, 16513])).
% 2.74/2.91 tff(16515,plain,
% 2.74/2.91 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[152, 16514])).
% 2.74/2.91 tff(16516,plain,
% 2.74/2.91 (~(s(s(elem!1)) = elem!1)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[16512, 3, 2, 10425])).
% 2.74/2.91 tff(16517,plain,
% 2.74/2.91 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[143, 16516])).
% 2.74/2.91 tff(16518,plain,
% 2.74/2.91 (b(s(s(elem!1)), elem!1)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[47, 16516, 6])).
% 2.74/2.91 tff(16519,plain,
% 2.74/2.91 (r(s(elem!1), elem!1)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[13306, 16516, 2, 6])).
% 2.74/2.91 tff(16520,plain,
% 2.74/2.91 (~r(s(z), elem!1)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[14510, 802, 374, 13994])).
% 2.74/2.91 tff(16521,plain,
% 2.74/2.91 (b(s(z), elem!1)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[16180, 16520])).
% 2.74/2.91 tff(16522,plain,
% 2.74/2.91 ((s(s(s(s(s(s(z)))))) = s(s(s(s(z))))) <=> (elem!1 = s(s(s(s(z)))))),
% 2.74/2.91 inference(monotonicity,[status(thm)],[4273])).
% 2.74/2.91 tff(16523,plain,
% 2.74/2.91 ((s(s(s(s(s(s(z)))))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = elem!1)),
% 2.74/2.91 inference(transitivity,[status(thm)],[16522, 8778])).
% 2.74/2.91 tff(16524,plain,
% 2.74/2.91 ((~(s(s(s(s(s(s(z)))))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 2.74/2.91 inference(monotonicity,[status(thm)],[16523])).
% 2.74/2.91 tff(16525,plain,
% 2.74/2.91 (~(s(s(s(s(z)))) = elem!1)),
% 2.74/2.91 inference(modus_ponens,[status(thm)],[10661, 16524])).
% 2.74/2.91 tff(16526,plain,
% 2.74/2.91 ((s(s(s(z))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(z))) = elem!1)),
% 2.74/2.91 inference(monotonicity,[status(thm)],[4273])).
% 2.74/2.91 tff(16527,plain,
% 2.74/2.91 ((~(s(s(s(z))) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(s(z))) = elem!1))),
% 2.74/2.91 inference(monotonicity,[status(thm)],[16526])).
% 2.74/2.91 tff(16528,plain,
% 2.74/2.91 (~(s(s(s(z))) = elem!1)),
% 2.74/2.91 inference(modus_ponens,[status(thm)],[556, 16527])).
% 2.74/2.91 tff(16529,plain,
% 2.74/2.91 (r(s(s(s(z))), elem!1)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[1489, 16528, 1])).
% 2.74/2.91 tff(16530,plain,
% 2.74/2.91 ((s(s(s(z))) = s(s(s(s(s(s(z))))))) <=> (elem!1 = s(s(s(z))))),
% 2.74/2.91 inference(transitivity,[status(thm)],[16526, 6881])).
% 2.74/2.91 tff(16531,plain,
% 2.74/2.91 ((~(s(s(s(z))) = s(s(s(s(s(s(z)))))))) <=> (~(elem!1 = s(s(s(z)))))),
% 2.74/2.91 inference(monotonicity,[status(thm)],[16530])).
% 2.74/2.91 tff(16532,plain,
% 2.74/2.91 (~(elem!1 = s(s(s(z))))),
% 2.74/2.91 inference(modus_ponens,[status(thm)],[556, 16531])).
% 2.74/2.91 tff(16533,plain,
% 2.74/2.91 (r(elem!1, s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[2304, 16532, 3])).
% 2.74/2.91 tff(16534,plain,
% 2.74/2.91 (~r(z, s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[3392, 16533, 246])).
% 2.74/2.91 tff(16535,plain,
% 2.74/2.91 (b(z, s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[11982, 16534])).
% 2.74/2.91 tff(16536,plain,
% 2.74/2.91 (~r(s(s(s(s(z)))), elem!1)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[16458, 16535, 16529, 374])).
% 2.74/2.91 tff(16537,plain,
% 2.74/2.91 (b(s(s(s(s(z)))), elem!1)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[9832, 16536, 16525])).
% 2.74/2.91 tff(16538,plain,
% 2.74/2.91 (((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.74/2.91 inference(rewrite,[status(thm)],[])).
% 2.74/2.91 tff(16539,plain,
% 2.74/2.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1))))),
% 2.74/2.91 inference(monotonicity,[status(thm)],[16538])).
% 2.74/2.91 tff(16540,plain,
% 2.74/2.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.74/2.91 inference(transitivity,[status(thm)],[16539, 10131])).
% 2.74/2.91 tff(16541,plain,
% 2.74/2.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 2.74/2.91 inference(quant_inst,[status(thm)],[])).
% 2.74/2.91 tff(16542,plain,
% 2.74/2.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1))),
% 2.74/2.91 inference(modus_ponens,[status(thm)],[16541, 16540])).
% 2.74/2.91 tff(16543,plain,
% 2.74/2.91 (~b(s(s(s(s(z)))), s(z))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[16542, 306, 2831, 15960, 16537])).
% 2.74/2.91 tff(16544,plain,
% 2.74/2.91 (r(s(s(s(s(z)))), s(z))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[4490, 16543])).
% 2.74/2.91 tff(16545,plain,
% 2.74/2.91 (~b(s(s(elem!1)), s(z))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[16321, 2831, 30])).
% 2.74/2.91 tff(16546,plain,
% 2.74/2.91 (r(s(s(elem!1)), s(z))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[3989, 16545])).
% 2.74/2.91 tff(16547,plain,
% 2.74/2.91 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.74/2.91 inference(rewrite,[status(thm)],[])).
% 2.74/2.91 tff(16548,plain,
% 2.74/2.91 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.74/2.91 inference(quant_inst,[status(thm)],[])).
% 2.74/2.91 tff(16549,plain,
% 2.74/2.91 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 2.74/2.91 inference(modus_ponens,[status(thm)],[16548, 16547])).
% 2.74/2.91 tff(16550,plain,
% 2.74/2.91 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[16549, 124, 16546, 16544])).
% 2.74/2.91 tff(16551,plain,
% 2.74/2.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.74/2.91 inference(rewrite,[status(thm)],[])).
% 2.74/2.91 tff(16552,plain,
% 2.74/2.91 (((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.74/2.91 inference(rewrite,[status(thm)],[])).
% 2.74/2.91 tff(16553,plain,
% 2.74/2.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1))))))),
% 2.74/2.91 inference(monotonicity,[status(thm)],[16552])).
% 2.74/2.91 tff(16554,plain,
% 2.74/2.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.74/2.91 inference(transitivity,[status(thm)],[16553, 16551])).
% 2.74/2.91 tff(16555,plain,
% 2.74/2.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.74/2.91 inference(quant_inst,[status(thm)],[])).
% 2.74/2.91 tff(16556,plain,
% 2.74/2.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 2.74/2.91 inference(modus_ponens,[status(thm)],[16555, 16554])).
% 2.74/2.91 tff(16557,plain,
% 2.74/2.91 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[16556, 306, 30, 2831, 15960, 16537])).
% 2.74/2.91 tff(16558,plain,
% 2.74/2.91 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[14390, 43, 16557, 16550])).
% 2.74/2.91 tff(16559,plain,
% 2.74/2.91 (inj_0(s(s(s(s(z))))) = inj_0(s(s(elem!1)))),
% 2.74/2.91 inference(monotonicity,[status(thm)],[16558])).
% 2.74/2.91 tff(16560,plain,
% 2.74/2.91 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(z)))))),
% 2.74/2.91 inference(symmetry,[status(thm)],[16559])).
% 2.74/2.91 tff(16561,plain,
% 2.74/2.91 (s(elem!1) = s(s(s(z)))),
% 2.74/2.91 inference(transitivity,[status(thm)],[67, 16560, 320])).
% 2.74/2.91 tff(16562,plain,
% 2.74/2.91 ($false),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[5385, 16561])).
% 2.74/2.91 tff(16563,plain,((~(s(s(s(s(s(s(z)))))) = elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, z)) | b(elem!1, s(s(s(z)))) | b(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.91 tff(16564,plain,
% 2.74/2.91 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[16563, 1, 30, 374, 246, 3, 16521])).
% 2.74/2.91 tff(16565,plain,
% 2.74/2.91 (r(s(s(s(z))), elem!1)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[1489, 1483, 1])).
% 2.74/2.91 tff(16566,plain,
% 2.74/2.91 (~r(s(s(s(z))), z)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[6831, 16565, 374])).
% 2.74/2.91 tff(16567,plain,
% 2.74/2.91 (r(elem!1, s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[2304, 9082, 3])).
% 2.74/2.91 tff(16568,plain,
% 2.74/2.91 (~b(s(s(s(z))), z)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[16499, 16567, 374, 2858])).
% 2.74/2.91 tff(16569,plain,
% 2.74/2.91 ($false),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[2197, 16568, 16566])).
% 2.74/2.91 tff(16570,plain,((s(s(s(z))) = elem!1) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | b(elem!1, s(s(s(z)))) | b(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.91 tff(16571,plain,
% 2.74/2.91 (s(s(s(z))) = elem!1),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[16570, 2858, 374, 3, 1])).
% 2.74/2.91 tff(16572,plain,
% 2.74/2.91 (s(s(s(s(z)))) = s(elem!1)),
% 2.74/2.91 inference(monotonicity,[status(thm)],[16571])).
% 2.74/2.91 tff(16573,plain,
% 2.74/2.91 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 2.74/2.91 inference(monotonicity,[status(thm)],[16572])).
% 2.74/2.91 tff(16574,plain,
% 2.74/2.91 (s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))),
% 2.74/2.91 inference(monotonicity,[status(thm)],[16573])).
% 2.74/2.91 tff(16575,plain,
% 2.74/2.91 (s(s(s(elem!1))) = s(s(s(s(s(s(z))))))),
% 2.74/2.91 inference(symmetry,[status(thm)],[16574])).
% 2.74/2.91 tff(16576,plain,
% 2.74/2.91 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.74/2.91 inference(monotonicity,[status(thm)],[16575])).
% 2.74/2.91 tff(16577,plain,
% 2.74/2.91 (r(s(s(s(s(s(s(z)))))), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 2.74/2.91 inference(symmetry,[status(thm)],[16576])).
% 2.74/2.92 tff(16578,plain,
% 2.74/2.92 (r(s(s(s(elem!1))), elem!1)),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[2858, 16577])).
% 2.74/2.92 tff(16579,plain,
% 2.74/2.92 (elem!1 = s(s(s(z)))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[12937, 16571])).
% 2.74/2.92 tff(16580,plain,
% 2.74/2.92 (~r(s(s(s(s(z)))), z)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[411, 16579, 7920])).
% 2.74/2.92 tff(16581,plain,
% 2.74/2.92 (b(s(s(s(s(z)))), z)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[695, 16580])).
% 2.74/2.92 tff(16582,plain,
% 2.74/2.92 (r(z, s(s(s(s(s(s(z))))))) <=> r(z, s(s(s(elem!1))))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[241])).
% 2.74/2.92 tff(16583,plain,
% 2.74/2.92 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(s(s(s(z)))))))),
% 2.74/2.92 inference(symmetry,[status(thm)],[16582])).
% 2.74/2.92 tff(16584,plain,
% 2.74/2.92 (r(z, s(s(s(s(s(s(z)))))))),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[564, 16583])).
% 2.74/2.92 tff(16585,assumption,(~r(z, s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 2.74/2.92 tff(16586,plain,
% 2.74/2.92 ($false),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[16585, 16584])).
% 2.74/2.92 tff(16587,plain,(r(z, s(s(s(s(s(s(z))))))) | (~r(z, s(s(s(elem!1))))) | (~(elem!1 = s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.92 tff(16588,plain,
% 2.74/2.92 (~r(z, s(s(s(elem!1))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[16587, 16579, 5442])).
% 2.74/2.92 tff(16589,plain,
% 2.74/2.92 (b(z, s(s(s(elem!1))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[585, 16588])).
% 2.74/2.92 tff(16590,plain,
% 2.74/2.92 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[963, 16589, 16579, 16581, 5454])).
% 2.74/2.92 tff(16591,plain,
% 2.74/2.92 (r(s(s(s(elem!1))), s(elem!1))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[664, 16590, 150])).
% 2.74/2.92 tff(16592,plain,
% 2.74/2.92 ($false),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[9032, 124, 16591, 802, 16578])).
% 2.74/2.92 tff(16593,plain,((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(elem!1), elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (~r(z, elem!1)) | b(elem!1, s(s(s(z)))) | b(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.92 tff(16594,plain,
% 2.74/2.92 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[16593, 1, 150, 374, 3, 802])).
% 2.74/2.92 tff(16595,plain,
% 2.74/2.92 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[1144, 16594, 16564])).
% 2.74/2.92 tff(16596,plain,
% 2.74/2.92 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[16264, 306, 16521, 15960, 16595])).
% 2.74/2.92 tff(16597,plain,
% 2.74/2.92 (r(s(s(s(s(s(s(z)))))), s(z))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[651, 43, 2844, 16596])).
% 2.74/2.92 tff(16598,plain,
% 2.74/2.92 (~b(s(s(elem!1)), s(z))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[16321, 16521, 30])).
% 2.74/2.92 tff(16599,plain,
% 2.74/2.92 (r(s(s(elem!1)), s(z))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[3989, 16598])).
% 2.74/2.92 tff(16600,plain,
% 2.74/2.92 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))))),
% 2.74/2.92 inference(rewrite,[status(thm)],[])).
% 2.74/2.92 tff(16601,plain,
% 2.74/2.92 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))))),
% 2.74/2.92 inference(quant_inst,[status(thm)],[])).
% 2.74/2.92 tff(16602,plain,
% 2.74/2.92 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1))))),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[16601, 16600])).
% 2.74/2.92 tff(16603,plain,
% 2.74/2.92 (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[16602, 124, 16599, 16597])).
% 2.74/2.92 tff(16604,plain,
% 2.74/2.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 2.74/2.92 inference(rewrite,[status(thm)],[])).
% 2.74/2.92 tff(16605,plain,
% 2.74/2.92 (((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1))))) <=> ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 2.74/2.92 inference(rewrite,[status(thm)],[])).
% 2.74/2.92 tff(16606,plain,
% 2.74/2.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), elem!1))))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[16605])).
% 2.74/2.92 tff(16607,plain,
% 2.74/2.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 2.74/2.92 inference(transitivity,[status(thm)],[16606, 16604])).
% 2.74/2.92 tff(16608,plain,
% 2.74/2.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))))),
% 2.74/2.92 inference(quant_inst,[status(thm)],[])).
% 2.74/2.92 tff(16609,plain,
% 2.74/2.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), elem!1))),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[16608, 16607])).
% 2.74/2.92 tff(16610,plain,
% 2.74/2.92 (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[16609, 306, 30, 16521, 15960, 16595])).
% 2.74/2.92 tff(16611,plain,
% 2.74/2.92 ((s(s(s(s(s(s(z)))))) = s(s(elem!1))) | r(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[3247, 43, 16610])).
% 2.74/2.92 tff(16612,plain,
% 2.74/2.92 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[16611, 16603])).
% 2.74/2.92 tff(16613,plain,
% 2.74/2.92 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(elem!1)))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[16612])).
% 2.74/2.92 tff(16614,plain,
% 2.74/2.92 (s(s(s(s(s(z))))) = s(elem!1)),
% 2.74/2.92 inference(transitivity,[status(thm)],[2823, 16613, 66])).
% 2.74/2.92 tff(16615,plain,
% 2.74/2.92 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(elem!1))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[16614])).
% 2.74/2.92 tff(16616,plain,
% 2.74/2.92 (s(s(s(s(z)))) = elem!1),
% 2.74/2.92 inference(transitivity,[status(thm)],[497, 16615, 135])).
% 2.74/2.92 tff(16617,plain,
% 2.74/2.92 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[16616])).
% 2.74/2.92 tff(16618,plain,
% 2.74/2.92 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(z))) = elem!1)),
% 2.74/2.92 inference(transitivity,[status(thm)],[16617, 1414])).
% 2.74/2.92 tff(16619,plain,
% 2.74/2.92 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 2.74/2.92 inference(transitivity,[status(thm)],[16618, 6881])).
% 2.74/2.92 tff(16620,plain,
% 2.74/2.92 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(elem!1 = s(s(s(z)))))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[16619])).
% 2.74/2.92 tff(16621,plain,
% 2.74/2.92 (~(elem!1 = s(s(s(z))))),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[4470, 16620])).
% 2.74/2.92 tff(16622,plain,
% 2.74/2.92 (r(elem!1, s(s(s(z))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[2304, 16621, 3])).
% 2.74/2.92 tff(16623,plain,
% 2.74/2.92 (~r(s(elem!1), s(s(s(z))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[7904, 16622, 802])).
% 2.74/2.92 tff(16624,plain,
% 2.74/2.92 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(z)) = elem!1)),
% 2.74/2.92 inference(monotonicity,[status(thm)],[16616])).
% 2.74/2.92 tff(16625,plain,
% 2.74/2.92 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(z)) = elem!1))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[16624])).
% 2.74/2.92 tff(16626,plain,
% 2.74/2.92 (~(s(s(z)) = elem!1)),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[1612, 16625])).
% 2.74/2.92 tff(16627,plain,
% 2.74/2.92 (~(s(elem!1) = s(s(s(z))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[5384, 16626])).
% 2.74/2.92 tff(16628,plain,
% 2.74/2.92 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(z))) = elem!1))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[16618])).
% 2.74/2.92 tff(16629,plain,
% 2.74/2.92 (~(s(s(s(z))) = elem!1)),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[4470, 16628])).
% 2.74/2.92 tff(16630,plain,
% 2.74/2.92 (r(s(s(s(z))), elem!1)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[1489, 16629, 1])).
% 2.74/2.92 tff(16631,plain,
% 2.74/2.92 (~r(s(s(s(z))), z)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[6831, 16630, 374])).
% 2.74/2.92 tff(16632,plain,
% 2.74/2.92 (b(s(s(s(z))), z)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[2197, 16631])).
% 2.74/2.92 tff(16633,plain,
% 2.74/2.92 (~r(z, s(s(s(z))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[3392, 16622, 246])).
% 2.74/2.92 tff(16634,plain,
% 2.74/2.92 (b(z, s(s(s(z))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[11982, 16633])).
% 2.74/2.92 tff(16635,plain,
% 2.74/2.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 2.74/2.92 inference(rewrite,[status(thm)],[])).
% 2.74/2.92 tff(16636,plain,
% 2.74/2.92 (((~b(z, s(elem!1))) | (~b(s(s(s(z))), z)) | (~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(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 2.74/2.92 inference(rewrite,[status(thm)],[])).
% 2.74/2.92 tff(16637,plain,
% 2.74/2.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z)))))))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[16636])).
% 2.74/2.92 tff(16638,plain,
% 2.74/2.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 2.74/2.92 inference(transitivity,[status(thm)],[16637, 16635])).
% 2.74/2.92 tff(16639,plain,
% 2.74/2.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(elem!1))))),
% 2.74/2.92 inference(quant_inst,[status(thm)],[])).
% 2.74/2.92 tff(16640,plain,
% 2.74/2.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z)))))),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[16639, 16638])).
% 2.74/2.92 tff(16641,plain,
% 2.74/2.92 ($false),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[16640, 306, 817, 1531, 859, 2455])).
% 2.74/2.92 tff(16642,plain,((~b(s(elem!1), s(s(s(z))))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.92 tff(16643,plain,
% 2.74/2.92 (~b(s(elem!1), s(s(s(z))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[16642, 16634, 7919, 16632])).
% 2.74/2.92 tff(16644,plain,
% 2.74/2.92 ($false),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[2367, 43, 16643, 16627, 16623])).
% 2.74/2.92 tff(16645,plain,(b(s(s(s(z))), elem!1) | (~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~r(z, elem!1)) | b(elem!1, s(s(s(z)))) | (~b(s(s(elem!1)), elem!1)) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.92 tff(16646,plain,
% 2.74/2.92 (b(s(s(s(z))), elem!1)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[16645, 16519, 10451, 10425, 3, 16518, 16517])).
% 2.74/2.92 tff(16647,plain,
% 2.74/2.92 (~r(s(z), elem!1)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[14510, 16519, 10425, 13303])).
% 2.74/2.92 tff(16648,plain,
% 2.74/2.92 (b(s(z), elem!1)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[16180, 16647])).
% 2.74/2.92 tff(16649,plain,
% 2.74/2.92 ((~b(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[7970, 15960, 15980])).
% 2.74/2.92 tff(16650,plain,
% 2.74/2.92 (~r(s(s(s(z))), s(z))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[16649, 16646, 16518, 16648])).
% 2.74/2.92 tff(16651,plain,
% 2.74/2.92 (b(s(s(s(z))), s(z))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[113, 16650])).
% 2.74/2.92 tff(16652,plain,
% 2.74/2.92 ($false),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[7567, 306, 16651, 16648, 16646, 15960])).
% 2.74/2.92 tff(16653,plain,(b(elem!1, s(s(s(z)))) | b(elem!1, z) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.92 tff(16654,plain,
% 2.74/2.92 (r(s(s(elem!1)), elem!1)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[16653, 2, 3])).
% 2.74/2.92 tff(16655,plain,
% 2.74/2.92 (~(elem!1 = z)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[10449, 16449])).
% 2.74/2.92 tff(16656,plain,
% 2.74/2.92 (~(z = elem!1)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[1618, 16655])).
% 2.74/2.92 tff(16657,plain,
% 2.74/2.92 (~r(z, s(s(elem!1)))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[5837, 16654, 16449])).
% 2.74/2.92 tff(16658,plain,
% 2.74/2.92 (b(z, s(s(elem!1)))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[460, 16657])).
% 2.74/2.92 tff(16659,plain,
% 2.74/2.92 (r(elem!1, z)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[174, 2, 16655])).
% 2.74/2.92 tff(16660,plain,
% 2.74/2.92 (~r(s(s(elem!1)), z)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[7786, 16659, 16654])).
% 2.74/2.92 tff(16661,plain,
% 2.74/2.92 (b(s(s(elem!1)), z)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[476, 16660])).
% 2.74/2.92 tff(16662,plain,
% 2.74/2.92 (~(s(elem!1) = elem!1)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[180, 16513])).
% 2.74/2.92 tff(16663,plain,
% 2.74/2.92 (~(s(s(elem!1)) = s(elem!1))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[195, 16662])).
% 2.74/2.92 tff(16664,plain,
% 2.74/2.92 (~r(s(elem!1), elem!1)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[10562, 16663, 16449, 16654, 16661, 16658])).
% 2.74/2.92 tff(16665,plain,
% 2.74/2.92 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[7090, 16664, 16656, 16513])).
% 2.74/2.92 tff(16666,plain,
% 2.74/2.92 (~r(s(s(s(elem!1))), elem!1)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[7780, 16665, 16654])).
% 2.74/2.92 tff(16667,plain,
% 2.74/2.92 (~(elem!1 = s(elem!1))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[364, 16662])).
% 2.74/2.92 tff(16668,plain,
% 2.74/2.92 (b(s(elem!1), elem!1)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[813, 16664, 16662])).
% 2.74/2.92 tff(16669,plain,
% 2.74/2.92 (~r(s(z), elem!1)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[8838, 16659, 16449, 16654])).
% 2.74/2.92 tff(16670,plain,
% 2.74/2.92 (b(s(z), elem!1)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[16180, 16669])).
% 2.74/2.92 tff(16671,plain,
% 2.74/2.92 ((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z)))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[5422, 15960])).
% 2.74/2.92 tff(16672,plain,
% 2.74/2.92 (~b(s(elem!1), s(z))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[16671, 16668, 16670])).
% 2.74/2.92 tff(16673,plain,
% 2.74/2.92 (b(s(s(s(elem!1))), s(elem!1)) | b(s(elem!1), s(z)) | (z = elem!1) | (~b(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | b(s(s(s(z))), elem!1) | (s(s(s(elem!1))) = s(elem!1))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[11573, 15978])).
% 2.74/2.92 tff(16674,plain,
% 2.74/2.92 (b(s(s(s(elem!1))), s(elem!1))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[16673, 16672, 16654, 16656, 1, 16668, 16665, 16514])).
% 2.74/2.92 tff(16675,plain,
% 2.74/2.92 (s(s(s(elem!1))) = elem!1),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[7812, 16674, 16654, 16659, 16668, 16667, 16666, 16515])).
% 2.74/2.92 tff(16676,plain,
% 2.74/2.92 (elem!1 = s(s(s(elem!1)))),
% 2.74/2.92 inference(symmetry,[status(thm)],[16675])).
% 2.74/2.92 tff(16677,plain,
% 2.74/2.92 (~(s(elem!1) = s(z))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[2689, 16656])).
% 2.74/2.92 tff(16678,plain,
% 2.74/2.92 (~(s(s(s(z))) = elem!1)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[4105, 16675, 16677])).
% 2.74/2.92 tff(16679,plain,
% 2.74/2.92 (~(elem!1 = s(s(s(z))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[4555, 16678])).
% 2.74/2.92 tff(16680,plain,
% 2.74/2.92 (r(elem!1, s(s(s(z))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[2304, 16679, 3])).
% 2.74/2.92 tff(16681,plain,
% 2.74/2.92 (~r(z, s(s(s(z))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[3392, 16680, 16659])).
% 2.74/2.92 tff(16682,plain,
% 2.74/2.92 (b(z, s(s(s(z))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[11982, 16681])).
% 2.74/2.92 tff(16683,plain,
% 2.74/2.92 (b(s(s(elem!1)), elem!1)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[12776, 16672, 16656, 16514, 16664, 1])).
% 2.74/2.92 tff(16684,plain,
% 2.74/2.92 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[16563, 16683, 3, 1, 16449, 16659, 16670])).
% 2.74/2.92 tff(16685,plain,
% 2.74/2.92 (r(s(s(s(z))), elem!1)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[1489, 16678, 1])).
% 2.74/2.92 tff(16686,plain,
% 2.74/2.92 (~r(s(s(s(z))), z)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[6831, 16685, 16449])).
% 2.74/2.92 tff(16687,plain,
% 2.74/2.92 (b(s(s(s(z))), z)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[2197, 16686])).
% 2.74/2.92 tff(16688,plain,
% 2.74/2.92 (s(s(s(s(z)))) = elem!1),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[16470, 16687, 16449, 1, 16684, 16682, 16678])).
% 2.74/2.92 tff(16689,plain,
% 2.74/2.92 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 2.74/2.92 inference(transitivity,[status(thm)],[16688, 16676])).
% 2.74/2.92 tff(16690,plain,
% 2.74/2.92 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(elem!1))))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[16689])).
% 2.74/2.92 tff(16691,plain,
% 2.74/2.92 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(z)))))),
% 2.74/2.92 inference(symmetry,[status(thm)],[16690])).
% 2.74/2.92 tff(16692,plain,
% 2.74/2.92 (s(s(elem!1)) = s(s(s(z)))),
% 2.74/2.92 inference(transitivity,[status(thm)],[140, 16691, 320])).
% 2.74/2.92 tff(16693,plain,
% 2.74/2.92 ($false),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[16439, 16692])).
% 2.74/2.92 tff(16694,plain,(b(elem!1, z) | b(s(s(s(z))), elem!1) | b(elem!1, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.92 tff(16695,plain,
% 2.74/2.92 (b(elem!1, z)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[16694, 1, 3])).
% 2.74/2.92 tff(16696,plain,
% 2.74/2.92 (~(elem!1 = s(elem!1))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[15072, 1484, 1, 16439])).
% 2.74/2.92 tff(16697,plain,
% 2.74/2.92 (~(s(elem!1) = elem!1)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[2571, 16696])).
% 2.74/2.92 tff(16698,plain,
% 2.74/2.92 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[15967])).
% 2.74/2.92 tff(16699,plain,
% 2.74/2.92 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(elem!1)), elem!1)),
% 2.74/2.92 inference(monotonicity,[status(thm)],[16698, 15966])).
% 2.74/2.92 tff(16700,plain,
% 2.74/2.92 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.74/2.92 inference(symmetry,[status(thm)],[16699])).
% 2.74/2.92 tff(16701,plain,
% 2.74/2.92 (elem!1 = s(s(s(z)))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[12937, 15966])).
% 2.74/2.92 tff(16702,plain,
% 2.74/2.92 (~(s(s(elem!1)) = elem!1)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[16106, 16701])).
% 2.74/2.92 tff(16703,plain,
% 2.74/2.92 (b(s(s(elem!1)), elem!1)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[47, 16702, 6])).
% 2.74/2.92 tff(16704,plain,
% 2.74/2.92 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[16703, 16700])).
% 2.74/2.92 tff(16705,plain,
% 2.74/2.92 (b(s(s(s(z))), z) <=> b(elem!1, z)),
% 2.74/2.92 inference(monotonicity,[status(thm)],[15966])).
% 2.74/2.92 tff(16706,plain,
% 2.74/2.92 (b(elem!1, z) <=> b(s(s(s(z))), z)),
% 2.74/2.92 inference(symmetry,[status(thm)],[16705])).
% 2.74/2.92 tff(16707,plain,
% 2.74/2.92 (b(s(s(s(z))), z)),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[16695, 16706])).
% 2.74/2.92 tff(16708,plain,
% 2.74/2.92 (b(s(elem!1), s(s(s(z)))) <=> b(s(elem!1), elem!1)),
% 2.74/2.92 inference(monotonicity,[status(thm)],[1430])).
% 2.74/2.92 tff(16709,plain,
% 2.74/2.92 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(z))))),
% 2.74/2.92 inference(symmetry,[status(thm)],[16708])).
% 2.74/2.92 tff(16710,plain,
% 2.74/2.92 (~r(s(elem!1), elem!1)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[14510, 4, 374, 13994])).
% 2.74/2.92 tff(16711,plain,
% 2.74/2.92 (b(s(elem!1), elem!1)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[813, 16710, 193])).
% 2.74/2.92 tff(16712,plain,
% 2.74/2.92 (b(s(elem!1), s(s(s(z))))),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[16711, 16709])).
% 2.74/2.92 tff(16713,plain,
% 2.74/2.92 (b(s(s(s(z))), s(z))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[15976, 1430])).
% 2.74/2.92 tff(16714,plain,
% 2.74/2.92 (elem!1 = s(s(s(z)))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[12937, 1430])).
% 2.74/2.92 tff(16715,plain,
% 2.74/2.92 (~(s(s(elem!1)) = elem!1)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[16106, 16714])).
% 2.74/2.92 tff(16716,plain,
% 2.74/2.92 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[7090, 16710, 13980, 16715])).
% 2.74/2.92 tff(16717,plain,
% 2.74/2.92 (b(s(s(s(s(s(s(z)))))), s(s(s(z)))) <=> b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.74/2.92 inference(monotonicity,[status(thm)],[1430])).
% 2.74/2.92 tff(16718,plain,
% 2.74/2.92 (b(s(s(s(s(s(s(z)))))), elem!1) <=> b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.74/2.92 inference(symmetry,[status(thm)],[16717])).
% 2.74/2.92 tff(16719,plain,
% 2.74/2.92 (elem!1 = s(s(s(z)))),
% 2.74/2.92 inference(symmetry,[status(thm)],[1430])).
% 2.74/2.92 tff(16720,plain,
% 2.74/2.92 ((s(s(s(s(s(s(z)))))) = elem!1) <=> (s(s(s(s(s(s(z)))))) = s(s(s(z))))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[16719])).
% 2.74/2.92 tff(16721,plain,
% 2.74/2.92 ((s(s(s(s(s(s(z)))))) = elem!1) <=> (s(s(s(z))) = s(s(s(s(s(s(z)))))))),
% 2.74/2.92 inference(transitivity,[status(thm)],[16720, 1122])).
% 2.74/2.92 tff(16722,plain,
% 2.74/2.92 ((s(s(s(z))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = elem!1)),
% 2.74/2.92 inference(symmetry,[status(thm)],[16721])).
% 2.74/2.92 tff(16723,plain,
% 2.74/2.92 ((~(s(s(s(z))) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(s(s(s(s(z)))))) = elem!1))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[16722])).
% 2.74/2.92 tff(16724,plain,
% 2.74/2.92 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[556, 16723])).
% 2.74/2.92 tff(16725,plain,
% 2.74/2.92 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[7186, 16489, 374, 4])).
% 2.74/2.92 tff(16726,plain,
% 2.74/2.92 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[1144, 16725, 16724])).
% 2.74/2.92 tff(16727,plain,
% 2.74/2.92 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[16726, 16718])).
% 2.74/2.92 tff(16728,plain,
% 2.74/2.92 (~(s(s(s(elem!1))) = elem!1)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[4105, 1430, 13994])).
% 2.74/2.92 tff(16729,plain,
% 2.74/2.92 (~(s(s(elem!1)) = s(elem!1))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[1564, 16728])).
% 2.74/2.92 tff(16730,plain,
% 2.74/2.92 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[143, 16715])).
% 2.74/2.92 tff(16731,plain,
% 2.74/2.92 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(z)))), elem!1)),
% 2.74/2.92 inference(monotonicity,[status(thm)],[1430])).
% 2.74/2.92 tff(16732,plain,
% 2.74/2.92 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/2.92 inference(symmetry,[status(thm)],[16731])).
% 2.74/2.92 tff(16733,plain,
% 2.74/2.92 (r(s(s(s(s(z)))), elem!1) <=> r(s(elem!1), elem!1)),
% 2.74/2.92 inference(monotonicity,[status(thm)],[1437])).
% 2.74/2.92 tff(16734,plain,
% 2.74/2.92 (r(s(elem!1), elem!1) <=> r(s(s(s(s(z)))), elem!1)),
% 2.74/2.92 inference(symmetry,[status(thm)],[16733])).
% 2.74/2.92 tff(16735,plain,
% 2.74/2.92 (r(s(elem!1), elem!1) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/2.92 inference(transitivity,[status(thm)],[16734, 16732])).
% 2.74/2.92 tff(16736,plain,
% 2.74/2.92 ((~r(s(elem!1), elem!1)) <=> (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[16735])).
% 2.74/2.92 tff(16737,plain,
% 2.74/2.92 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[16710, 16736])).
% 2.74/2.92 tff(16738,plain,
% 2.74/2.92 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[4471, 16737])).
% 2.74/2.92 tff(16739,plain,
% 2.74/2.92 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[11125, 16738, 16714, 245, 16730, 16729, 16727, 16716])).
% 2.74/2.92 tff(16740,plain,
% 2.74/2.92 (r(elem!1, s(elem!1))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[11127, 16739, 16714])).
% 2.74/2.92 tff(16741,plain,
% 2.74/2.92 (~r(z, s(elem!1))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[5668, 16740, 374])).
% 2.74/2.92 tff(16742,plain,
% 2.74/2.92 (b(z, s(elem!1))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[275, 16741])).
% 2.74/2.92 tff(16743,plain,
% 2.74/2.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)))),
% 2.74/2.92 inference(rewrite,[status(thm)],[])).
% 2.74/2.92 tff(16744,plain,
% 2.74/2.92 (((~b(s(elem!1), s(s(s(z))))) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(z, s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)))),
% 2.74/2.92 inference(rewrite,[status(thm)],[])).
% 2.74/2.92 tff(16745,plain,
% 2.74/2.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z))))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[16744])).
% 2.74/2.93 tff(16746,plain,
% 2.74/2.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)))),
% 2.74/2.93 inference(transitivity,[status(thm)],[16745, 16743])).
% 2.74/2.93 tff(16747,plain,
% 2.74/2.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 2.74/2.93 inference(quant_inst,[status(thm)],[])).
% 2.74/2.93 tff(16748,plain,
% 2.74/2.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[16747, 16746])).
% 2.74/2.93 tff(16749,plain,
% 2.74/2.93 ($false),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[16748, 306, 817, 2284, 1531, 2455, 247])).
% 2.74/2.93 tff(16750,plain,((~b(s(elem!1), s(s(s(z))))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.93 tff(16751,plain,
% 2.74/2.93 (~b(s(elem!1), s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[16750, 16742, 16713, 1531, 16489])).
% 2.74/2.93 tff(16752,plain,
% 2.74/2.93 ($false),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[16751, 16712])).
% 2.74/2.93 tff(16753,plain,((~r(s(z), elem!1)) | (~(s(s(s(z))) = elem!1)) | (~b(s(s(s(z))), z)) | (~r(z, elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (s(elem!1) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.93 tff(16754,plain,
% 2.74/2.93 (~r(s(z), elem!1)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[16753, 15966, 16707, 16449, 16704, 16697])).
% 2.74/2.93 tff(16755,plain,
% 2.74/2.93 (b(s(z), elem!1)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[16180, 16754])).
% 2.74/2.93 tff(16756,plain,
% 2.74/2.93 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[143, 16702])).
% 2.74/2.93 tff(16757,plain,
% 2.74/2.93 (s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[16698])).
% 2.74/2.93 tff(16758,plain,
% 2.74/2.93 (s(s(s(elem!1))) = s(s(s(s(s(s(z))))))),
% 2.74/2.93 inference(symmetry,[status(thm)],[16757])).
% 2.74/2.93 tff(16759,plain,
% 2.74/2.93 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.74/2.93 inference(monotonicity,[status(thm)],[16758])).
% 2.74/2.93 tff(16760,plain,
% 2.74/2.93 (~(s(s(s(elem!1))) = elem!1)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[4105, 15966, 16677])).
% 2.74/2.93 tff(16761,plain,
% 2.74/2.93 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[152, 16756])).
% 2.74/2.93 tff(16762,plain,
% 2.74/2.93 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[159, 16761])).
% 2.74/2.93 tff(16763,plain,
% 2.74/2.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(16764,plain,
% 2.74/2.93 (((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(16765,plain,
% 2.74/2.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z)))))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[16764])).
% 2.74/2.93 tff(16766,plain,
% 2.74/2.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))))),
% 2.74/2.93 inference(transitivity,[status(thm)],[16765, 16763])).
% 2.74/2.93 tff(16767,plain,
% 2.74/2.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))))),
% 2.74/2.93 inference(quant_inst,[status(thm)],[])).
% 2.74/2.93 tff(16768,plain,
% 2.74/2.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z)))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[16767, 16766])).
% 2.74/2.93 tff(16769,plain,
% 2.74/2.93 (~b(s(z), s(s(elem!1)))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[16768, 306, 30, 2831, 15960])).
% 2.74/2.93 tff(16770,plain,
% 2.74/2.93 (r(s(z), s(s(elem!1)))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[3997, 43, 16769, 79])).
% 2.74/2.93 tff(16771,plain,
% 2.74/2.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(16772,plain,
% 2.74/2.93 (((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(16773,plain,
% 2.74/2.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[16772])).
% 2.74/2.93 tff(16774,plain,
% 2.74/2.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 2.74/2.93 inference(transitivity,[status(thm)],[16773, 16771])).
% 2.74/2.93 tff(16775,plain,
% 2.74/2.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 2.74/2.93 inference(quant_inst,[status(thm)],[])).
% 2.74/2.93 tff(16776,plain,
% 2.74/2.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[16775, 16774])).
% 2.74/2.93 tff(16777,plain,
% 2.74/2.93 (~b(s(z), s(s(s(elem!1))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[16776, 306, 1664, 2831, 15960])).
% 2.74/2.93 tff(16778,plain,
% 2.74/2.93 (r(s(z), s(s(s(elem!1))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[3017, 43, 645, 16777])).
% 2.74/2.93 tff(16779,plain,
% 2.74/2.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(16780,plain,
% 2.74/2.93 (((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(16781,plain,
% 2.74/2.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z)))))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[16780])).
% 2.74/2.93 tff(16782,plain,
% 2.74/2.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))))),
% 2.74/2.93 inference(transitivity,[status(thm)],[16781, 16779])).
% 2.74/2.93 tff(16783,plain,
% 2.74/2.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.74/2.93 inference(quant_inst,[status(thm)],[])).
% 2.74/2.93 tff(16784,plain,
% 2.74/2.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z)))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[16783, 16782])).
% 2.74/2.93 tff(16785,plain,
% 2.74/2.93 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[16784, 306, 30, 1664, 2831, 15960])).
% 2.74/2.93 tff(16786,plain,
% 2.74/2.93 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[610, 16785, 739])).
% 2.74/2.93 tff(16787,plain,
% 2.74/2.93 ($false),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[11437, 124, 16786, 16778, 16770])).
% 2.74/2.93 tff(16788,plain,((~b(s(s(s(elem!1))), elem!1)) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.93 tff(16789,plain,
% 2.74/2.93 (~b(s(s(s(elem!1))), elem!1)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[16788, 16762, 16755, 16703])).
% 2.74/2.93 tff(16790,plain,
% 2.74/2.93 (r(s(s(s(elem!1))), elem!1)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[1636, 16789, 16760])).
% 2.74/2.93 tff(16791,plain,
% 2.74/2.93 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[16790, 16759])).
% 2.74/2.93 tff(16792,plain,
% 2.74/2.93 (~r(s(elem!1), elem!1)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[16593, 16791, 3, 1, 16449, 16756])).
% 2.74/2.93 tff(16793,plain,
% 2.74/2.93 (b(s(elem!1), elem!1)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[813, 16792, 16697])).
% 2.74/2.93 tff(16794,plain,
% 2.74/2.93 (~b(s(elem!1), s(z))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[16671, 16793, 16755])).
% 2.74/2.93 tff(16795,plain,
% 2.74/2.93 (r(s(elem!1), s(z))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[2964, 16794, 16677])).
% 2.74/2.93 tff(16796,plain,
% 2.74/2.93 (b(s(elem!1), s(s(s(z)))) <=> b(s(elem!1), elem!1)),
% 2.74/2.93 inference(monotonicity,[status(thm)],[15966])).
% 2.74/2.93 tff(16797,plain,
% 2.74/2.93 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(z))))),
% 2.74/2.93 inference(symmetry,[status(thm)],[16796])).
% 2.74/2.93 tff(16798,plain,
% 2.74/2.93 (b(s(elem!1), s(s(s(z))))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[16793, 16797])).
% 2.74/2.93 tff(16799,plain,
% 2.74/2.93 (~r(z, s(s(s(elem!1))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[6199, 124, 16449, 16790])).
% 2.74/2.93 tff(16800,plain,
% 2.74/2.93 (b(z, s(s(s(elem!1))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[585, 16799])).
% 2.74/2.93 tff(16801,plain,
% 2.74/2.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(16802,plain,
% 2.74/2.93 (((~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(16803,plain,
% 2.74/2.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[16802])).
% 2.74/2.93 tff(16804,plain,
% 2.74/2.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.74/2.93 inference(transitivity,[status(thm)],[16803, 16801])).
% 2.74/2.93 tff(16805,plain,
% 2.74/2.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.74/2.93 inference(quant_inst,[status(thm)],[])).
% 2.74/2.93 tff(16806,plain,
% 2.74/2.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[16805, 16804])).
% 2.74/2.93 tff(16807,plain,
% 2.74/2.93 (~b(s(s(elem!1)), s(elem!1))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[16806, 306, 16695, 16703, 16800, 16793])).
% 2.74/2.93 tff(16808,plain,
% 2.74/2.93 (r(elem!1, s(elem!1))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[7449, 16807, 6, 16697, 16677, 16755, 16792])).
% 2.74/2.93 tff(16809,plain,
% 2.74/2.93 (~r(z, s(elem!1))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[5668, 16808, 16449])).
% 2.74/2.93 tff(16810,plain,
% 2.74/2.93 (b(z, s(elem!1))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[275, 16809])).
% 2.74/2.93 tff(16811,plain,
% 2.74/2.93 (~b(s(z), z)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[16750, 16810, 15977, 16707, 16798])).
% 2.74/2.93 tff(16812,plain,
% 2.74/2.93 (r(s(z), z)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[221, 16811])).
% 2.74/2.93 tff(16813,plain,
% 2.74/2.93 (~(elem!1 = s(s(s(elem!1))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[1641, 16760])).
% 2.74/2.93 tff(16814,plain,
% 2.74/2.93 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(16815,plain,
% 2.74/2.93 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)))),
% 2.74/2.93 inference(quant_inst,[status(thm)],[])).
% 2.74/2.93 tff(16816,plain,
% 2.74/2.93 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[16815, 16814])).
% 2.74/2.93 tff(16817,plain,
% 2.74/2.93 (~r(s(s(s(elem!1))), z)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[16816, 124, 16449, 16790])).
% 2.74/2.93 tff(16818,plain,
% 2.74/2.93 (b(s(s(s(elem!1))), z)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[3033, 43, 579, 16817])).
% 2.74/2.93 tff(16819,plain,
% 2.74/2.93 (((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(16820,plain,
% 2.74/2.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[16819])).
% 2.74/2.93 tff(16821,plain,
% 2.74/2.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 2.74/2.93 inference(transitivity,[status(thm)],[16820, 11509])).
% 2.74/2.93 tff(16822,plain,
% 2.74/2.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))))),
% 2.74/2.93 inference(quant_inst,[status(thm)],[])).
% 2.74/2.93 tff(16823,plain,
% 2.74/2.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[16822, 16821])).
% 2.74/2.93 tff(16824,plain,
% 2.74/2.93 (~b(elem!1, s(s(s(elem!1))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[16823, 306, 16695, 16800, 16818])).
% 2.74/2.93 tff(16825,plain,
% 2.74/2.93 (r(elem!1, s(s(s(elem!1))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[3284, 16824, 16813])).
% 2.74/2.93 tff(16826,plain,
% 2.74/2.93 (~b(s(elem!1), z)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[6042, 16810, 16449, 16756, 16825, 16808])).
% 2.74/2.93 tff(16827,plain,
% 2.74/2.93 (r(s(elem!1), z)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[2380, 16826])).
% 2.74/2.93 tff(16828,plain,
% 2.74/2.93 ($false),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[2634, 16827, 16812, 16795])).
% 2.74/2.93 tff(16829,plain,(r(s(s(s(z))), elem!1) | r(s(s(elem!1)), elem!1) | b(elem!1, s(s(s(z)))) | b(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.93 tff(16830,plain,
% 2.74/2.93 (r(s(s(s(z))), elem!1)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[16829, 6, 3, 1])).
% 2.74/2.93 tff(16831,plain,
% 2.74/2.93 (b(z, s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[11982, 14176])).
% 2.74/2.93 tff(16832,plain,
% 2.74/2.93 (~b(s(z), s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[7148, 16461, 374, 1, 2715])).
% 2.74/2.93 tff(16833,plain,
% 2.74/2.93 (~r(s(z), s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[3790, 16461, 2859])).
% 2.74/2.93 tff(16834,plain,
% 2.74/2.93 ($false),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[3302, 16833, 16832])).
% 2.74/2.93 tff(16835,plain,(b(s(z), elem!1) | (~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | b(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.93 tff(16836,plain,
% 2.74/2.93 (b(s(z), elem!1)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[16835, 2859, 374, 1])).
% 2.74/2.93 tff(16837,plain,
% 2.74/2.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(s(z))))))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(16838,plain,
% 2.74/2.93 (((~b(z, s(s(s(z))))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(s(z))))))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(16839,plain,
% 2.74/2.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(s(z)))))))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[16838])).
% 2.74/2.94 tff(16840,plain,
% 2.74/2.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(s(z))))))),
% 2.74/2.94 inference(transitivity,[status(thm)],[16839, 16837])).
% 2.74/2.94 tff(16841,plain,
% 2.74/2.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~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))))),
% 2.74/2.94 inference(quant_inst,[status(thm)],[])).
% 2.74/2.94 tff(16842,plain,
% 2.74/2.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(s(z)))))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[16841, 16840])).
% 2.74/2.94 tff(16843,plain,
% 2.74/2.94 (~b(s(s(elem!1)), s(elem!1))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[16842, 306, 4012, 30, 14729, 859])).
% 2.74/2.94 tff(16844,plain,
% 2.74/2.94 (r(elem!1, s(elem!1))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[7449, 16843, 6, 193, 2249, 2831, 808])).
% 2.74/2.94 tff(16845,plain,
% 2.74/2.94 (r(s(s(elem!1)), s(elem!1))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[994, 16843, 392])).
% 2.74/2.94 tff(16846,plain,
% 2.74/2.94 (~r(elem!1, s(s(elem!1)))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[1238, 16845, 16844])).
% 2.74/2.94 tff(16847,plain,
% 2.74/2.94 (b(elem!1, s(s(elem!1)))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[516, 16846, 360])).
% 2.74/2.94 tff(16848,plain,
% 2.74/2.94 (~r(s(elem!1), s(s(elem!1)))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[6427, 16847, 14729, 2249, 2831, 30])).
% 2.74/2.94 tff(16849,plain,
% 2.74/2.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(s(z))))))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(16850,plain,
% 2.74/2.94 (((~b(z, s(s(s(z))))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(s(z))))))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(16851,plain,
% 2.74/2.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(s(z)))))))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[16850])).
% 2.74/2.94 tff(16852,plain,
% 2.74/2.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(s(z))))))),
% 2.74/2.94 inference(transitivity,[status(thm)],[16851, 16849])).
% 2.74/2.94 tff(16853,plain,
% 2.74/2.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 2.74/2.94 inference(quant_inst,[status(thm)],[])).
% 2.74/2.94 tff(16854,plain,
% 2.74/2.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(s(z)))))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[16853, 16852])).
% 2.74/2.94 tff(16855,plain,
% 2.74/2.94 (~b(s(elem!1), s(s(elem!1)))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[16854, 306, 4012, 30, 14729, 859])).
% 2.74/2.94 tff(16856,plain,
% 2.74/2.94 ($false),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[1684, 43, 16855, 16848, 8841])).
% 2.74/2.94 tff(16857,plain,(r(s(elem!1), elem!1) | (s(elem!1) = s(z)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (elem!1 = s(s(elem!1))) | r(s(s(elem!1)), elem!1) | (s(elem!1) = elem!1) | (~b(elem!1, z)) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.94 tff(16858,plain,
% 2.74/2.94 (r(s(elem!1), elem!1)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[16857, 92, 16836, 13994, 187, 6, 181, 4012, 16831])).
% 2.74/2.94 tff(16859,plain,
% 2.74/2.94 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(16860,plain,
% 2.74/2.94 (((~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(z)))))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(16861,plain,
% 2.74/2.94 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z)))))))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[16860])).
% 2.74/2.94 tff(16862,plain,
% 2.74/2.94 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))))),
% 2.74/2.94 inference(transitivity,[status(thm)],[16861, 16859])).
% 2.74/2.94 tff(16863,plain,
% 2.74/2.94 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(z))))))),
% 2.74/2.94 inference(quant_inst,[status(thm)],[])).
% 2.74/2.94 tff(16864,plain,
% 2.74/2.94 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z)))))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[16863, 16862])).
% 2.74/2.94 tff(16865,plain,
% 2.74/2.94 (~r(s(elem!1), s(s(s(z))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[16864, 124, 16858, 2859])).
% 2.74/2.94 tff(16866,plain,
% 2.74/2.94 (~r(z, s(elem!1))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[7870, 124, 374, 16858])).
% 2.74/2.94 tff(16867,plain,
% 2.74/2.94 (b(z, s(elem!1))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[275, 16866])).
% 2.74/2.94 tff(16868,plain,
% 2.74/2.94 (~b(s(elem!1), s(s(s(z))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[16642, 16867, 16831, 7136])).
% 2.74/2.94 tff(16869,plain,
% 2.74/2.94 (s(elem!1) = s(s(s(z)))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[2367, 43, 16868, 16865])).
% 2.74/2.94 tff(16870,plain,
% 2.74/2.94 ((s(elem!1) = elem!1) <=> (s(s(s(z))) = elem!1)),
% 2.74/2.94 inference(monotonicity,[status(thm)],[16869])).
% 2.74/2.94 tff(16871,plain,
% 2.74/2.94 ((~(s(elem!1) = elem!1)) <=> (~(s(s(s(z))) = elem!1))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[16870])).
% 2.74/2.94 tff(16872,plain,
% 2.74/2.94 (~(s(s(s(z))) = elem!1)),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[181, 16871])).
% 2.74/2.94 tff(16873,plain,
% 2.74/2.94 (s(s(z)) = elem!1),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[5384, 16869])).
% 2.74/2.94 tff(16874,plain,
% 2.74/2.94 ((s(s(z)) = s(s(s(s(z))))) <=> (elem!1 = s(s(s(s(z)))))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[16873])).
% 2.74/2.94 tff(16875,plain,
% 2.74/2.94 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = elem!1)),
% 2.74/2.94 inference(transitivity,[status(thm)],[16874, 8778])).
% 2.74/2.94 tff(16876,plain,
% 2.74/2.94 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[16875])).
% 2.74/2.94 tff(16877,plain,
% 2.74/2.94 (~(s(s(s(s(z)))) = elem!1)),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[1612, 16876])).
% 2.74/2.94 tff(16878,plain,
% 2.74/2.94 ((s(s(z)) = s(s(s(s(s(s(z))))))) <=> (elem!1 = s(s(s(s(s(s(z)))))))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[16873])).
% 2.74/2.94 tff(16879,plain,
% 2.74/2.94 ((s(s(z)) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = elem!1)),
% 2.74/2.94 inference(transitivity,[status(thm)],[16878, 3891])).
% 2.74/2.94 tff(16880,plain,
% 2.74/2.94 ((~(s(s(z)) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(s(s(s(s(z)))))) = elem!1))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[16879])).
% 2.74/2.94 tff(16881,plain,
% 2.74/2.94 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[2826, 16880])).
% 2.74/2.94 tff(16882,plain,
% 2.74/2.94 ($false),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[16470, 16881, 16877, 374, 1, 16831, 16872, 7136])).
% 2.74/2.94 tff(16883,plain,((s(s(elem!1)) = elem!1) | (~r(z, elem!1)) | b(s(s(s(z))), elem!1) | (~r(s(s(s(z))), elem!1)) | r(s(s(elem!1)), elem!1) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.94 tff(16884,plain,
% 2.74/2.94 ($false),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[16883, 16830, 6, 1, 16449, 16476, 16695])).
% 2.74/2.94 tff(16885,plain,(r(s(s(elem!1)), elem!1) | b(s(s(s(z))), elem!1) | b(elem!1, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.94 tff(16886,plain,
% 2.74/2.94 (r(s(s(elem!1)), elem!1)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[16885, 1, 3])).
% 2.74/2.94 tff(16887,plain,
% 2.74/2.94 (~r(z, s(s(elem!1)))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[5837, 16886, 16449])).
% 2.74/2.94 tff(16888,plain,
% 2.74/2.94 (b(z, s(s(elem!1)))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[460, 16887])).
% 2.74/2.94 tff(16889,plain,
% 2.74/2.94 (~r(s(s(elem!1)), z)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[6539, 124, 16449, 16886])).
% 2.74/2.94 tff(16890,plain,
% 2.74/2.94 (b(s(s(elem!1)), z)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[476, 16889])).
% 2.74/2.94 tff(16891,plain,
% 2.74/2.94 (~r(s(elem!1), elem!1)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[10562, 16890, 16449, 16478, 16886, 16888])).
% 2.74/2.94 tff(16892,plain,
% 2.74/2.94 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[7090, 16891, 16656, 16476])).
% 2.74/2.94 tff(16893,plain,
% 2.74/2.94 (~r(s(s(s(elem!1))), elem!1)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[7780, 16892, 16886])).
% 2.74/2.94 tff(16894,plain,
% 2.74/2.94 (b(s(elem!1), elem!1)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[813, 16891, 16477])).
% 2.74/2.94 tff(16895,plain,
% 2.74/2.94 (~r(s(z), z)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[12117, 16461, 16449])).
% 2.74/2.94 tff(16896,plain,
% 2.74/2.94 (b(s(z), z)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[221, 16895])).
% 2.74/2.94 tff(16897,plain,
% 2.74/2.94 (~r(s(s(s(z))), elem!1)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[16835, 2715, 16449, 1])).
% 2.74/2.94 tff(16898,plain,
% 2.74/2.94 (r(s(s(elem!1)), elem!1)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[16829, 16897, 3, 1])).
% 2.74/2.94 tff(16899,plain,
% 2.74/2.94 (~r(z, s(s(elem!1)))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[5837, 16898, 16449])).
% 2.74/2.94 tff(16900,plain,
% 2.74/2.94 (b(z, s(s(elem!1)))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[460, 16899])).
% 2.74/2.94 tff(16901,plain,
% 2.74/2.94 (~r(s(elem!1), elem!1)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[14510, 16461, 16449, 16677])).
% 2.74/2.94 tff(16902,plain,
% 2.74/2.94 (b(s(elem!1), elem!1)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[813, 16901, 16477])).
% 2.74/2.94 tff(16903,plain,
% 2.74/2.94 (~(elem!1 = s(elem!1))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[364, 16477])).
% 2.74/2.94 tff(16904,plain,
% 2.74/2.94 (s(s(s(z))) = elem!1),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[16463, 2715, 1, 16449])).
% 2.74/2.94 tff(16905,plain,
% 2.74/2.94 (~(s(s(s(elem!1))) = elem!1)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[4105, 16904, 16677])).
% 2.74/2.94 tff(16906,plain,
% 2.74/2.94 (~(elem!1 = s(s(elem!1)))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[186, 16476])).
% 2.74/2.94 tff(16907,plain,
% 2.74/2.94 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[7090, 16901, 16656, 16476])).
% 2.74/2.94 tff(16908,plain,
% 2.74/2.94 (~r(s(s(elem!1)), s(elem!1))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[13111, 16898, 16695, 16907, 16906, 16905, 16479, 16903, 16902])).
% 2.74/2.94 tff(16909,plain,
% 2.74/2.94 (b(s(s(elem!1)), s(elem!1))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[994, 16908, 16478])).
% 2.74/2.94 tff(16910,plain,
% 2.74/2.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(z), z)))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(16911,plain,
% 2.74/2.94 (((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(z), z)))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(16912,plain,
% 2.74/2.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(z), z))))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[16911])).
% 2.74/2.94 tff(16913,plain,
% 2.74/2.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(z), z)))),
% 2.74/2.94 inference(transitivity,[status(thm)],[16912, 16910])).
% 2.74/2.94 tff(16914,plain,
% 2.74/2.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))),
% 2.74/2.94 inference(quant_inst,[status(thm)],[])).
% 2.74/2.94 tff(16915,plain,
% 2.74/2.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(z), z))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[16914, 16913])).
% 2.74/2.94 tff(16916,plain,
% 2.74/2.94 ($false),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[16915, 306, 4012, 1005, 1198, 4346, 247])).
% 2.74/2.94 tff(16917,plain,((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.94 tff(16918,plain,
% 2.74/2.94 ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), z))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[16917, 15960])).
% 2.74/2.94 tff(16919,plain,
% 2.74/2.94 ($false),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[16918, 16909, 16900, 16695, 16896])).
% 2.74/2.94 tff(16920,plain,(b(s(z), elem!1) | b(elem!1, s(s(s(z)))) | b(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.94 tff(16921,plain,
% 2.74/2.94 (b(s(z), elem!1)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[16920, 1, 3])).
% 2.74/2.94 tff(16922,plain,
% 2.74/2.94 (~b(s(elem!1), s(z))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[16671, 16894, 16921])).
% 2.74/2.94 tff(16923,plain,
% 2.74/2.94 (b(s(s(s(elem!1))), s(elem!1))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[16673, 16922, 16886, 16656, 1, 16894, 16892, 16479])).
% 2.74/2.94 tff(16924,plain,
% 2.74/2.94 ((~b(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (z = elem!1) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | b(s(s(s(z))), elem!1) | (~b(s(s(s(elem!1))), s(elem!1))) | r(s(s(s(elem!1))), elem!1) | (s(s(elem!1)) = s(s(s(elem!1))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[12759, 15978])).
% 2.74/2.94 tff(16925,plain,
% 2.74/2.94 (~b(s(s(elem!1)), s(elem!1))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[16924, 16923, 1, 16656, 16695, 16894, 16886, 16893, 16480])).
% 2.74/2.94 tff(16926,plain,
% 2.74/2.94 ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | b(s(elem!1), s(z)) | (z = elem!1) | (~b(s(elem!1), elem!1)) | b(s(s(s(z))), elem!1) | (~b(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (elem!1 = s(elem!1))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[12697, 15978])).
% 2.74/2.94 tff(16927,plain,
% 2.74/2.94 (~r(s(s(elem!1)), s(elem!1))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[16926, 16923, 1, 16656, 16886, 16894, 16922, 16892, 16903])).
% 2.74/2.94 tff(16928,plain,
% 2.74/2.94 ($false),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[994, 16927, 16925, 16478])).
% 2.74/2.94 tff(16929,plain,(b(s(s(s(z))), elem!1) | b(elem!1, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.94 tff(16930,plain,
% 2.74/2.94 (b(s(s(s(z))), elem!1)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[16929, 3])).
% 2.74/2.94 tff(16931,plain,
% 2.74/2.94 (~r(s(z), z)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[1049, 246, 16461])).
% 2.74/2.94 tff(16932,plain,
% 2.74/2.94 (~b(s(z), z)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[10847, 246, 2715, 3, 8, 2])).
% 2.74/2.94 tff(16933,plain,
% 2.74/2.94 ($false),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[221, 16932, 16931])).
% 2.74/2.94 tff(16934,plain,((~r(elem!1, z)) | b(s(z), elem!1) | b(elem!1, s(s(s(z)))) | (~b(s(z), s(s(s(z))))) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.94 tff(16935,plain,
% 2.74/2.94 (~r(elem!1, z)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[16934, 8, 3, 2715, 2])).
% 2.74/2.94 tff(16936,plain,
% 2.74/2.94 (elem!1 = z),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[174, 16935, 2])).
% 2.74/2.94 tff(16937,plain,
% 2.74/2.94 (s(elem!1) = s(z)),
% 2.74/2.94 inference(monotonicity,[status(thm)],[16936])).
% 2.74/2.94 tff(16938,plain,
% 2.74/2.94 (s(s(elem!1)) = s(s(z))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[16937])).
% 2.74/2.94 tff(16939,plain,
% 2.74/2.94 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[16938])).
% 2.74/2.94 tff(16940,plain,
% 2.74/2.94 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(z)))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[16939, 16938])).
% 2.74/2.94 tff(16941,plain,
% 2.74/2.94 (~(elem!1 = s(s(elem!1)))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[15853, 16654])).
% 2.74/2.94 tff(16942,plain,
% 2.74/2.94 (~(s(s(elem!1)) = elem!1)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[1174, 16941])).
% 2.74/2.94 tff(16943,plain,
% 2.74/2.94 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[143, 16942])).
% 2.74/2.94 tff(16944,plain,
% 2.74/2.94 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[152, 16943])).
% 2.74/2.94 tff(16945,plain,
% 2.74/2.94 (~r(s(s(elem!1)), s(z))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[8826, 16461, 16654])).
% 2.74/2.94 tff(16946,plain,
% 2.74/2.94 (b(s(s(elem!1)), s(z))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[3989, 16945])).
% 2.74/2.94 tff(16947,plain,
% 2.74/2.94 (~r(s(z), s(s(elem!1)))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[13075, 16461, 16654])).
% 2.74/2.94 tff(16948,plain,
% 2.74/2.94 (b(s(z), s(s(elem!1)))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[3997, 43, 79, 16947])).
% 2.74/2.94 tff(16949,plain,
% 2.74/2.94 (~b(s(s(elem!1)), elem!1)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[7610, 306, 16948, 15960, 16946])).
% 2.74/2.94 tff(16950,plain,
% 2.74/2.94 (b(s(elem!1), z)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[2709, 1502, 816])).
% 2.74/2.94 tff(16951,plain,
% 2.74/2.94 ($false),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[2718, 16950, 1502, 2715])).
% 2.74/2.94 tff(16952,plain,((~(z = elem!1)) | b(s(z), elem!1) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.94 tff(16953,plain,
% 2.74/2.94 (~(z = elem!1)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[16952, 816, 2715])).
% 2.74/2.94 tff(16954,plain,
% 2.74/2.94 (~r(s(s(s(elem!1))), elem!1)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[16405, 16953, 16949, 16942])).
% 2.74/2.94 tff(16955,plain,
% 2.74/2.94 (~(s(elem!1) = elem!1)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[180, 16942])).
% 2.74/2.94 tff(16956,plain,
% 2.74/2.94 (~(elem!1 = s(elem!1))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[364, 16955])).
% 2.74/2.94 tff(16957,plain,
% 2.74/2.94 (~(elem!1 = z)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[2172, 16953])).
% 2.74/2.94 tff(16958,plain,
% 2.74/2.94 (r(elem!1, z)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[174, 16957, 2])).
% 2.74/2.94 tff(16959,plain,
% 2.74/2.94 (~(s(elem!1) = s(z))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[2689, 16953])).
% 2.74/2.94 tff(16960,plain,
% 2.74/2.94 (~b(s(z), s(s(s(z))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[16934, 16958, 3, 2715, 2])).
% 2.74/2.94 tff(16961,plain,
% 2.74/2.94 (r(s(z), s(s(s(z))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[3302, 16960])).
% 2.74/2.94 tff(16962,plain,
% 2.74/2.94 (~r(elem!1, s(s(s(z))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[3347, 16961, 16461])).
% 2.74/2.94 tff(16963,plain,
% 2.74/2.94 (elem!1 = s(s(s(z)))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[2304, 16962, 3])).
% 2.74/2.94 tff(16964,plain,
% 2.74/2.94 (s(s(s(z))) = elem!1),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[4555, 16963])).
% 2.74/2.94 tff(16965,plain,
% 2.74/2.94 (~(s(s(s(elem!1))) = elem!1)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[4105, 16964, 16959])).
% 2.74/2.94 tff(16966,plain,
% 2.74/2.94 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[7812, 16965, 16958, 16654, 816, 16956, 16954, 16944])).
% 2.74/2.94 tff(16967,plain,
% 2.74/2.94 (~r(s(z), z)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[1049, 16958, 16461])).
% 2.74/2.94 tff(16968,plain,
% 2.74/2.94 (b(s(z), z)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[221, 16967])).
% 2.74/2.94 tff(16969,plain,
% 2.74/2.94 (b(z, elem!1)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[835, 16953, 7])).
% 2.74/2.94 tff(16970,plain,
% 2.74/2.94 (b(s(s(s(elem!1))), elem!1)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[1636, 16965, 16954])).
% 2.74/2.94 tff(16971,plain,
% 2.74/2.94 ((~r(s(s(s(elem!1))), s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), elem!1))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[11398, 15960])).
% 2.74/2.94 tff(16972,plain,
% 2.74/2.94 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[16971, 16970, 816, 16969, 16968])).
% 2.74/2.94 tff(16973,plain,
% 2.74/2.94 ($false),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[664, 16972, 16966, 16943])).
% 2.74/2.94 tff(16974,plain,((~b(s(elem!1), elem!1)) | b(elem!1, s(s(s(z)))) | b(s(z), elem!1) | b(elem!1, z) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.94 tff(16975,plain,
% 2.74/2.94 (~b(s(elem!1), elem!1)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[16974, 2715, 3, 2, 7])).
% 2.74/2.94 tff(16976,plain,
% 2.74/2.94 (~b(elem!1, s(s(elem!1)))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[16004, 306, 16948, 15960, 16946])).
% 2.74/2.94 tff(16977,plain,
% 2.74/2.94 (z = elem!1),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[2172, 16936])).
% 2.74/2.94 tff(16978,plain,
% 2.74/2.94 (~b(z, s(s(elem!1)))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[2757, 16977, 16976])).
% 2.74/2.94 tff(16979,plain,
% 2.74/2.94 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[13850, 16978, 7, 16949, 16976, 16975, 16935])).
% 2.74/2.94 tff(16980,plain,
% 2.74/2.94 (b(s(s(s(z))), s(s(z)))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[16979, 16940])).
% 2.74/2.94 tff(16981,plain,
% 2.74/2.94 (s(s(z)) = s(s(elem!1))),
% 2.74/2.94 inference(symmetry,[status(thm)],[16938])).
% 2.74/2.94 tff(16982,plain,
% 2.74/2.94 (b(s(s(z)), s(z)) <=> b(s(s(elem!1)), s(z))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[16981])).
% 2.74/2.94 tff(16983,plain,
% 2.74/2.94 (b(s(s(elem!1)), s(z)) <=> b(s(s(z)), s(z))),
% 2.74/2.94 inference(symmetry,[status(thm)],[16982])).
% 2.74/2.94 tff(16984,plain,
% 2.74/2.94 (b(s(s(z)), s(z))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[16946, 16983])).
% 2.74/2.94 tff(16985,plain,
% 2.74/2.94 (b(s(z), s(s(z))) <=> b(s(z), s(s(elem!1)))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[16981])).
% 2.74/2.94 tff(16986,plain,
% 2.74/2.94 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(z)))),
% 2.74/2.94 inference(symmetry,[status(thm)],[16985])).
% 2.74/2.94 tff(16987,plain,
% 2.74/2.94 (b(s(z), s(s(z)))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[16948, 16986])).
% 2.74/2.94 tff(16988,plain,
% 2.74/2.94 (((~b(s(z), s(s(z)))) | (~b(s(s(z)), 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(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(16989,plain,
% 2.74/2.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z))))))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[16988])).
% 2.74/2.94 tff(16990,plain,
% 2.74/2.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.74/2.94 inference(transitivity,[status(thm)],[16989, 13997])).
% 2.74/2.94 tff(16991,plain,
% 2.74/2.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))),
% 2.74/2.94 inference(quant_inst,[status(thm)],[])).
% 2.74/2.94 tff(16992,plain,
% 2.74/2.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z))))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[16991, 16990])).
% 2.74/2.94 tff(16993,plain,
% 2.74/2.94 ($false),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[16992, 306, 8, 16987, 16984, 16980])).
% 2.74/2.94 tff(16994,plain,((~b(s(z), s(s(s(z))))) | r(z, elem!1) | b(elem!1, z) | b(elem!1, s(s(s(z)))) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.94 tff(16995,plain,
% 2.74/2.94 (~b(s(z), s(s(s(z))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[16994, 2715, 2, 3, 7])).
% 2.74/2.94 tff(16996,plain,
% 2.74/2.94 (r(s(z), s(s(s(z))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[3302, 16995])).
% 2.74/2.94 tff(16997,plain,
% 2.74/2.94 (~r(elem!1, s(s(s(z))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[3347, 16996, 16461])).
% 2.74/2.94 tff(16998,plain,
% 2.74/2.94 (elem!1 = s(s(s(z)))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[2304, 16997, 3])).
% 2.74/2.94 tff(16999,plain,
% 2.74/2.94 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(s(z))))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[16998])).
% 2.74/2.94 tff(17000,plain,
% 2.74/2.94 (b(s(s(s(z))), s(s(s(z)))) <=> b(s(s(s(z))), elem!1)),
% 2.74/2.94 inference(symmetry,[status(thm)],[16999])).
% 2.74/2.94 tff(17001,plain,
% 2.74/2.94 ((~b(s(s(s(z))), s(s(s(z))))) <=> (~b(s(s(s(z))), elem!1))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[17000])).
% 2.74/2.94 tff(17002,plain,
% 2.74/2.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(z))))))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(17003,plain,
% 2.74/2.94 (((~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(z)))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(z))))))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(17004,plain,
% 2.74/2.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(z)))))))),
% 2.74/2.95 inference(monotonicity,[status(thm)],[17003])).
% 2.74/2.95 tff(17005,plain,
% 2.74/2.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(z))))))),
% 2.74/2.95 inference(transitivity,[status(thm)],[17004, 17002])).
% 2.74/2.95 tff(17006,plain,
% 2.74/2.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(z))))))),
% 2.74/2.95 inference(quant_inst,[status(thm)],[])).
% 2.74/2.95 tff(17007,plain,
% 2.74/2.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(z)))))),
% 2.74/2.95 inference(modus_ponens,[status(thm)],[17006, 17005])).
% 2.74/2.95 tff(17008,plain,
% 2.74/2.95 (~b(s(s(s(z))), s(s(s(z))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[17007, 306, 16948, 16930, 15960])).
% 2.74/2.95 tff(17009,plain,
% 2.74/2.95 (~b(s(s(s(z))), elem!1)),
% 2.74/2.95 inference(modus_ponens,[status(thm)],[17008, 17001])).
% 2.74/2.95 tff(17010,plain,
% 2.74/2.95 ($false),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[16930, 17009])).
% 2.74/2.95 tff(17011,plain,(b(s(z), elem!1) | b(elem!1, s(s(s(z)))) | b(elem!1, z) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.95 tff(17012,plain,
% 2.74/2.95 (b(s(z), elem!1)),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[17011, 7, 2, 3])).
% 2.74/2.95 tff(17013,plain,
% 2.74/2.95 (~b(s(s(s(z))), s(z))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[7567, 306, 17012, 16930, 15960])).
% 2.74/2.95 tff(17014,plain,
% 2.74/2.95 (r(s(s(s(z))), s(z))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[113, 17013])).
% 2.74/2.95 tff(17015,plain,
% 2.74/2.95 (((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)))),
% 2.74/2.95 inference(rewrite,[status(thm)],[])).
% 2.74/2.95 tff(17016,plain,
% 2.74/2.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1))))),
% 2.74/2.95 inference(monotonicity,[status(thm)],[17015])).
% 2.74/2.95 tff(17017,plain,
% 2.74/2.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)))),
% 2.74/2.95 inference(transitivity,[status(thm)],[17016, 16505])).
% 2.74/2.95 tff(17018,plain,
% 2.74/2.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 2.74/2.95 inference(quant_inst,[status(thm)],[])).
% 2.74/2.95 tff(17019,plain,
% 2.74/2.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1))),
% 2.74/2.95 inference(modus_ponens,[status(thm)],[17018, 17017])).
% 2.74/2.95 tff(17020,plain,
% 2.74/2.95 (~b(s(z), s(s(s(z))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[17019, 306, 17012, 16930, 15960])).
% 2.74/2.95 tff(17021,plain,
% 2.74/2.95 (~(s(s(s(z))) = elem!1)),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[16191, 17020, 17012])).
% 2.74/2.95 tff(17022,plain,
% 2.74/2.95 (~(elem!1 = s(s(s(z))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[4555, 17021])).
% 2.74/2.95 tff(17023,plain,
% 2.74/2.95 (r(elem!1, s(s(s(z))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[2304, 17022, 3])).
% 2.74/2.95 tff(17024,plain,
% 2.74/2.95 (~r(z, s(s(s(z))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[3392, 5612, 3313])).
% 2.74/2.95 tff(17025,plain,
% 2.74/2.95 (b(z, s(s(s(z))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[11982, 17024])).
% 2.74/2.95 tff(17026,plain,
% 2.74/2.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))))),
% 2.74/2.95 inference(rewrite,[status(thm)],[])).
% 2.74/2.95 tff(17027,plain,
% 2.74/2.95 (((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z)))))) <=> ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))))),
% 2.74/2.95 inference(rewrite,[status(thm)],[])).
% 2.74/2.95 tff(17028,plain,
% 2.74/2.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z)))))))),
% 2.74/2.95 inference(monotonicity,[status(thm)],[17027])).
% 2.74/2.95 tff(17029,plain,
% 2.74/2.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))))),
% 2.74/2.95 inference(transitivity,[status(thm)],[17028, 17026])).
% 2.74/2.95 tff(17030,plain,
% 2.74/2.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))))),
% 2.74/2.95 inference(quant_inst,[status(thm)],[])).
% 2.74/2.95 tff(17031,plain,
% 2.74/2.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z)))))),
% 2.74/2.95 inference(modus_ponens,[status(thm)],[17030, 17029])).
% 2.74/2.95 tff(17032,plain,
% 2.74/2.95 ($false),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[17031, 306, 3105, 2831, 1967, 15960, 17025])).
% 2.74/2.95 tff(17033,plain,((z = elem!1) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | b(elem!1, z) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.95 tff(17034,plain,
% 2.74/2.95 (z = elem!1),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[17033, 17012, 16930, 17023, 2, 7])).
% 2.74/2.95 tff(17035,plain,
% 2.74/2.95 (s(z) = s(elem!1)),
% 2.74/2.95 inference(monotonicity,[status(thm)],[17034])).
% 2.74/2.95 tff(17036,plain,
% 2.74/2.95 (s(s(z)) = s(s(elem!1))),
% 2.74/2.95 inference(monotonicity,[status(thm)],[17035])).
% 2.74/2.95 tff(17037,plain,
% 2.74/2.95 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.74/2.95 inference(monotonicity,[status(thm)],[17036])).
% 2.74/2.95 tff(17038,plain,
% 2.74/2.95 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 2.74/2.95 inference(monotonicity,[status(thm)],[17037])).
% 2.74/2.95 tff(17039,plain,
% 2.74/2.95 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(elem!1)))), s(z))),
% 2.74/2.95 inference(monotonicity,[status(thm)],[17038])).
% 2.74/2.95 tff(17040,plain,
% 2.74/2.95 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 2.74/2.95 inference(symmetry,[status(thm)],[17039])).
% 2.74/2.95 tff(17041,plain,
% 2.74/2.95 (s(elem!1) = s(z)),
% 2.74/2.95 inference(symmetry,[status(thm)],[17035])).
% 2.74/2.95 tff(17042,plain,
% 2.74/2.95 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(s(s(s(s(elem!1)))), s(z))),
% 2.74/2.95 inference(monotonicity,[status(thm)],[17041])).
% 2.74/2.95 tff(17043,plain,
% 2.74/2.95 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(z))),
% 2.74/2.95 inference(transitivity,[status(thm)],[17042, 17040])).
% 2.74/2.95 tff(17044,plain,
% 2.74/2.95 ((~b(s(s(s(s(elem!1)))), s(elem!1))) <=> (~b(s(s(s(s(z)))), s(z)))),
% 2.74/2.95 inference(monotonicity,[status(thm)],[17043])).
% 2.74/2.95 tff(17045,plain,
% 2.74/2.95 (b(z, s(elem!1)) <=> b(elem!1, s(elem!1))),
% 2.74/2.95 inference(monotonicity,[status(thm)],[17034])).
% 2.74/2.95 tff(17046,plain,
% 2.74/2.95 ((~(z = elem!1)) | b(z, s(elem!1))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[4412, 15960])).
% 2.74/2.95 tff(17047,plain,
% 2.74/2.95 (b(z, s(elem!1))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[17046, 17034])).
% 2.74/2.95 tff(17048,plain,
% 2.74/2.95 (b(elem!1, s(elem!1))),
% 2.74/2.95 inference(modus_ponens,[status(thm)],[17047, 17045])).
% 2.74/2.95 tff(17049,plain,
% 2.74/2.95 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 2.74/2.95 inference(monotonicity,[status(thm)],[17038])).
% 2.74/2.95 tff(17050,plain,
% 2.74/2.95 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 2.74/2.95 inference(monotonicity,[status(thm)],[17034])).
% 2.74/2.95 tff(17051,plain,
% 2.74/2.95 ((~(s(s(s(s(z)))) = z)) <=> (~(s(s(s(s(z)))) = elem!1))),
% 2.74/2.95 inference(monotonicity,[status(thm)],[17050])).
% 2.74/2.95 tff(17052,plain,
% 2.74/2.95 (~(s(s(s(s(z)))) = elem!1)),
% 2.74/2.95 inference(modus_ponens,[status(thm)],[291, 17051])).
% 2.74/2.95 tff(17053,plain,
% 2.74/2.95 (b(s(s(s(z))), z) <=> b(s(s(s(z))), elem!1)),
% 2.74/2.95 inference(monotonicity,[status(thm)],[17034])).
% 2.74/2.95 tff(17054,plain,
% 2.74/2.95 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), z)),
% 2.74/2.95 inference(symmetry,[status(thm)],[17053])).
% 2.74/2.95 tff(17055,plain,
% 2.74/2.95 (b(s(s(s(z))), z)),
% 2.74/2.95 inference(modus_ponens,[status(thm)],[16930, 17054])).
% 2.74/2.95 tff(17056,plain,
% 2.74/2.95 (r(s(z), s(s(s(z))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[3302, 17020])).
% 2.74/2.95 tff(17057,plain,
% 2.74/2.95 (b(z, elem!1) <=> b(elem!1, elem!1)),
% 2.74/2.95 inference(monotonicity,[status(thm)],[17034])).
% 2.74/2.95 tff(17058,plain,
% 2.74/2.95 (b(elem!1, elem!1) <=> b(z, elem!1)),
% 2.74/2.95 inference(symmetry,[status(thm)],[17057])).
% 2.74/2.95 tff(17059,plain,
% 2.74/2.95 ((~b(elem!1, elem!1)) <=> (~b(z, elem!1))),
% 2.74/2.95 inference(monotonicity,[status(thm)],[17058])).
% 2.74/2.95 tff(17060,plain,
% 2.74/2.95 (~b(z, elem!1)),
% 2.74/2.95 inference(modus_ponens,[status(thm)],[1468, 17059])).
% 2.74/2.95 tff(17061,plain,
% 2.74/2.95 (r(s(s(s(z))), elem!1)),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[9791, 17060, 2, 17013, 17056])).
% 2.74/2.95 tff(17062,plain,
% 2.74/2.95 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[16502, 17056, 16930, 17012])).
% 2.74/2.95 tff(17063,plain,
% 2.74/2.95 ((s(s(s(s(s(s(z)))))) = z) <=> (s(s(s(s(s(s(z)))))) = elem!1)),
% 2.74/2.95 inference(monotonicity,[status(thm)],[17034])).
% 2.74/2.95 tff(17064,plain,
% 2.74/2.95 ((~(s(s(s(s(s(s(z)))))) = z)) <=> (~(s(s(s(s(s(s(z)))))) = elem!1))),
% 2.74/2.95 inference(monotonicity,[status(thm)],[17063])).
% 2.74/2.95 tff(17065,plain,
% 2.74/2.95 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 2.74/2.95 inference(modus_ponens,[status(thm)],[554, 17064])).
% 2.74/2.95 tff(17066,plain,
% 2.74/2.95 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[1144, 17065, 17062])).
% 2.74/2.95 tff(17067,plain,
% 2.74/2.95 (~r(s(s(s(s(z)))), elem!1)),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[16375, 17066, 17061, 17055])).
% 2.74/2.95 tff(17068,plain,
% 2.74/2.95 (b(s(s(s(s(z)))), elem!1)),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[9832, 17067, 17052])).
% 2.74/2.95 tff(17069,plain,
% 2.74/2.95 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.74/2.95 inference(modus_ponens,[status(thm)],[17068, 17049])).
% 2.74/2.95 tff(17070,plain,
% 2.74/2.95 (b(s(z), elem!1) <=> b(s(elem!1), elem!1)),
% 2.74/2.95 inference(monotonicity,[status(thm)],[17035])).
% 2.74/2.95 tff(17071,plain,
% 2.74/2.95 (b(s(elem!1), elem!1)),
% 2.74/2.95 inference(modus_ponens,[status(thm)],[17012, 17070])).
% 2.74/2.95 tff(17072,plain,
% 2.74/2.95 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[4442, 306, 17071, 17069, 17048])).
% 2.74/2.95 tff(17073,plain,
% 2.74/2.95 (~b(s(s(s(s(z)))), s(z))),
% 2.74/2.95 inference(modus_ponens,[status(thm)],[17072, 17044])).
% 2.74/2.95 tff(17074,plain,
% 2.74/2.95 (r(s(s(s(s(z)))), s(z))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[4490, 17073])).
% 2.74/2.95 tff(17075,plain,
% 2.74/2.95 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 2.74/2.95 inference(symmetry,[status(thm)],[17038])).
% 2.74/2.95 tff(17076,plain,
% 2.74/2.95 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.74/2.95 inference(symmetry,[status(thm)],[17037])).
% 2.74/2.95 tff(17077,plain,
% 2.74/2.95 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 2.74/2.95 inference(monotonicity,[status(thm)],[17076, 17075])).
% 2.74/2.95 tff(17078,plain,
% 2.74/2.95 ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) <=> (~b(s(s(s(z))), s(s(s(s(z))))))),
% 2.74/2.95 inference(monotonicity,[status(thm)],[17077])).
% 2.74/2.95 tff(17079,plain,
% 2.74/2.95 (b(s(s(s(z))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 2.74/2.95 inference(monotonicity,[status(thm)],[17037])).
% 2.74/2.95 tff(17080,plain,
% 2.74/2.95 (b(s(s(s(elem!1))), elem!1)),
% 2.74/2.95 inference(modus_ponens,[status(thm)],[16930, 17079])).
% 2.74/2.95 tff(17081,plain,
% 2.74/2.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.74/2.95 inference(rewrite,[status(thm)],[])).
% 2.74/2.95 tff(17082,plain,
% 2.74/2.95 (((~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(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.74/2.95 inference(rewrite,[status(thm)],[])).
% 2.74/2.95 tff(17083,plain,
% 2.74/2.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 2.74/2.95 inference(monotonicity,[status(thm)],[17082])).
% 2.74/2.95 tff(17084,plain,
% 2.74/2.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.74/2.95 inference(transitivity,[status(thm)],[17083, 17081])).
% 2.74/2.95 tff(17085,plain,
% 2.74/2.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~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)))))))),
% 2.74/2.95 inference(quant_inst,[status(thm)],[])).
% 2.74/2.95 tff(17086,plain,
% 2.74/2.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 2.74/2.95 inference(modus_ponens,[status(thm)],[17085, 17084])).
% 2.74/2.95 tff(17087,plain,
% 2.74/2.95 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[17086, 306, 17080, 17071, 17069, 17048])).
% 2.74/2.95 tff(17088,plain,
% 2.74/2.95 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.74/2.95 inference(modus_ponens,[status(thm)],[17087, 17078])).
% 2.74/2.95 tff(17089,plain,
% 2.74/2.95 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[10124, 17088])).
% 2.74/2.95 tff(17090,plain,
% 2.74/2.95 ($false),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[10128, 17089, 17074, 17014])).
% 2.74/2.95 tff(17091,plain,(r(z, elem!1) | b(elem!1, z) | b(elem!1, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.95 tff(17092,plain,
% 2.74/2.95 (r(z, elem!1)),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[17091, 2, 3])).
% 2.74/2.95 tff(17093,plain,
% 2.74/2.95 (~(elem!1 = z)),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[10449, 17092])).
% 2.74/2.95 tff(17094,plain,
% 2.74/2.95 (r(elem!1, z)),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[174, 17093, 2])).
% 2.74/2.95 tff(17095,plain,
% 2.74/2.95 (~r(s(z), elem!1)),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[8838, 17094, 17092, 16654])).
% 2.74/2.95 tff(17096,plain,
% 2.74/2.95 (b(s(z), elem!1)),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[16180, 17095])).
% 2.74/2.95 tff(17097,plain,
% 2.74/2.95 (~b(s(z), s(s(s(z))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[17019, 306, 17096, 16930, 15960])).
% 2.74/2.95 tff(17098,plain,
% 2.74/2.95 (~(s(s(s(z))) = elem!1)),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[16191, 17097, 17096])).
% 2.74/2.95 tff(17099,plain,
% 2.74/2.95 (~(elem!1 = s(s(s(z))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[4555, 17098])).
% 2.74/2.95 tff(17100,plain,
% 2.74/2.95 (r(elem!1, s(s(s(z))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[2304, 17099, 3])).
% 2.74/2.95 tff(17101,plain,
% 2.74/2.95 (r(s(z), s(s(s(z))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[3302, 17097])).
% 2.74/2.95 tff(17102,plain,
% 2.74/2.95 (~(z = elem!1)),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[1618, 17093])).
% 2.74/2.95 tff(17103,plain,
% 2.74/2.95 (~r(z, s(s(elem!1)))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[5837, 17092, 16654])).
% 2.74/2.95 tff(17104,plain,
% 2.74/2.95 (b(z, s(s(elem!1)))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[460, 17103])).
% 2.74/2.95 tff(17105,plain,
% 2.74/2.95 (~(s(s(elem!1)) = s(elem!1))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[195, 16955])).
% 2.74/2.95 tff(17106,plain,
% 2.74/2.95 (~r(s(s(elem!1)), z)),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[7786, 17094, 16654])).
% 2.74/2.95 tff(17107,plain,
% 2.74/2.95 (b(s(s(elem!1)), z)),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[476, 17106])).
% 2.74/2.95 tff(17108,plain,
% 2.74/2.95 (~r(s(elem!1), elem!1)),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[10562, 17107, 17092, 17105, 16654, 17104])).
% 2.74/2.95 tff(17109,plain,
% 2.74/2.95 (~b(s(s(s(z))), s(z))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[7567, 306, 17096, 16930, 15960])).
% 2.74/2.95 tff(17110,plain,
% 2.74/2.95 (r(s(s(s(z))), s(z))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[113, 17109])).
% 2.74/2.95 tff(17111,plain,
% 2.74/2.95 (r(s(elem!1), elem!1) | b(elem!1, z) | (~r(s(s(s(z))), s(z))) | (z = elem!1) | (~r(s(z), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~b(s(s(s(z))), z))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[7856, 15960, 15979])).
% 2.74/2.95 tff(17112,plain,
% 2.74/2.95 (~b(s(s(s(z))), z)),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[17111, 17110, 16930, 2, 17092, 17108, 17102, 17101, 17096])).
% 2.74/2.95 tff(17113,plain,
% 2.74/2.95 (r(s(s(s(z))), z)),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[2197, 17112])).
% 2.74/2.95 tff(17114,plain,
% 2.74/2.95 ($false),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[2312, 17113, 17100, 17094])).
% 2.74/2.95 tff(17115,plain,(b(elem!1, z) | b(elem!1, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.95 tff(17116,plain,
% 2.74/2.95 (b(elem!1, z)),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[17115, 3])).
% 2.74/2.95 tff(17117,plain,
% 2.74/2.95 (~(z = elem!1)),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[11005, 17116])).
% 2.74/2.95 tff(17118,plain,
% 2.74/2.95 (~b(z, s(s(s(z))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[15758, 306, 838, 17116, 16930])).
% 2.74/2.95 tff(17119,plain,
% 2.74/2.95 (~(elem!1 = s(s(s(z))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[842, 17118, 838])).
% 2.74/2.95 tff(17120,plain,
% 2.74/2.95 (r(elem!1, s(s(s(z))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[2304, 17119, 3])).
% 2.74/2.95 tff(17121,plain,
% 2.74/2.95 (~r(s(z), s(s(s(z))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[3347, 17120, 4])).
% 2.74/2.95 tff(17122,plain,
% 2.74/2.95 (b(s(z), s(s(s(z))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[3302, 17121])).
% 2.74/2.95 tff(17123,plain,
% 2.74/2.95 (~b(s(z), z)),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[16048, 838, 17116])).
% 2.74/2.95 tff(17124,plain,
% 2.74/2.95 (r(s(z), z)),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[221, 17123])).
% 2.74/2.95 tff(17125,plain,
% 2.74/2.95 (~b(s(s(s(z))), z)),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[12285, 306, 838, 17116, 16930])).
% 2.74/2.95 tff(17126,plain,
% 2.74/2.95 (r(s(s(s(z))), z)),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[2197, 17125])).
% 2.74/2.95 tff(17127,plain,
% 2.74/2.95 (~r(s(s(s(z))), s(z))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[211, 17126, 17124])).
% 2.74/2.95 tff(17128,plain,
% 2.74/2.95 (b(s(s(s(z))), s(z))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[113, 17127])).
% 2.74/2.95 tff(17129,plain,
% 2.74/2.95 ($false),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[4666, 306, 17128, 17122, 16930, 15960])).
% 2.74/2.95 tff(17130,plain,((~b(z, elem!1)) | (~r(s(z), elem!1)) | b(elem!1, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.95 tff(17131,plain,
% 2.74/2.95 (~b(z, elem!1)),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[17130, 4, 3])).
% 2.74/2.95 tff(17132,plain,
% 2.74/2.95 (r(z, elem!1)),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[835, 17131, 17117])).
% 2.74/2.95 tff(17133,plain,
% 2.74/2.95 (~r(z, s(z))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[6096, 17132, 4])).
% 2.74/2.95 tff(17134,plain,
% 2.74/2.95 (b(z, s(z))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[2263, 17133])).
% 2.74/2.95 tff(17135,plain,
% 2.74/2.95 (~r(s(z), z)),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[12117, 17132, 4])).
% 2.74/2.95 tff(17136,plain,
% 2.74/2.95 (b(s(z), z)),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[221, 17135])).
% 2.74/2.95 tff(17137,plain,
% 2.74/2.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), z)))),
% 2.74/2.95 inference(rewrite,[status(thm)],[])).
% 2.74/2.95 tff(17138,plain,
% 2.74/2.95 (((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), z)))),
% 2.74/2.95 inference(rewrite,[status(thm)],[])).
% 2.74/2.95 tff(17139,plain,
% 2.74/2.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), z))))),
% 2.74/2.95 inference(monotonicity,[status(thm)],[17138])).
% 2.74/2.95 tff(17140,plain,
% 2.74/2.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), z)))),
% 2.74/2.95 inference(transitivity,[status(thm)],[17139, 17137])).
% 2.74/2.95 tff(17141,plain,
% 2.74/2.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))),
% 2.74/2.95 inference(quant_inst,[status(thm)],[])).
% 2.74/2.95 tff(17142,plain,
% 2.74/2.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), z))),
% 2.74/2.95 inference(modus_ponens,[status(thm)],[17141, 17140])).
% 2.74/2.95 tff(17143,plain,
% 2.74/2.95 ($false),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[17142, 306, 17116, 15960, 17136, 17134])).
% 2.74/2.95 tff(17144,plain,((~r(s(z), elem!1)) | b(elem!1, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.95 tff(17145,plain,
% 2.74/2.95 (~r(s(z), elem!1)),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[17144, 3])).
% 2.74/2.95 tff(17146,plain,
% 2.74/2.95 (b(s(z), elem!1)),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[16180, 17145])).
% 2.74/2.95 tff(17147,plain,
% 2.74/2.95 (~b(s(z), s(s(s(z))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[17019, 306, 17146, 16930, 15960])).
% 2.74/2.96 tff(17148,plain,
% 2.74/2.96 (r(s(z), s(s(s(z))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[3302, 17147])).
% 2.74/2.96 tff(17149,plain,
% 2.74/2.96 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[16502, 17148, 16930, 17146])).
% 2.74/2.96 tff(17150,plain,
% 2.74/2.96 (~b(s(s(s(z))), s(z))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[7567, 306, 17146, 16930, 15960])).
% 2.74/2.96 tff(17151,plain,
% 2.74/2.96 (r(s(s(s(z))), s(z))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[113, 17150])).
% 2.74/2.96 tff(17152,plain,
% 2.74/2.96 (~(s(elem!1) = s(z))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[2689, 17117])).
% 2.74/2.96 tff(17153,plain,
% 2.74/2.96 (~b(s(z), z)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[16048, 838, 4012])).
% 2.74/2.96 tff(17154,plain,
% 2.74/2.96 (r(s(z), z)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[221, 17153])).
% 2.74/2.96 tff(17155,plain,
% 2.74/2.96 (~r(s(s(s(z))), z)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[211, 17154, 206])).
% 2.74/2.96 tff(17156,plain,
% 2.74/2.96 (b(s(s(s(z))), z)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[2197, 17155])).
% 2.74/2.96 tff(17157,plain,
% 2.74/2.96 ($false),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[12285, 306, 838, 4012, 1967, 17156])).
% 2.74/2.96 tff(17158,plain,((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.96 tff(17159,plain,
% 2.74/2.96 (~b(z, elem!1)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[17158, 17116, 16930, 17151])).
% 2.74/2.96 tff(17160,plain,
% 2.74/2.96 (r(z, elem!1)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[835, 17159, 17117])).
% 2.74/2.96 tff(17161,plain,
% 2.74/2.96 (~b(s(s(elem!1)), elem!1)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[16649, 17151, 16930, 17146])).
% 2.74/2.96 tff(17162,plain,
% 2.74/2.96 (~b(s(s(s(z))), s(z))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[7567, 306, 2831, 1967, 15960])).
% 2.74/2.96 tff(17163,plain,
% 2.74/2.96 (r(s(s(s(z))), s(z))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[113, 17162])).
% 2.74/2.96 tff(17164,plain,
% 2.74/2.96 (~b(s(z), s(s(s(z))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[17019, 306, 2831, 1967, 15960])).
% 2.74/2.96 tff(17165,plain,
% 2.74/2.96 (r(s(z), s(s(s(z))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[3302, 17164])).
% 2.74/2.96 tff(17166,plain,
% 2.74/2.96 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[16502, 17165, 1967, 2831])).
% 2.74/2.96 tff(17167,plain,
% 2.74/2.96 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[1144, 4918, 17166])).
% 2.74/2.96 tff(17168,plain,
% 2.74/2.96 (~b(z, elem!1)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[17158, 4012, 1967, 17163])).
% 2.74/2.96 tff(17169,plain,
% 2.74/2.96 (r(z, elem!1)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[835, 17168, 12587])).
% 2.74/2.96 tff(17170,plain,
% 2.74/2.96 (~r(z, s(s(s(s(s(s(z)))))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[5441, 124, 17169, 17167])).
% 2.74/2.96 tff(17171,plain,
% 2.74/2.96 ((z = s(s(s(s(s(s(z))))))) | b(z, s(s(s(s(s(s(z)))))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[5445, 43, 17170])).
% 2.74/2.96 tff(17172,plain,
% 2.74/2.96 (b(z, s(s(s(s(s(s(z)))))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[17171, 5435])).
% 2.74/2.96 tff(17173,plain,
% 2.74/2.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 2.74/2.96 inference(rewrite,[status(thm)],[])).
% 2.74/2.96 tff(17174,plain,
% 2.74/2.96 (((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 2.74/2.96 inference(rewrite,[status(thm)],[])).
% 2.74/2.96 tff(17175,plain,
% 2.74/2.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z))))))))))),
% 2.74/2.96 inference(monotonicity,[status(thm)],[17174])).
% 2.74/2.96 tff(17176,plain,
% 2.74/2.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 2.74/2.96 inference(transitivity,[status(thm)],[17175, 17173])).
% 2.74/2.96 tff(17177,plain,
% 2.74/2.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), z)))),
% 2.74/2.96 inference(quant_inst,[status(thm)],[])).
% 2.74/2.96 tff(17178,plain,
% 2.74/2.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z))))))))),
% 2.74/2.96 inference(modus_ponens,[status(thm)],[17177, 17176])).
% 2.74/2.96 tff(17179,plain,
% 2.74/2.96 (~b(s(s(s(s(z)))), z)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[17178, 306, 5454, 16364, 5447])).
% 2.74/2.96 tff(17180,plain,
% 2.74/2.96 ($false),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[695, 17179, 14269])).
% 2.74/2.96 tff(17181,plain,((~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.96 tff(17182,plain,
% 2.74/2.96 (~r(s(s(s(s(z)))), elem!1)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[17181, 17167, 17169])).
% 2.74/2.96 tff(17183,plain,
% 2.74/2.96 (b(s(s(s(s(z)))), elem!1)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[9832, 17182, 10291])).
% 2.74/2.96 tff(17184,plain,
% 2.74/2.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 2.74/2.96 inference(rewrite,[status(thm)],[])).
% 2.74/2.96 tff(17185,plain,
% 2.74/2.96 (((~b(z, s(s(s(s(s(s(z)))))))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 2.74/2.96 inference(rewrite,[status(thm)],[])).
% 2.74/2.96 tff(17186,plain,
% 2.74/2.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(s(s(z))))))))))),
% 2.74/2.96 inference(monotonicity,[status(thm)],[17185])).
% 2.74/2.96 tff(17187,plain,
% 2.74/2.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 2.74/2.96 inference(transitivity,[status(thm)],[17186, 17184])).
% 2.74/2.96 tff(17188,plain,
% 2.74/2.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 2.74/2.96 inference(quant_inst,[status(thm)],[])).
% 2.74/2.96 tff(17189,plain,
% 2.74/2.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(s(s(z))))))))),
% 2.74/2.96 inference(modus_ponens,[status(thm)],[17188, 17187])).
% 2.74/2.96 tff(17190,plain,
% 2.74/2.96 (~b(s(s(s(s(z)))), s(z))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[17189, 306, 4012, 2831, 17183, 17172])).
% 2.74/2.96 tff(17191,plain,
% 2.74/2.96 (r(s(s(s(s(z)))), s(z))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[4490, 17190])).
% 2.74/2.96 tff(17192,plain,
% 2.74/2.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 2.74/2.96 inference(rewrite,[status(thm)],[])).
% 2.74/2.96 tff(17193,plain,
% 2.74/2.96 (((~b(z, s(s(s(s(s(s(z)))))))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(elem!1, z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 2.74/2.96 inference(rewrite,[status(thm)],[])).
% 2.74/2.96 tff(17194,plain,
% 2.74/2.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(s(s(z))))))))))),
% 2.74/2.96 inference(monotonicity,[status(thm)],[17193])).
% 2.74/2.96 tff(17195,plain,
% 2.74/2.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 2.74/2.96 inference(transitivity,[status(thm)],[17194, 17192])).
% 2.74/2.96 tff(17196,plain,
% 2.74/2.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.74/2.96 inference(quant_inst,[status(thm)],[])).
% 2.74/2.96 tff(17197,plain,
% 2.74/2.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(s(s(z))))))))),
% 2.74/2.96 inference(modus_ponens,[status(thm)],[17196, 17195])).
% 2.74/2.96 tff(17198,plain,
% 2.74/2.96 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[17197, 306, 4012, 1967, 17183, 17172])).
% 2.74/2.96 tff(17199,plain,
% 2.74/2.96 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[10124, 17198])).
% 2.74/2.96 tff(17200,plain,
% 2.74/2.96 ($false),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[10128, 17199, 17191, 17163])).
% 2.74/2.96 tff(17201,plain,((~(s(s(elem!1)) = elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.96 tff(17202,plain,
% 2.74/2.96 (~(s(s(elem!1)) = elem!1)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[17201, 17116, 16930, 17146])).
% 2.74/2.96 tff(17203,plain,
% 2.74/2.96 (r(s(s(elem!1)), elem!1)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[47, 17202, 17161])).
% 2.74/2.96 tff(17204,plain,
% 2.74/2.96 (~r(z, s(s(elem!1)))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[5837, 17203, 17160])).
% 2.74/2.96 tff(17205,plain,
% 2.74/2.96 (b(z, s(s(elem!1)))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[460, 17204])).
% 2.74/2.96 tff(17206,plain,
% 2.74/2.96 (~(s(elem!1) = elem!1)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[180, 17202])).
% 2.74/2.96 tff(17207,plain,
% 2.74/2.96 (~(s(s(elem!1)) = s(elem!1))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[195, 17206])).
% 2.74/2.96 tff(17208,plain,
% 2.74/2.96 (~r(s(s(elem!1)), z)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[6539, 124, 17160, 17203])).
% 2.74/2.96 tff(17209,plain,
% 2.74/2.96 (b(s(s(elem!1)), z)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[476, 17208])).
% 2.74/2.96 tff(17210,plain,
% 2.74/2.96 (~r(s(elem!1), elem!1)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[10562, 17209, 17160, 17207, 17203, 17205])).
% 2.74/2.96 tff(17211,plain,
% 2.74/2.96 ((~(s(s(s(s(s(s(z)))))) = elem!1)) | (~r(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (s(elem!1) = s(z)) | r(s(elem!1), elem!1)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[5429, 15960])).
% 2.74/2.96 tff(17212,plain,
% 2.74/2.96 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[17211, 17210, 16930, 17146, 17152, 17151])).
% 2.74/2.96 tff(17213,plain,
% 2.74/2.96 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[1144, 17212, 17149])).
% 2.74/2.96 tff(17214,plain,
% 2.74/2.96 (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[8458, 124, 17203, 17213])).
% 2.74/2.96 tff(17215,plain,
% 2.74/2.96 (b(s(elem!1), elem!1)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[813, 17210, 17206])).
% 2.74/2.96 tff(17216,plain,
% 2.74/2.96 (~(elem!1 = s(elem!1))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[364, 17206])).
% 2.74/2.96 tff(17217,plain,
% 2.74/2.96 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[143, 17202])).
% 2.74/2.96 tff(17218,plain,
% 2.74/2.96 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[7090, 17210, 17117, 17202])).
% 2.74/2.96 tff(17219,plain,
% 2.74/2.96 (~(elem!1 = s(s(elem!1)))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[186, 17202])).
% 2.74/2.96 tff(17220,plain,
% 2.74/2.96 (~(s(s(s(z))) = elem!1)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[16191, 17147, 17146])).
% 2.74/2.96 tff(17221,plain,
% 2.74/2.96 (~(elem!1 = s(s(s(z))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[4555, 17220])).
% 2.74/2.96 tff(17222,plain,
% 2.74/2.96 (r(elem!1, s(s(s(z))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[2304, 17221, 3])).
% 2.74/2.96 tff(17223,plain,
% 2.74/2.96 (~b(s(s(s(z))), z)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[16499, 17213, 17160, 17222])).
% 2.74/2.96 tff(17224,plain,
% 2.74/2.96 (r(s(s(s(z))), z)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[2197, 17223])).
% 2.74/2.96 tff(17225,plain,
% 2.74/2.96 (~r(s(z), z)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[211, 17224, 17151])).
% 2.74/2.96 tff(17226,plain,
% 2.74/2.96 (b(s(z), z)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[221, 17225])).
% 2.74/2.96 tff(17227,plain,
% 2.74/2.96 (~b(s(s(elem!1)), s(elem!1))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[16918, 17226, 17116, 17205])).
% 2.74/2.96 tff(17228,plain,
% 2.74/2.96 (r(s(s(elem!1)), s(elem!1))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[994, 17227, 17207])).
% 2.74/2.96 tff(17229,plain,
% 2.74/2.96 (s(s(s(elem!1))) = elem!1),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[13111, 17228, 17116, 17203, 17219, 17218, 17217, 17216, 17215])).
% 2.74/2.96 tff(17230,plain,
% 2.74/2.96 (~(s(s(s(s(s(s(z)))))) = s(s(elem!1)))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[7206, 17229])).
% 2.74/2.96 tff(17231,plain,
% 2.74/2.96 (b(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[3247, 43, 17230, 17214])).
% 2.74/2.96 tff(17232,plain,
% 2.74/2.96 (~r(s(s(s(s(s(s(z)))))), z)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[5452, 17213, 17160])).
% 2.74/2.96 tff(17233,plain,
% 2.74/2.96 (b(s(s(s(s(s(s(z)))))), z)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[4232, 17232])).
% 2.74/2.96 tff(17234,plain,
% 2.74/2.96 ($false),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[9768, 306, 17205, 17209, 17233, 17231])).
% 2.74/2.96 tff(17235,plain,(b(elem!1, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.96 tff(17236,plain,
% 2.74/2.96 (r(s(s(elem!1)), elem!1)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[10424, 7, 2])).
% 2.74/2.96 tff(17237,plain,
% 2.74/2.96 (~r(s(z), s(s(elem!1)))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[13075, 4, 17236])).
% 2.74/2.96 tff(17238,plain,
% 2.74/2.96 (b(s(z), s(s(elem!1)))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[3997, 43, 79, 17237])).
% 2.74/2.96 tff(17239,plain,
% 2.74/2.96 (~r(s(s(elem!1)), z)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[7786, 5612, 17236])).
% 2.74/2.96 tff(17240,plain,
% 2.74/2.96 (b(s(s(elem!1)), z)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[476, 17239])).
% 2.74/2.96 tff(17241,plain,
% 2.74/2.96 (~(elem!1 = s(s(elem!1)))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[15853, 17236])).
% 2.74/2.96 tff(17242,plain,
% 2.74/2.96 (~r(s(s(elem!1)), s(z))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[8826, 4, 17236])).
% 2.74/2.96 tff(17243,plain,
% 2.74/2.96 (b(s(s(elem!1)), s(z))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[3989, 17242])).
% 2.74/2.96 tff(17244,plain,
% 2.74/2.96 (~b(elem!1, s(s(elem!1)))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[16004, 306, 17238, 15960, 17243])).
% 2.74/2.96 tff(17245,plain,
% 2.74/2.96 (r(elem!1, s(s(elem!1)))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[516, 17244, 17241])).
% 2.74/2.96 tff(17246,plain,
% 2.74/2.96 (~r(z, s(s(elem!1)))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[978, 5612, 17245])).
% 2.74/2.96 tff(17247,plain,
% 2.74/2.96 (b(z, s(s(elem!1)))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[460, 17246])).
% 2.74/2.96 tff(17248,plain,
% 2.74/2.96 ($false),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[16019, 306, 3105, 17247, 17240, 17238, 8715])).
% 2.74/2.96 tff(17249,plain,((z = elem!1) | (~r(s(z), elem!1)) | b(elem!1, z) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.96 tff(17250,plain,
% 2.74/2.96 (z = elem!1),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[17249, 16461, 2, 7])).
% 2.74/2.96 tff(17251,plain,
% 2.74/2.96 (s(z) = s(elem!1)),
% 2.74/2.96 inference(monotonicity,[status(thm)],[17250])).
% 2.74/2.96 tff(17252,plain,
% 2.74/2.96 (b(s(z), s(s(elem!1))) <=> b(s(elem!1), s(s(elem!1)))),
% 2.74/2.96 inference(monotonicity,[status(thm)],[17251])).
% 2.74/2.96 tff(17253,plain,
% 2.74/2.96 (~r(s(z), s(s(elem!1)))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[13075, 16461, 17236])).
% 2.74/2.96 tff(17254,plain,
% 2.74/2.96 (b(s(z), s(s(elem!1)))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[3997, 43, 79, 17253])).
% 2.74/2.96 tff(17255,plain,
% 2.74/2.96 (b(s(elem!1), s(s(elem!1)))),
% 2.74/2.96 inference(modus_ponens,[status(thm)],[17254, 17252])).
% 2.74/2.96 tff(17256,plain,
% 2.74/2.96 (~r(elem!1, z)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[9879, 17250])).
% 2.74/2.96 tff(17257,plain,
% 2.74/2.96 (~b(s(elem!1), elem!1)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[16952, 17250, 2715])).
% 2.74/2.96 tff(17258,plain,
% 2.74/2.96 (~r(s(s(elem!1)), s(z))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[8826, 16461, 17236])).
% 2.74/2.96 tff(17259,plain,
% 2.74/2.96 (b(s(s(elem!1)), s(z))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[3989, 17258])).
% 2.74/2.96 tff(17260,plain,
% 2.74/2.96 (~b(elem!1, s(s(elem!1)))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[16004, 306, 17254, 15960, 17259])).
% 2.74/2.96 tff(17261,plain,
% 2.74/2.96 (~b(s(s(elem!1)), elem!1)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[7610, 306, 17254, 15960, 17259])).
% 2.74/2.96 tff(17262,plain,
% 2.74/2.96 (~b(z, s(s(elem!1)))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[2757, 17250, 17260])).
% 2.74/2.96 tff(17263,plain,
% 2.74/2.96 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[13850, 17262, 7, 17261, 17260, 17257, 17256])).
% 2.74/2.96 tff(17264,plain,
% 2.74/2.96 (~(s(s(elem!1)) = elem!1)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[1174, 17241])).
% 2.74/2.96 tff(17265,plain,
% 2.74/2.96 (~(s(elem!1) = elem!1)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[180, 17264])).
% 2.74/2.96 tff(17266,plain,
% 2.74/2.96 (~(s(s(elem!1)) = s(elem!1))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[195, 17265])).
% 2.74/2.96 tff(17267,plain,
% 2.74/2.96 (r(s(elem!1), elem!1)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[813, 17257, 17265])).
% 2.74/2.96 tff(17268,plain,
% 2.74/2.96 (~r(s(s(elem!1)), s(elem!1))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[7985, 17267, 17236])).
% 2.74/2.96 tff(17269,plain,
% 2.74/2.96 (b(s(s(elem!1)), s(elem!1))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[994, 17268, 17266])).
% 2.74/2.96 tff(17270,plain,
% 2.74/2.96 (s(s(z)) = s(s(elem!1))),
% 2.74/2.96 inference(monotonicity,[status(thm)],[17251])).
% 2.74/2.96 tff(17271,plain,
% 2.74/2.96 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.74/2.96 inference(monotonicity,[status(thm)],[17270])).
% 2.74/2.96 tff(17272,plain,
% 2.74/2.96 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.74/2.96 inference(symmetry,[status(thm)],[17271])).
% 2.74/2.96 tff(17273,plain,
% 2.74/2.96 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(z))), s(elem!1))),
% 2.74/2.96 inference(monotonicity,[status(thm)],[17272])).
% 2.74/2.96 tff(17274,plain,
% 2.74/2.96 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 2.74/2.96 inference(symmetry,[status(thm)],[17273])).
% 2.74/2.96 tff(17275,plain,
% 2.74/2.96 (b(s(s(s(z))), s(z)) <=> b(s(s(s(z))), s(elem!1))),
% 2.74/2.96 inference(monotonicity,[status(thm)],[17251])).
% 2.74/2.96 tff(17276,plain,
% 2.74/2.96 (~(s(s(s(z))) = elem!1)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[1472, 17235])).
% 2.74/2.96 tff(17277,plain,
% 2.74/2.96 (~r(s(s(s(z))), elem!1)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[15985, 16461, 17236])).
% 2.74/2.96 tff(17278,plain,
% 2.74/2.96 (b(s(s(s(z))), elem!1)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[1489, 17277, 17276])).
% 2.74/2.96 tff(17279,plain,
% 2.74/2.96 ((~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z)))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[4999, 15960])).
% 2.74/2.96 tff(17280,plain,
% 2.74/2.96 (~b(s(z), s(s(s(z))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[17279, 17278, 17235])).
% 2.74/2.96 tff(17281,plain,
% 2.74/2.96 (r(s(z), s(s(s(z))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[3302, 17280])).
% 2.74/2.96 tff(17282,plain,
% 2.74/2.96 (elem!1 = z),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[1618, 17250])).
% 2.74/2.96 tff(17283,plain,
% 2.74/2.96 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[1511, 17250])).
% 2.74/2.96 tff(17284,plain,
% 2.74/2.96 (~(elem!1 = s(s(s(elem!1))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[1518, 17283])).
% 2.74/2.96 tff(17285,plain,
% 2.74/2.96 (~(s(s(s(elem!1))) = elem!1)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[2187, 17284])).
% 2.74/2.96 tff(17286,plain,
% 2.74/2.96 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[143, 17264])).
% 2.74/2.96 tff(17287,plain,
% 2.74/2.96 (~r(s(s(s(elem!1))), elem!1)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[12859, 17269, 17236, 17267, 17286, 17263])).
% 2.74/2.96 tff(17288,plain,
% 2.74/2.96 (b(s(s(s(elem!1))), elem!1)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[1636, 17287, 17285])).
% 2.74/2.96 tff(17289,plain,
% 2.74/2.96 (b(s(s(s(z))), z)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[2946, 17288, 17282])).
% 2.74/2.96 tff(17290,plain,
% 2.74/2.96 (~b(z, elem!1)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[2228, 17289, 17235, 17278])).
% 2.74/2.96 tff(17291,plain,
% 2.74/2.96 (b(s(s(s(z))), s(z))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[9791, 17290, 2, 17277, 17281])).
% 2.74/2.96 tff(17292,plain,
% 2.74/2.96 (b(s(s(s(z))), s(elem!1))),
% 2.74/2.96 inference(modus_ponens,[status(thm)],[17291, 17275])).
% 2.74/2.96 tff(17293,plain,
% 2.74/2.96 (b(s(s(s(elem!1))), s(elem!1))),
% 2.74/2.96 inference(modus_ponens,[status(thm)],[17292, 17274])).
% 2.74/2.96 tff(17294,plain,
% 2.74/2.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), 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(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.74/2.96 inference(rewrite,[status(thm)],[])).
% 2.74/2.96 tff(17295,plain,
% 2.74/2.96 (((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(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(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(elem!1))))),
% 2.74/2.96 inference(rewrite,[status(thm)],[])).
% 2.74/2.96 tff(17296,plain,
% 2.74/2.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1)))))),
% 2.74/2.96 inference(monotonicity,[status(thm)],[17295])).
% 2.74/2.96 tff(17297,plain,
% 2.74/2.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.74/2.96 inference(transitivity,[status(thm)],[17296, 17294])).
% 2.74/2.96 tff(17298,plain,
% 2.74/2.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), 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))))),
% 2.74/2.96 inference(quant_inst,[status(thm)],[])).
% 2.74/2.96 tff(17299,plain,
% 2.74/2.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1)))),
% 2.74/2.96 inference(modus_ponens,[status(thm)],[17298, 17297])).
% 2.74/2.96 tff(17300,plain,
% 2.74/2.96 ($false),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[17299, 306, 17293, 17269, 17263, 17255])).
% 2.74/2.96 tff(17301,plain,(b(s(z), elem!1) | b(elem!1, z) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.96 tff(17302,plain,
% 2.74/2.96 (b(s(z), elem!1)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[17301, 7, 2])).
% 2.74/2.96 tff(17303,plain,
% 2.74/2.96 ($false),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[7747, 306, 2284, 2831, 15960, 1470])).
% 2.74/2.96 tff(17304,plain,((~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.96 tff(17305,plain,
% 2.74/2.96 (~b(s(s(s(z))), s(z))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[17304, 17302, 17235])).
% 2.74/2.96 tff(17306,plain,
% 2.74/2.96 (r(s(s(s(z))), s(z))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[113, 17305])).
% 2.74/2.96 tff(17307,plain,
% 2.74/2.96 (~b(s(s(s(z))), s(z))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[17304, 2831, 17235])).
% 2.74/2.96 tff(17308,plain,
% 2.74/2.96 (r(s(s(s(z))), s(z))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[113, 17307])).
% 2.74/2.96 tff(17309,plain,
% 2.74/2.96 (~b(z, s(z))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[10305, 306, 838, 2831, 15960])).
% 2.74/2.96 tff(17310,plain,
% 2.74/2.96 (r(z, s(z))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[2263, 17309])).
% 2.74/2.96 tff(17311,plain,
% 2.74/2.96 (~b(s(z), z)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[10111, 306, 838, 2831, 15960])).
% 2.74/2.96 tff(17312,plain,
% 2.74/2.96 (r(s(z), z)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[221, 17311])).
% 2.74/2.96 tff(17313,plain,
% 2.74/2.96 ($false),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[10420, 17312, 17310, 17235, 17308, 838])).
% 2.74/2.96 tff(17314,plain,((~b(z, elem!1)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.96 tff(17315,plain,
% 2.74/2.96 (~b(z, elem!1)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[17314, 17302])).
% 2.74/2.96 tff(17316,plain,
% 2.74/2.96 (z = elem!1),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[835, 17315, 7])).
% 2.74/2.96 tff(17317,plain,
% 2.74/2.96 (s(z) = s(elem!1)),
% 2.74/2.96 inference(monotonicity,[status(thm)],[17316])).
% 2.74/2.96 tff(17318,plain,
% 2.74/2.96 (s(s(z)) = s(s(elem!1))),
% 2.74/2.96 inference(monotonicity,[status(thm)],[17317])).
% 2.74/2.96 tff(17319,plain,
% 2.74/2.96 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.74/2.96 inference(monotonicity,[status(thm)],[17318])).
% 2.74/2.96 tff(17320,plain,
% 2.74/2.96 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 2.74/2.97 inference(monotonicity,[status(thm)],[17319])).
% 2.74/2.97 tff(17321,plain,
% 2.74/2.97 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 2.74/2.97 inference(symmetry,[status(thm)],[17320])).
% 2.74/2.97 tff(17322,plain,
% 2.74/2.97 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.74/2.97 inference(symmetry,[status(thm)],[17319])).
% 2.74/2.97 tff(17323,plain,
% 2.74/2.97 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 2.74/2.97 inference(monotonicity,[status(thm)],[17322, 17321])).
% 2.74/2.97 tff(17324,plain,
% 2.74/2.97 ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) <=> (~b(s(s(s(z))), s(s(s(s(z))))))),
% 2.74/2.97 inference(monotonicity,[status(thm)],[17323])).
% 2.74/2.97 tff(17325,plain,
% 2.74/2.97 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 2.74/2.97 inference(monotonicity,[status(thm)],[17320])).
% 2.74/2.97 tff(17326,plain,
% 2.74/2.97 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 2.74/2.97 inference(monotonicity,[status(thm)],[17316])).
% 2.74/2.97 tff(17327,plain,
% 2.74/2.97 ((~(s(s(s(s(z)))) = z)) <=> (~(s(s(s(s(z)))) = elem!1))),
% 2.74/2.97 inference(monotonicity,[status(thm)],[17326])).
% 2.74/2.97 tff(17328,plain,
% 2.74/2.97 (~(s(s(s(s(z)))) = elem!1)),
% 2.74/2.97 inference(modus_ponens,[status(thm)],[291, 17327])).
% 2.74/2.97 tff(17329,plain,
% 2.74/2.97 (b(s(s(s(z))), z) <=> b(s(s(s(z))), elem!1)),
% 2.74/2.97 inference(monotonicity,[status(thm)],[17316])).
% 2.74/2.97 tff(17330,plain,
% 2.74/2.97 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), z)),
% 2.74/2.97 inference(symmetry,[status(thm)],[17329])).
% 2.74/2.97 tff(17331,plain,
% 2.74/2.97 (b(s(s(s(z))), elem!1)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[16291, 17316, 17236, 17302])).
% 2.74/2.97 tff(17332,plain,
% 2.74/2.97 (b(s(s(s(z))), z)),
% 2.74/2.97 inference(modus_ponens,[status(thm)],[17331, 17330])).
% 2.74/2.97 tff(17333,plain,
% 2.74/2.97 (~b(s(z), s(s(s(z))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[17279, 17331, 17235])).
% 2.74/2.97 tff(17334,plain,
% 2.74/2.97 (r(s(z), s(s(s(z))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[3302, 17333])).
% 2.74/2.97 tff(17335,plain,
% 2.74/2.97 (r(s(s(s(z))), elem!1)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[9791, 17334, 2, 17305, 17315])).
% 2.74/2.97 tff(17336,plain,
% 2.74/2.97 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[16502, 17334, 17302, 17331])).
% 2.74/2.97 tff(17337,plain,
% 2.74/2.97 ((s(s(s(s(s(s(z)))))) = z) <=> (s(s(s(s(s(s(z)))))) = elem!1)),
% 2.74/2.97 inference(monotonicity,[status(thm)],[17316])).
% 2.74/2.97 tff(17338,plain,
% 2.74/2.97 ((~(s(s(s(s(s(s(z)))))) = z)) <=> (~(s(s(s(s(s(s(z)))))) = elem!1))),
% 2.74/2.97 inference(monotonicity,[status(thm)],[17337])).
% 2.74/2.97 tff(17339,plain,
% 2.74/2.97 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 2.74/2.97 inference(modus_ponens,[status(thm)],[554, 17338])).
% 2.74/2.97 tff(17340,plain,
% 2.74/2.97 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[1144, 17339, 17336])).
% 2.74/2.97 tff(17341,plain,
% 2.74/2.97 (~r(s(s(s(s(z)))), elem!1)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[16375, 17340, 17335, 17332])).
% 2.74/2.97 tff(17342,plain,
% 2.74/2.97 (b(s(s(s(s(z)))), elem!1)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[9832, 17341, 17328])).
% 2.74/2.97 tff(17343,plain,
% 2.74/2.97 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.74/2.97 inference(modus_ponens,[status(thm)],[17342, 17325])).
% 2.74/2.97 tff(17344,plain,
% 2.74/2.97 (b(s(s(s(z))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 2.74/2.97 inference(monotonicity,[status(thm)],[17319])).
% 2.74/2.97 tff(17345,plain,
% 2.74/2.97 (b(s(s(s(elem!1))), elem!1)),
% 2.74/2.97 inference(modus_ponens,[status(thm)],[17331, 17344])).
% 2.74/2.97 tff(17346,plain,
% 2.74/2.97 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(s(elem!1))))),
% 2.74/2.97 inference(monotonicity,[status(thm)],[17319])).
% 2.74/2.97 tff(17347,plain,
% 2.74/2.97 (b(elem!1, s(s(s(elem!1))))),
% 2.74/2.97 inference(modus_ponens,[status(thm)],[17235, 17346])).
% 2.74/2.97 tff(17348,plain,
% 2.74/2.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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)))))))),
% 2.74/2.97 inference(rewrite,[status(thm)],[])).
% 2.74/2.97 tff(17349,plain,
% 2.74/2.97 (((~b(s(s(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(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(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)))))))),
% 2.74/2.97 inference(rewrite,[status(thm)],[])).
% 2.74/2.97 tff(17350,plain,
% 2.74/2.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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))))))))),
% 2.74/2.97 inference(monotonicity,[status(thm)],[17349])).
% 2.74/2.97 tff(17351,plain,
% 2.74/2.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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)))))))),
% 2.74/2.97 inference(transitivity,[status(thm)],[17350, 17348])).
% 2.74/2.97 tff(17352,plain,
% 2.74/2.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(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)))))))),
% 2.74/2.97 inference(quant_inst,[status(thm)],[])).
% 2.74/2.97 tff(17353,plain,
% 2.74/2.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(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))))))),
% 2.74/2.97 inference(modus_ponens,[status(thm)],[17352, 17351])).
% 2.74/2.97 tff(17354,plain,
% 2.74/2.97 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[17353, 306, 17347, 17345, 17343])).
% 2.74/2.97 tff(17355,plain,
% 2.74/2.97 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.74/2.97 inference(modus_ponens,[status(thm)],[17354, 17324])).
% 2.74/2.97 tff(17356,plain,
% 2.74/2.97 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[10124, 17355])).
% 2.74/2.97 tff(17357,plain,
% 2.74/2.97 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(elem!1)))), s(z))),
% 2.74/2.97 inference(monotonicity,[status(thm)],[17320])).
% 2.74/2.97 tff(17358,plain,
% 2.74/2.97 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 2.74/2.97 inference(symmetry,[status(thm)],[17357])).
% 2.74/2.97 tff(17359,plain,
% 2.74/2.97 (s(elem!1) = s(z)),
% 2.74/2.97 inference(symmetry,[status(thm)],[17317])).
% 2.74/2.97 tff(17360,plain,
% 2.74/2.97 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(s(s(s(s(elem!1)))), s(z))),
% 2.74/2.97 inference(monotonicity,[status(thm)],[17359])).
% 2.74/2.97 tff(17361,plain,
% 2.74/2.97 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(z))),
% 2.74/2.97 inference(transitivity,[status(thm)],[17360, 17358])).
% 2.74/2.97 tff(17362,plain,
% 2.74/2.97 ((~b(s(s(s(s(elem!1)))), s(elem!1))) <=> (~b(s(s(s(s(z)))), s(z)))),
% 2.74/2.97 inference(monotonicity,[status(thm)],[17361])).
% 2.74/2.97 tff(17363,plain,
% 2.74/2.97 (b(s(z), elem!1) <=> b(s(elem!1), elem!1)),
% 2.74/2.97 inference(monotonicity,[status(thm)],[17317])).
% 2.74/2.97 tff(17364,plain,
% 2.74/2.97 (b(s(elem!1), elem!1)),
% 2.74/2.97 inference(modus_ponens,[status(thm)],[17302, 17363])).
% 2.74/2.97 tff(17365,plain,
% 2.74/2.97 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[6593, 306, 17347, 17345, 17364, 17343])).
% 2.74/2.97 tff(17366,plain,
% 2.74/2.97 (~b(s(s(s(s(z)))), s(z))),
% 2.74/2.97 inference(modus_ponens,[status(thm)],[17365, 17362])).
% 2.74/2.97 tff(17367,plain,
% 2.74/2.97 (r(s(s(s(s(z)))), s(z))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[4490, 17366])).
% 2.74/2.97 tff(17368,plain,
% 2.74/2.97 ($false),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[10128, 17367, 17356, 17306])).
% 2.74/2.97 tff(17369,plain,(r(z, elem!1) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.97 tff(17370,plain,
% 2.74/2.97 (r(z, elem!1)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[17369, 2])).
% 2.74/2.97 tff(17371,plain,
% 2.74/2.97 (~r(z, s(z))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[6096, 16461, 17370])).
% 2.74/2.97 tff(17372,plain,
% 2.74/2.97 (b(z, s(z))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[2263, 17371])).
% 2.74/2.97 tff(17373,plain,
% 2.74/2.97 (~(elem!1 = z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[10449, 17370])).
% 2.74/2.97 tff(17374,plain,
% 2.74/2.97 (r(elem!1, z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[174, 17373, 2])).
% 2.74/2.97 tff(17375,plain,
% 2.74/2.97 (~r(s(z), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[1049, 16461, 17374])).
% 2.74/2.97 tff(17376,plain,
% 2.74/2.97 (b(s(z), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[221, 17375])).
% 2.74/2.97 tff(17377,plain,
% 2.74/2.97 (b(s(s(s(z))), elem!1)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[16463, 2715, 17276, 17370])).
% 2.74/2.97 tff(17378,plain,
% 2.74/2.97 (~b(s(z), s(s(s(z))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[17279, 17377, 17235])).
% 2.74/2.97 tff(17379,plain,
% 2.74/2.97 (r(s(z), s(s(s(z))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[3302, 17378])).
% 2.74/2.97 tff(17380,plain,
% 2.74/2.97 (~(z = elem!1)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[1618, 17373])).
% 2.74/2.97 tff(17381,plain,
% 2.74/2.97 (~(s(elem!1) = s(z))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[2689, 17380])).
% 2.74/2.97 tff(17382,plain,
% 2.74/2.97 (~r(s(s(elem!1)), elem!1)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[8838, 16461, 17370, 17374])).
% 2.74/2.97 tff(17383,plain,
% 2.74/2.97 (~r(s(s(s(z))), elem!1)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[3790, 17379, 16461])).
% 2.74/2.97 tff(17384,plain,
% 2.74/2.97 (b(s(s(s(z))), s(z))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[9710, 17383, 2, 17370, 17382, 17381, 17374, 17235, 17376, 17379, 17276])).
% 2.74/2.97 tff(17385,plain,
% 2.74/2.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), z)))),
% 2.74/2.97 inference(rewrite,[status(thm)],[])).
% 2.74/2.97 tff(17386,plain,
% 2.74/2.97 (((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), z)))),
% 2.74/2.97 inference(rewrite,[status(thm)],[])).
% 2.74/2.97 tff(17387,plain,
% 2.74/2.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), z))))),
% 2.74/2.97 inference(monotonicity,[status(thm)],[17386])).
% 2.74/2.97 tff(17388,plain,
% 2.74/2.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), z)))),
% 2.74/2.97 inference(transitivity,[status(thm)],[17387, 17385])).
% 2.74/2.97 tff(17389,plain,
% 2.74/2.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))))),
% 2.74/2.97 inference(quant_inst,[status(thm)],[])).
% 2.74/2.97 tff(17390,plain,
% 2.74/2.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), z))),
% 2.74/2.97 inference(modus_ponens,[status(thm)],[17389, 17388])).
% 2.74/2.97 tff(17391,plain,
% 2.74/2.97 ($false),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[17390, 306, 17384, 15960, 17376, 17235, 17372])).
% 2.74/2.97 tff(17392,plain,(b(s(z), elem!1) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.97 tff(17393,plain,
% 2.74/2.97 (b(s(z), elem!1)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[17392, 2])).
% 2.74/2.97 tff(17394,plain,
% 2.74/2.97 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[6921, 124, 206, 8821])).
% 2.74/2.97 tff(17395,plain,
% 2.74/2.97 (b(s(s(s(z))), s(s(elem!1)))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[2986, 43, 17394, 15980])).
% 2.74/2.97 tff(17396,plain,
% 2.74/2.97 (~r(s(s(elem!1)), s(s(s(z))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[7968, 124, 206, 8821])).
% 2.74/2.97 tff(17397,plain,
% 2.74/2.97 (b(s(s(elem!1)), s(s(s(z))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[7962, 43, 16, 17396])).
% 2.74/2.97 tff(17398,plain,
% 2.74/2.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.74/2.97 inference(rewrite,[status(thm)],[])).
% 2.74/2.97 tff(17399,plain,
% 2.74/2.97 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.74/2.97 inference(rewrite,[status(thm)],[])).
% 2.74/2.97 tff(17400,plain,
% 2.74/2.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 2.74/2.97 inference(monotonicity,[status(thm)],[17399])).
% 2.74/2.97 tff(17401,plain,
% 2.74/2.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.74/2.97 inference(transitivity,[status(thm)],[17400, 17398])).
% 2.74/2.97 tff(17402,plain,
% 2.74/2.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)))),
% 2.74/2.97 inference(quant_inst,[status(thm)],[])).
% 2.74/2.97 tff(17403,plain,
% 2.74/2.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1))))),
% 2.74/2.97 inference(modus_ponens,[status(thm)],[17402, 17401])).
% 2.74/2.97 tff(17404,plain,
% 2.74/2.97 ($false),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[17403, 306, 30, 17397, 17395, 1470])).
% 2.74/2.97 tff(17405,plain,((~r(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (s(s(elem!1)) = s(s(s(z)))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.97 tff(17406,plain,
% 2.74/2.97 (~r(s(s(elem!1)), s(z))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[17405, 30, 16439, 17235, 17308])).
% 2.74/2.97 tff(17407,plain,
% 2.74/2.97 ($false),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[3989, 17406, 16322])).
% 2.74/2.97 tff(17408,plain,((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.97 tff(17409,plain,
% 2.74/2.97 (~b(s(s(elem!1)), elem!1)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[17408, 17393])).
% 2.74/2.97 tff(17410,plain,
% 2.74/2.97 (~(s(s(elem!1)) = elem!1)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[16475, 1, 374])).
% 2.74/2.97 tff(17411,plain,
% 2.74/2.97 (~(s(elem!1) = elem!1)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[180, 17410])).
% 2.74/2.97 tff(17412,plain,
% 2.74/2.97 (~b(s(s(elem!1)), elem!1)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[17408, 2831])).
% 2.74/2.97 tff(17413,plain,
% 2.74/2.97 (r(s(s(elem!1)), elem!1)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[47, 17410, 17412])).
% 2.74/2.97 tff(17414,plain,
% 2.74/2.97 (~r(z, s(s(elem!1)))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[5837, 17413, 374])).
% 2.74/2.97 tff(17415,plain,
% 2.74/2.97 (b(z, s(s(elem!1)))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[460, 17414])).
% 2.74/2.97 tff(17416,plain,
% 2.74/2.97 (~(s(s(elem!1)) = s(elem!1))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[195, 17411])).
% 2.74/2.97 tff(17417,plain,
% 2.74/2.97 (~r(s(s(elem!1)), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[7786, 17413, 246])).
% 2.74/2.97 tff(17418,plain,
% 2.74/2.97 (b(s(s(elem!1)), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[476, 17417])).
% 2.74/2.97 tff(17419,plain,
% 2.74/2.97 (~r(s(elem!1), elem!1)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[10562, 17418, 374, 17416, 17413, 17415])).
% 2.74/2.97 tff(17420,plain,
% 2.74/2.97 (b(s(elem!1), elem!1)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[813, 17419, 17411])).
% 2.74/2.97 tff(17421,plain,
% 2.74/2.97 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[143, 17410])).
% 2.74/2.97 tff(17422,plain,
% 2.74/2.97 (b(s(elem!1), s(z))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[12776, 17419, 17412, 1, 17421, 13980])).
% 2.74/2.97 tff(17423,plain,
% 2.74/2.97 ($false),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[16671, 17422, 17420, 2831])).
% 2.74/2.97 tff(17424,plain,(b(s(s(s(z))), elem!1) | (~b(s(z), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.97 tff(17425,plain,
% 2.74/2.97 (b(s(s(s(z))), elem!1)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[17424, 17393, 17370, 17374])).
% 2.74/2.97 tff(17426,plain,
% 2.74/2.97 (~b(s(z), s(s(s(z))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[17279, 17425, 17235])).
% 2.74/2.97 tff(17427,plain,
% 2.74/2.97 (r(s(z), s(s(s(z))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[3302, 17426])).
% 2.74/2.97 tff(17428,plain,
% 2.74/2.97 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[16502, 17427, 17393, 17425])).
% 2.74/2.97 tff(17429,plain,
% 2.74/2.97 (~b(s(s(s(z))), s(z))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[17304, 17393, 17235])).
% 2.74/2.97 tff(17430,plain,
% 2.74/2.97 (~b(z, elem!1)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[17314, 17393])).
% 2.74/2.97 tff(17431,plain,
% 2.74/2.97 (r(s(s(s(z))), elem!1)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[9784, 17427, 2, 17380, 17430, 17429])).
% 2.74/2.97 tff(17432,plain,
% 2.74/2.97 (r(s(s(s(z))), s(z))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[113, 17429])).
% 2.74/2.97 tff(17433,plain,
% 2.74/2.97 (~r(s(s(s(z))), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[6831, 17431, 17370])).
% 2.74/2.97 tff(17434,plain,
% 2.74/2.97 (b(s(s(s(z))), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[2197, 17433])).
% 2.74/2.97 tff(17435,plain,
% 2.74/2.97 (r(s(elem!1), elem!1)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[17111, 17434, 2, 17370, 17432, 17425, 17380, 17427, 17393])).
% 2.74/2.97 tff(17436,plain,
% 2.74/2.97 (~b(s(z), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[5482, 16347, 374, 2831, 1034, 7136])).
% 2.74/2.97 tff(17437,plain,
% 2.74/2.97 (r(s(z), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[221, 17436])).
% 2.74/2.97 tff(17438,plain,
% 2.74/2.97 (~r(s(s(s(s(z)))), elem!1)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[16375, 16347, 2859, 7136])).
% 2.74/2.97 tff(17439,plain,
% 2.74/2.97 (b(s(s(s(s(z)))), elem!1)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[9832, 17438, 10291])).
% 2.74/2.97 tff(17440,plain,
% 2.74/2.97 (~b(s(s(s(s(z)))), s(z))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[16542, 306, 2831, 15960, 17439])).
% 2.74/2.97 tff(17441,plain,
% 2.74/2.97 (r(s(s(s(s(z)))), s(z))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[4490, 17440])).
% 2.74/2.97 tff(17442,plain,
% 2.74/2.97 (~r(s(s(s(s(z)))), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[10160, 17441, 17437])).
% 2.74/2.97 tff(17443,plain,
% 2.74/2.97 (b(s(s(s(s(z)))), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[695, 17442])).
% 2.74/2.97 tff(17444,plain,
% 2.74/2.97 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[10128, 17441, 17308])).
% 2.74/2.97 tff(17445,plain,
% 2.74/2.97 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[4481, 17444])).
% 2.74/2.97 tff(17446,plain,
% 2.74/2.97 (b(z, s(s(s(elem!1)))) <=> b(z, s(elem!1))),
% 2.74/2.97 inference(monotonicity,[status(thm)],[1424])).
% 2.74/2.97 tff(17447,plain,
% 2.74/2.97 (~b(z, elem!1)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[17314, 2831])).
% 2.74/2.97 tff(17448,plain,
% 2.74/2.97 (~b(z, s(s(elem!1)))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[14596, 1423, 17447])).
% 2.74/2.97 tff(17449,plain,
% 2.74/2.97 (r(z, s(s(elem!1)))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[460, 17448])).
% 2.74/2.97 tff(17450,plain,
% 2.74/2.97 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.74/2.97 inference(symmetry,[status(thm)],[8955])).
% 2.74/2.97 tff(17451,plain,
% 2.74/2.97 (r(s(s(s(elem!1))), elem!1) <=> r(s(elem!1), elem!1)),
% 2.74/2.97 inference(monotonicity,[status(thm)],[1424])).
% 2.74/2.97 tff(17452,plain,
% 2.74/2.97 (r(s(elem!1), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 2.74/2.97 inference(symmetry,[status(thm)],[17451])).
% 2.74/2.97 tff(17453,plain,
% 2.74/2.97 (r(s(elem!1), elem!1) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.74/2.97 inference(transitivity,[status(thm)],[17452, 17450])).
% 2.74/2.97 tff(17454,plain,
% 2.74/2.97 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.74/2.97 inference(modus_ponens,[status(thm)],[802, 17453])).
% 2.74/2.97 tff(17455,plain,
% 2.74/2.97 (~r(z, s(s(s(elem!1))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[950, 17454, 17449])).
% 2.74/2.97 tff(17456,plain,
% 2.74/2.97 (b(z, s(s(s(elem!1))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[585, 17455])).
% 2.74/2.97 tff(17457,plain,
% 2.74/2.97 (b(z, s(elem!1))),
% 2.74/2.97 inference(modus_ponens,[status(thm)],[17456, 17446])).
% 2.74/2.97 tff(17458,plain,
% 2.74/2.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)))),
% 2.74/2.97 inference(rewrite,[status(thm)],[])).
% 2.74/2.97 tff(17459,plain,
% 2.74/2.97 (((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~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(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)))),
% 2.74/2.97 inference(rewrite,[status(thm)],[])).
% 2.74/2.97 tff(17460,plain,
% 2.74/2.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z))))),
% 2.74/2.97 inference(monotonicity,[status(thm)],[17459])).
% 2.74/2.97 tff(17461,plain,
% 2.74/2.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)))),
% 2.74/2.97 inference(transitivity,[status(thm)],[17460, 17458])).
% 2.74/2.97 tff(17462,plain,
% 2.74/2.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.74/2.97 inference(quant_inst,[status(thm)],[])).
% 2.74/2.97 tff(17463,plain,
% 2.74/2.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z))),
% 2.74/2.97 inference(modus_ponens,[status(thm)],[17462, 17461])).
% 2.74/2.97 tff(17464,plain,
% 2.74/2.97 ($false),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[17463, 306, 7921, 17457, 17445, 17443, 7136])).
% 2.74/2.97 tff(17465,plain,((~(s(s(elem!1)) = elem!1)) | (~b(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | b(s(s(s(s(s(s(z)))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.97 tff(17466,plain,
% 2.74/2.97 (~(s(s(elem!1)) = elem!1)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[17465, 17393, 17435, 17370, 17427, 17431, 17428])).
% 2.74/2.97 tff(17467,plain,
% 2.74/2.97 (r(s(s(elem!1)), elem!1)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[47, 17466, 17409])).
% 2.74/2.97 tff(17468,plain,
% 2.74/2.97 (~(s(elem!1) = elem!1)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[180, 17466])).
% 2.74/2.97 tff(17469,plain,
% 2.74/2.97 (~(s(s(elem!1)) = s(elem!1))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[195, 17468])).
% 2.74/2.97 tff(17470,plain,
% 2.74/2.97 (~r(z, s(s(elem!1)))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[5837, 17467, 17370])).
% 2.74/2.97 tff(17471,plain,
% 2.74/2.97 (b(z, s(s(elem!1)))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[460, 17470])).
% 2.74/2.97 tff(17472,plain,
% 2.74/2.97 (~r(s(s(elem!1)), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[7786, 17467, 17374])).
% 2.74/2.97 tff(17473,plain,
% 2.74/2.97 (b(s(s(elem!1)), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[476, 17472])).
% 2.74/2.97 tff(17474,plain,
% 2.74/2.97 ($false),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[10562, 17473, 17471, 17370, 17435, 17469, 17467])).
% 2.74/2.97 tff(17475,plain,(b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.97 tff(17476,plain,
% 2.74/2.97 (~(z = elem!1)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[11005, 17475])).
% 2.74/2.97 tff(17477,plain,
% 2.74/2.97 (b(z, elem!1)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[835, 7, 17476])).
% 2.74/2.97 tff(17478,plain,
% 2.74/2.97 (r(s(s(s(z))), elem!1)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[1489, 1, 17276])).
% 2.74/2.97 tff(17479,plain,
% 2.74/2.97 (r(s(s(elem!1)), elem!1)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[16151, 1, 17475, 4, 7])).
% 2.74/2.97 tff(17480,plain,
% 2.74/2.97 ($false),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[15985, 17479, 17478, 4])).
% 2.74/2.97 tff(17481,plain,(b(s(s(s(z))), elem!1) | (~r(s(z), elem!1)) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.97 tff(17482,plain,
% 2.74/2.97 (b(s(s(s(z))), elem!1)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[17481, 7, 4])).
% 2.74/2.97 tff(17483,plain,
% 2.74/2.97 ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[3002, 15980])).
% 2.74/2.97 tff(17484,plain,
% 2.74/2.97 (~b(s(s(elem!1)), elem!1)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[17483, 17482, 17235, 17477])).
% 2.74/2.97 tff(17485,plain,
% 2.74/2.97 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[12298, 17482, 17475, 17477])).
% 2.74/2.97 tff(17486,plain,
% 2.74/2.97 (~b(s(s(s(z))), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[14674, 17477, 17235, 17475])).
% 2.74/2.97 tff(17487,plain,
% 2.74/2.97 (r(s(s(s(z))), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[2197, 17486])).
% 2.74/2.97 tff(17488,plain,
% 2.74/2.97 (~b(s(z), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[16048, 17477, 17475])).
% 2.74/2.97 tff(17489,plain,
% 2.74/2.97 (r(s(z), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[221, 17488])).
% 2.74/2.97 tff(17490,plain,
% 2.74/2.97 (~r(s(s(s(z))), s(z))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[211, 17489, 17487])).
% 2.74/2.97 tff(17491,plain,
% 2.74/2.97 (b(s(s(s(z))), s(z))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[113, 17490])).
% 2.74/2.97 tff(17492,plain,
% 2.74/2.97 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[9918, 124, 4, 2858])).
% 2.74/2.97 tff(17493,plain,
% 2.74/2.97 (b(s(z), s(s(s(s(s(s(z)))))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[5358, 43, 5355, 17492])).
% 2.74/2.97 tff(17494,plain,
% 2.74/2.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 2.74/2.98 inference(rewrite,[status(thm)],[])).
% 2.74/2.98 tff(17495,plain,
% 2.74/2.98 (((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 2.74/2.98 inference(rewrite,[status(thm)],[])).
% 2.74/2.98 tff(17496,plain,
% 2.74/2.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))))),
% 2.74/2.98 inference(monotonicity,[status(thm)],[17495])).
% 2.74/2.98 tff(17497,plain,
% 2.74/2.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 2.74/2.98 inference(transitivity,[status(thm)],[17496, 17494])).
% 2.74/2.98 tff(17498,plain,
% 2.74/2.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))))),
% 2.74/2.98 inference(quant_inst,[status(thm)],[])).
% 2.74/2.98 tff(17499,plain,
% 2.74/2.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 2.74/2.98 inference(modus_ponens,[status(thm)],[17498, 17497])).
% 2.74/2.98 tff(17500,plain,
% 2.74/2.98 ($false),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[17499, 306, 2284, 15960, 17235, 17493, 12205])).
% 2.74/2.98 tff(17501,plain,((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(z))), s(z))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.98 tff(17502,plain,
% 2.74/2.98 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[17501, 17491, 4])).
% 2.74/2.98 tff(17503,plain,
% 2.74/2.98 (s(s(s(s(s(s(z)))))) = elem!1),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[1144, 17502, 17485])).
% 2.74/2.98 tff(17504,plain,
% 2.74/2.98 (~(s(s(elem!1)) = elem!1)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[4284, 17503])).
% 2.74/2.98 tff(17505,plain,
% 2.74/2.98 (r(s(s(elem!1)), elem!1)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[47, 17504, 17484])).
% 2.74/2.98 tff(17506,plain,
% 2.74/2.98 (r(s(elem!1), elem!1)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[15916, 17505, 17475, 17477, 17482, 17487])).
% 2.74/2.98 tff(17507,plain,
% 2.74/2.98 (~(s(s(s(s(z)))) = s(elem!1))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[14363, 17276])).
% 2.74/2.98 tff(17508,plain,
% 2.74/2.98 (~(s(s(s(elem!1))) = elem!1)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[16418, 17503, 17507])).
% 2.74/2.98 tff(17509,plain,
% 2.74/2.98 (~(s(s(elem!1)) = s(elem!1))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[1564, 17508])).
% 2.74/2.98 tff(17510,plain,
% 2.74/2.98 ((s(s(elem!1)) = s(z)) <=> (s(z) = s(s(elem!1)))),
% 2.74/2.98 inference(symmetry,[status(thm)],[50])).
% 2.74/2.98 tff(17511,plain,
% 2.74/2.98 ((~(s(s(elem!1)) = s(z))) <=> (~(s(z) = s(s(elem!1))))),
% 2.74/2.98 inference(monotonicity,[status(thm)],[17510])).
% 2.74/2.98 tff(17512,plain,
% 2.74/2.98 (~(s(z) = s(s(elem!1)))),
% 2.74/2.98 inference(modus_ponens,[status(thm)],[1417, 17511])).
% 2.74/2.98 tff(17513,plain,
% 2.74/2.98 ((~(elem!1 = s(z))) <=> (~(s(z) = elem!1))),
% 2.74/2.98 inference(monotonicity,[status(thm)],[3092])).
% 2.74/2.98 tff(17514,plain,
% 2.74/2.98 (~(s(z) = elem!1)),
% 2.74/2.98 inference(modus_ponens,[status(thm)],[87, 17513])).
% 2.74/2.98 tff(17515,plain,
% 2.74/2.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))))),
% 2.74/2.98 inference(rewrite,[status(thm)],[])).
% 2.74/2.98 tff(17516,plain,
% 2.74/2.98 (((~b(elem!1, z)) | (~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, z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))))),
% 2.74/2.98 inference(rewrite,[status(thm)],[])).
% 2.74/2.98 tff(17517,plain,
% 2.74/2.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z)))))),
% 2.74/2.98 inference(monotonicity,[status(thm)],[17516])).
% 2.74/2.98 tff(17518,plain,
% 2.74/2.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))))),
% 2.74/2.98 inference(transitivity,[status(thm)],[17517, 17515])).
% 2.74/2.98 tff(17519,plain,
% 2.74/2.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))))),
% 2.74/2.98 inference(quant_inst,[status(thm)],[])).
% 2.74/2.98 tff(17520,plain,
% 2.74/2.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z)))),
% 2.74/2.98 inference(modus_ponens,[status(thm)],[17519, 17518])).
% 2.74/2.98 tff(17521,plain,
% 2.74/2.98 ($false),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[17520, 306, 4012, 2284, 2831, 4346, 1470])).
% 2.74/2.98 tff(17522,plain,((~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.98 tff(17523,plain,
% 2.74/2.98 (~b(s(z), elem!1)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[17522, 1470, 2284, 4346, 4012])).
% 2.74/2.98 tff(17524,plain,
% 2.74/2.98 ((s(z) = elem!1) | r(s(z), elem!1)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[1500, 43, 17523])).
% 2.74/2.98 tff(17525,plain,
% 2.74/2.98 (r(s(z), elem!1)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[17524, 17514])).
% 2.74/2.98 tff(17526,plain,
% 2.74/2.98 (~r(s(z), s(s(elem!1)))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[6326, 124, 1730, 17525])).
% 2.74/2.98 tff(17527,plain,
% 2.74/2.98 ((s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1)))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[3997, 43, 17526])).
% 2.74/2.98 tff(17528,plain,
% 2.74/2.98 (b(s(z), s(s(elem!1)))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[17527, 17512])).
% 2.74/2.98 tff(17529,plain,
% 2.74/2.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(z))))),
% 2.74/2.98 inference(rewrite,[status(thm)],[])).
% 2.74/2.98 tff(17530,plain,
% 2.74/2.98 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(z))))),
% 2.74/2.98 inference(rewrite,[status(thm)],[])).
% 2.74/2.98 tff(17531,plain,
% 2.74/2.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(z)))))),
% 2.74/2.98 inference(monotonicity,[status(thm)],[17530])).
% 2.74/2.98 tff(17532,plain,
% 2.74/2.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(z))))),
% 2.74/2.98 inference(transitivity,[status(thm)],[17531, 17529])).
% 2.74/2.98 tff(17533,plain,
% 2.74/2.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))))),
% 2.74/2.98 inference(quant_inst,[status(thm)],[])).
% 2.74/2.98 tff(17534,plain,
% 2.74/2.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(z)))),
% 2.74/2.98 inference(modus_ponens,[status(thm)],[17533, 17532])).
% 2.74/2.98 tff(17535,plain,
% 2.74/2.98 ($false),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[17534, 306, 1005, 2284, 17528, 4346, 1470])).
% 2.74/2.98 tff(17536,plain,((~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (s(s(elem!1)) = s(z)) | (~r(s(s(elem!1)), elem!1)) | (elem!1 = s(z)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.98 tff(17537,plain,
% 2.74/2.98 ((~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)) | (elem!1 = s(z)) | (~b(elem!1, z))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[17536, 80])).
% 2.74/2.98 tff(17538,plain,
% 2.74/2.98 ((~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), elem!1)) | (~b(elem!1, z))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[17537, 15960, 15979])).
% 2.74/2.98 tff(17539,plain,
% 2.74/2.98 (~b(s(s(elem!1)), s(elem!1))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[17538, 17505, 17235, 17475, 17491])).
% 2.74/2.98 tff(17540,plain,
% 2.74/2.98 (r(s(s(elem!1)), s(elem!1))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[994, 17539, 17509])).
% 2.74/2.98 tff(17541,plain,
% 2.74/2.98 ($false),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[7985, 17540, 17506, 17505])).
% 2.74/2.98 tff(17542,plain,(r(z, elem!1) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.98 tff(17543,plain,
% 2.74/2.98 (r(z, elem!1)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[17542, 4])).
% 2.74/2.98 tff(17544,plain,
% 2.74/2.98 (~r(z, s(z))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[6096, 17543, 4])).
% 2.74/2.98 tff(17545,plain,
% 2.74/2.98 (b(z, s(z))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[2263, 17544])).
% 2.74/2.98 tff(17546,plain,
% 2.74/2.98 (~r(s(z), z)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[12117, 17543, 4])).
% 2.74/2.98 tff(17547,plain,
% 2.74/2.98 (b(s(z), z)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[221, 17546])).
% 2.74/2.98 tff(17548,plain,
% 2.74/2.98 ($false),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[17142, 306, 17475, 15960, 17547, 17545])).
% 2.74/2.98 tff(17549,plain,(~r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.98 tff(17550,plain,
% 2.74/2.98 (b(s(z), elem!1)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[16180, 17549])).
% 2.74/2.98 tff(17551,plain,
% 2.74/2.98 (~b(z, elem!1)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[17314, 17550])).
% 2.74/2.98 tff(17552,plain,
% 2.74/2.98 (r(z, elem!1)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[835, 17551, 17476])).
% 2.74/2.98 tff(17553,plain,
% 2.74/2.98 ((~(s(s(elem!1)) = elem!1)) | b(s(s(s(z))), elem!1)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[16475, 17552])).
% 2.74/2.98 tff(17554,plain,
% 2.74/2.98 (~(s(s(elem!1)) = elem!1)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[17553, 1])).
% 2.74/2.98 tff(17555,plain,
% 2.74/2.98 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[143, 17554])).
% 2.74/2.98 tff(17556,plain,
% 2.74/2.98 (~b(s(s(elem!1)), elem!1)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[17408, 17550])).
% 2.74/2.98 tff(17557,plain,
% 2.74/2.98 ((s(s(elem!1)) = elem!1) | r(s(s(elem!1)), elem!1)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[47, 17556])).
% 2.74/2.98 tff(17558,plain,
% 2.74/2.98 (r(s(s(elem!1)), elem!1)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[17557, 17554])).
% 2.74/2.98 tff(17559,plain,
% 2.74/2.98 (~(s(elem!1) = elem!1)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[180, 17554])).
% 2.74/2.98 tff(17560,plain,
% 2.74/2.98 (~(s(s(elem!1)) = s(elem!1))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[195, 17559])).
% 2.74/2.98 tff(17561,plain,
% 2.74/2.98 ((~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[5837, 17552])).
% 2.74/2.98 tff(17562,plain,
% 2.74/2.98 (~r(z, s(s(elem!1)))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[17561, 17558])).
% 2.74/2.98 tff(17563,plain,
% 2.74/2.98 (b(z, s(s(elem!1)))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[460, 17562])).
% 2.74/2.98 tff(17564,plain,
% 2.74/2.98 (~r(s(s(elem!1)), z)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[6539, 124, 17552, 17558])).
% 2.74/2.98 tff(17565,plain,
% 2.74/2.98 (b(s(s(elem!1)), z)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[476, 17564])).
% 2.74/2.98 tff(17566,plain,
% 2.74/2.98 ((~r(s(elem!1), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (s(s(elem!1)) = s(elem!1)) | (~r(s(s(elem!1)), elem!1))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[10562, 17552])).
% 2.74/2.98 tff(17567,plain,
% 2.74/2.98 (~r(s(elem!1), elem!1)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[17566, 17565, 17563, 17560, 17558])).
% 2.74/2.98 tff(17568,plain,
% 2.74/2.98 ((s(s(s(elem!1))) = s(elem!1)) | b(s(s(s(z))), elem!1) | b(s(elem!1), s(z)) | r(s(elem!1), elem!1)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[12776, 17556, 17476])).
% 2.74/2.98 tff(17569,plain,
% 2.74/2.98 (b(s(elem!1), s(z))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[17568, 17567, 1, 17555])).
% 2.74/2.98 tff(17570,plain,
% 2.74/2.98 (b(s(elem!1), elem!1)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[813, 17567, 17559])).
% 2.74/2.98 tff(17571,plain,
% 2.74/2.98 ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z)))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[16671, 17550])).
% 2.74/2.98 tff(17572,plain,
% 2.74/2.98 ($false),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[17571, 17570, 17569])).
% 2.74/2.98 tff(17573,plain,(b(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.98 tff(17574,plain,
% 2.74/2.98 ((~(s(s(elem!1)) = elem!1)) | (~b(s(s(s(z))), elem!1))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[17201, 17475, 17550])).
% 2.74/2.98 tff(17575,plain,
% 2.74/2.98 (~(s(s(elem!1)) = elem!1)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[17574, 17573])).
% 2.74/2.98 tff(17576,plain,
% 2.74/2.98 (~(s(elem!1) = elem!1)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[180, 17575])).
% 2.74/2.98 tff(17577,plain,
% 2.74/2.98 (~(s(s(elem!1)) = s(elem!1))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[195, 17576])).
% 2.74/2.98 tff(17578,plain,
% 2.74/2.98 (r(s(s(elem!1)), elem!1)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[17557, 17575])).
% 2.74/2.98 tff(17579,plain,
% 2.74/2.98 (~r(z, s(s(elem!1)))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[17561, 17578])).
% 2.74/2.98 tff(17580,plain,
% 2.74/2.98 (b(z, s(s(elem!1)))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[460, 17579])).
% 2.74/2.98 tff(17581,plain,
% 2.74/2.98 (~r(s(s(elem!1)), z)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[6539, 124, 17552, 17578])).
% 2.74/2.98 tff(17582,plain,
% 2.74/2.98 (b(s(s(elem!1)), z)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[476, 17581])).
% 2.74/2.98 tff(17583,plain,
% 2.74/2.98 (~r(s(elem!1), elem!1)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[17566, 17582, 17580, 17577, 17578])).
% 2.74/2.98 tff(17584,plain,
% 2.74/2.98 (b(s(elem!1), elem!1)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[813, 17583, 17576])).
% 2.74/2.98 tff(17585,plain,
% 2.74/2.98 (~(elem!1 = s(elem!1))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[364, 17576])).
% 2.74/2.98 tff(17586,plain,
% 2.74/2.98 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[143, 17575])).
% 2.74/2.98 tff(17587,plain,
% 2.74/2.98 ((s(s(elem!1)) = elem!1) | r(s(s(s(elem!1))), s(s(elem!1))) | r(s(elem!1), elem!1)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[7090, 17476])).
% 2.74/2.98 tff(17588,plain,
% 2.74/2.98 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[17587, 17583, 17575])).
% 2.74/2.98 tff(17589,plain,
% 2.74/2.98 (~(elem!1 = s(s(elem!1)))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[186, 17575])).
% 2.74/2.98 tff(17590,plain,
% 2.74/2.98 ((~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z)))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[17279, 17235])).
% 2.74/2.98 tff(17591,plain,
% 2.74/2.98 (~b(s(z), s(s(s(z))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[17590, 17573])).
% 2.74/2.98 tff(17592,plain,
% 2.74/2.98 (r(s(z), s(s(s(z))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[3302, 17591])).
% 2.74/2.98 tff(17593,plain,
% 2.74/2.98 ((~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z)))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[16502, 17550])).
% 2.74/2.98 tff(17594,plain,
% 2.74/2.98 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[17593, 17592, 17573])).
% 2.74/2.98 tff(17595,plain,
% 2.74/2.98 ((~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z)))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[17522, 15960])).
% 2.74/2.98 tff(17596,plain,
% 2.74/2.98 (~b(s(s(s(z))), s(z))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[17595, 17550, 17235, 17475])).
% 2.74/2.98 tff(17597,plain,
% 2.74/2.98 (r(s(s(s(z))), s(z))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[113, 17596])).
% 2.74/2.98 tff(17598,plain,
% 2.74/2.98 (~(s(elem!1) = s(z))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[2689, 17476])).
% 2.74/2.98 tff(17599,plain,
% 2.74/2.98 ((~(s(s(s(s(s(s(z)))))) = elem!1)) | (~b(s(s(s(z))), elem!1)) | r(s(elem!1), elem!1)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[17211, 17550, 17598, 17597])).
% 2.74/2.98 tff(17600,plain,
% 2.74/2.98 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[17599, 17583, 17573])).
% 2.74/2.98 tff(17601,plain,
% 2.74/2.98 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[1144, 17600, 17594])).
% 2.74/2.98 tff(17602,plain,
% 2.74/2.98 ((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), z))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[5452, 17552])).
% 2.74/2.98 tff(17603,plain,
% 2.74/2.98 (~r(s(s(s(s(s(s(z)))))), z)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[17602, 17601])).
% 2.74/2.98 tff(17604,plain,
% 2.74/2.98 (b(s(s(s(s(s(s(z)))))), z)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[4232, 17603])).
% 2.74/2.98 tff(17605,plain,
% 2.74/2.98 (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[9768, 306, 17580, 17582, 17604])).
% 2.74/2.98 tff(17606,plain,
% 2.74/2.98 (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[8458, 124, 17578, 17601])).
% 2.74/2.98 tff(17607,plain,
% 2.74/2.98 ((s(s(s(s(s(s(z)))))) = s(s(elem!1))) | b(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[3247, 43, 17606])).
% 2.74/2.98 tff(17608,plain,
% 2.74/2.98 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[17607, 17605])).
% 2.74/2.98 tff(17609,plain,
% 2.74/2.98 (~(s(s(s(elem!1))) = elem!1)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[7206, 17608])).
% 2.74/2.98 tff(17610,plain,
% 2.74/2.98 ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (elem!1 = s(s(elem!1))) | (~b(s(elem!1), elem!1)) | (s(s(s(elem!1))) = elem!1) | (s(s(s(elem!1))) = s(elem!1)) | (elem!1 = s(elem!1)) | (~r(s(s(elem!1)), elem!1))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[13111, 17475])).
% 2.74/2.99 tff(17611,plain,
% 2.74/2.99 (~r(s(s(elem!1)), s(elem!1))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[17610, 17609, 17578, 17589, 17588, 17586, 17585, 17584])).
% 2.74/2.99 tff(17612,plain,
% 2.74/2.99 (b(s(s(elem!1)), s(elem!1))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[994, 17611, 17577])).
% 2.74/2.99 tff(17613,plain,
% 2.74/2.99 (~b(s(elem!1), s(z))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[17571, 17584])).
% 2.74/2.99 tff(17614,plain,
% 2.74/2.99 (r(s(elem!1), s(z)) | b(s(elem!1), s(z))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[2964, 17598])).
% 2.74/2.99 tff(17615,plain,
% 2.74/2.99 (r(s(elem!1), s(z))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[17614, 17613])).
% 2.74/2.99 tff(17616,plain,
% 2.74/2.99 ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), z))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[16918, 17475])).
% 2.74/2.99 tff(17617,plain,
% 2.74/2.99 (~b(s(z), z)),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[17616, 17612, 17580])).
% 2.74/2.99 tff(17618,plain,
% 2.74/2.99 (r(s(z), z)),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[221, 17617])).
% 2.74/2.99 tff(17619,plain,
% 2.74/2.99 (~r(s(elem!1), z)),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[2634, 17618, 17615])).
% 2.74/2.99 tff(17620,plain,
% 2.74/2.99 (b(s(elem!1), z)),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[2380, 17619])).
% 2.74/2.99 tff(17621,plain,
% 2.74/2.99 ((~r(s(s(s(elem!1))), elem!1)) | (s(s(elem!1)) = elem!1)),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[16405, 17476, 17556])).
% 2.74/2.99 tff(17622,plain,
% 2.74/2.99 (~r(s(s(s(elem!1))), elem!1)),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[17621, 17575])).
% 2.74/2.99 tff(17623,plain,
% 2.74/2.99 (~b(elem!1, s(s(elem!1)))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[6653, 306, 17475, 17580, 17582])).
% 2.74/2.99 tff(17624,plain,
% 2.74/2.99 (r(elem!1, s(s(elem!1)))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[516, 17623, 17589])).
% 2.74/2.99 tff(17625,plain,
% 2.74/2.99 (~r(elem!1, s(s(s(elem!1))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[1256, 124, 17624, 17588])).
% 2.74/2.99 tff(17626,plain,
% 2.74/2.99 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[7793, 17609, 17625, 17622, 17584])).
% 2.74/2.99 tff(17627,plain,
% 2.74/2.99 (r(s(s(s(elem!1))), s(elem!1))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[664, 17626, 17586])).
% 2.74/2.99 tff(17628,plain,
% 2.74/2.99 (~(elem!1 = s(s(s(elem!1))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[1641, 17609])).
% 2.74/2.99 tff(17629,plain,
% 2.74/2.99 ((~r(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | b(s(elem!1), s(z)) | (z = elem!1) | (~b(s(elem!1), elem!1)) | (~r(s(z), z)) | (elem!1 = s(s(elem!1))) | (elem!1 = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1)))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[11554, 15978])).
% 2.74/2.99 tff(17630,plain,
% 2.74/2.99 ((~r(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | b(s(elem!1), s(z)) | (~b(s(elem!1), elem!1)) | (~r(s(z), z)) | (elem!1 = s(s(elem!1))) | (elem!1 = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1)))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[17629, 17476])).
% 2.74/2.99 tff(17631,plain,
% 2.74/2.99 (~r(z, s(elem!1))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[17630, 17618, 17612, 17578, 17584, 17613, 17589, 17628, 17588, 17627])).
% 2.74/2.99 tff(17632,plain,
% 2.74/2.99 (b(z, s(elem!1))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[275, 17631])).
% 2.74/2.99 tff(17633,plain,
% 2.74/2.99 ($false),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[1218, 17632, 17620, 17580, 17612])).
% 2.74/2.99 % SZS output end Proof
% 2.74/2.99 % E exiting
%------------------------------------------------------------------------------